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Cyril Houdayer
|
Construction of type ${\rm II_1}$ factors with prescribed countable fundamental group
|
In the context of Free Probability Theory, we study two different constructions that provide new examples of factors of type ${\rm II_1}$ with prescribed fundamental group. First we investigate state-preserving group actions on the almost periodic free Araki-Woods factors satisfying both a condition of mixing and a condition of free malleability in the sense of Popa. Typical examples are given by the free Bogoliubov shifts. Take an ICC $w$-rigid group $G$ such that $\mathcal{F}(L(G)) = \{1\}$ (e.g. $G = \Z^2 \rtimes \SL(2, \Z)$). For any countable subgroup $S \subset \R^*_+$, we show that there exists an action of $G$ on $L(\F_\infty)$ such that $L(\F_\infty) \rtimes G$ is a type ${\rm II_1}$ factor and its fundamental group is $S$. The second construction is based on a free product. Take $(B(H), \psi)$ any factor of type ${\rm I}$ endowed with a faithful normal state and denote by $\Gamma \subset \R^*_+$ the subgroup generated by the point spectrum of $\psi$. We show that the centralizer $(L(G) \ast B(H))^{\tau \ast \psi}$ is a type ${\rm II_1}$ factor and its fundamental group is $\Gamma$. Our proofs rely on Popa's deformation/rigidity strategy using his intertwining-by-bimodules technique.
|
2025-07-17
| 2,025
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context free probabl theori studi two differ construct provid new exampl factor type rm ii prescrib fundament group first investig state preserv group action almost period free araki wood factor satisfi condit mix condit free malleabl sens popa typic exampl given free bogoliubov shift take icc w rigid group g mathcal f l g e g g z rtime sl z countabl subgroup subset r show exist action g l f infti l f infti rtime g type rm ii factor fundament group second construct base free product take b h psi factor type rm endow faith normal state denot gamma subset r subgroup gener point spectrum psi show central l g ast b h tau ast psi type rm ii factor fundament group gamma proof reli popa deform rigid strategi use intertwin bimodul techniqu
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1
| 1
|
Dhananjay P. Mehendale
|
Hamiltonian Graphs and the Traveling Salesman Problem
|
A new characterization of Hamiltonian graphs using f-cutset matrix is
proposed. Based on this new characterization, a new exact polynomial time
algorithm for the traveling salesman problem (TSP) is developed. We then define
the so-called ordered weighted adjacency list for given weighted complete graph
and proceed to the paper's main result, namely, the exact algorithm based on
the utilization of the ordered weighted adjacency list and the simple
properties that any path or circuit must satisfy. This algorithm performs
checking of sub-lists, containing (p-1) entries (edge pairs) for paths and p
entries (edge pairs) for circuits, chosen from ordered adjacency list in a well
defined sequence to determine exactly the shortest Hamiltonian path and
shortest Hamiltonian circuit in a weighted complete graph of p vertices. The
procedure has intrinsic advantage of landing on the desired solution in
quickest possible time and even in worst case in polynomial time. A new
characterization of the shortest Hamiltonian tour for a weighted complete graph
satisfying triangle inequality (i.e. for tours passing through every city on a
realistic map of cities where cities can be taken as points on a Euclidean
plane) is also proposed. Finally, we propose a classical algorithm for
unstructured search, three new quantum algorithms for unstructured search,
which exponentially speed up the searching ability in the unstructured
database, and one quantum algorithm for solving a K-SAT problem and indicate
its effect on traveling salesman problem and other NP-complete problems.
|
2025-02-26
| 2,025
|
new character hamiltonian graph use f cutset matrix propos base new character new exact polynomi time algorithm travel salesman problem tsp develop defin call order weight adjac list given weight complet graph proceed paper main result name exact algorithm base util order weight adjac list simpl properti path circuit must satisfi algorithm perform check sub list contain p entri edg pair path p entri edg pair circuit chosen order adjac list well defin sequenc determin exactli shortest hamiltonian path shortest hamiltonian circuit weight complet graph p vertic procedur intrins advantag land desir solut quickest possibl time even worst case polynomi time new character shortest hamiltonian tour weight complet graph satisfi triangl inequ e tour pass everi citi realist map citi citi taken point euclidean plane also propos final propos classic algorithm unstructur search three new quantum algorithm unstructur search exponenti speed search abil unstructur databas one quantum algorithm solv k sat problem indic effect travel salesman problem np complet problem
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2
| 2
|
Fabrizio Catanese, Fr\'ed\'eric Mangolte
|
Real singular Del Pezzo surfaces and threefolds fibred by rational curves, I
|
Let W -> X be a real smooth projective threefold fibred by rational curves. Koll\'ar proved that if W(R) is orientable a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces. Let k : = k(N) be the integer defined as follows: If g : N -> F is a Seifert fibration, one defines k : = k(N) as the number of multiple fibres of g, while, if N is a connected sum of lens spaces, k is defined as the number of lens spaces different from P^3(R). Our Main Theorem says: If X is a geometrically rational surface, then k <= 4. Moreover we show that if F is diffeomorphic to S^1xS^1, then W(R) is connected and k = 0. These results answer in the affirmative two questions of Koll\'ar who proved in 1999 that k <= 6 and suggested that 4 would be the sharp bound. We derive the Theorem from a careful study of real singular Del Pezzo surfaces with only Du Val singularities.
|
2025-05-26
| 2,025
|
let w x real smooth project threefold fibr ration curv koll ar prove w r orient connect compon n w r essenti either seifert fibr manifold connect sum len space let k k n integ defin follow g n f seifert fibrat one defin k k n number multipl fibr g n connect sum len space k defin number len space differ p r main theorem say x geometr ration surfac k moreov show f diffeomorph xs w r connect k result answer affirm two question koll ar prove k suggest would sharp bound deriv theorem care studi real singular del pezzo surfac du val singular
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3
| 3
|
Richard J. Mathar
|
Third Order Newton's Method for Zernike Polynomial Zeros
|
The Zernike radial polynomials are a system of orthogonal polynomials over the unit interval with weight x. They are used as basis functions in optics to expand fields over the cross section of circular pupils. To calculate the roots of Zernike polynomials, we optimize the generic iterative numerical Newton's Method that iterates on zeros of functions with third order convergence. The technique is based on rewriting the polynomials as Gauss Hypergeometric Functions, reduction of second order derivatives to first order derivatives, and evaluation of some ratios of derivatives by terminating continued fractions.
A PARI program and a short table of zeros complete up to polynomials of 40th order are included.
|
2025-10-13
| 2,025
|
zernik radial polynomi system orthogon polynomi unit interv weight x use basi function optic expand field cross section circular pupil calcul root zernik polynomi optim gener iter numer newton method iter zero function third order converg techniqu base rewrit polynomi gauss hypergeometr function reduct second order deriv first order deriv evalu ratio deriv termin continu fraction pari program short tabl zero complet polynomi th order includ
|
4
| 4
|
S. Ishikawa
|
Spin-dependent three-nucleon force effects on nucleon-deuteron
scattering
|
We construct a phenomenological three-nucleon force (3NF) model that gives a
good description of polarization observables in elastic nucleon-deuteron
(N-$d$) scattering at a low energy together with a realistic nucleon-nucleon
force and a 3NF arising from the exchange of two pions. Parameters of the
model, which consists of spin-independent, spin-orbit, and tensor components,
are determined to reproduce the three-nucleon binding energy and polarization
observables in N-d scattering at 3 MeV. Predictions of the model 3NF on N-d
polarization observables at higher energies are examined, and effects of each
component on the observables are investigated.
|
2025-03-20
| 2,025
|
construct phenomenolog three nucleon forc nf model give good descript polar observ elast nucleon deuteron n scatter low energi togeth realist nucleon nucleon forc nf aris exchang two pion paramet model consist spin independ spin orbit tensor compon determin reproduc three nucleon bind energi polar observ n scatter mev predict model nf n polar observ higher energi examin effect compon observ investig
|
5
| 5
|
Woong-Seob Jeong (1), Chris P. Pearson (1 and 2), Hyung Mok Lee (3), Shuji Matsuura (1), Mitsunobu Kawada (4), Takao Nakagawa (1), Sang Hoon Oh (3), Mai Shirahata (1), Sungho Lee (5), Ho Seong Hwang (3), Hideo Matsuhara (1) ((1) ISAS/JAXA, Japan, (2) ESAC, Spain, (3) Seoul Nat'l Univ., Korea, (4) Nagoya Univ., Japan, (5) KASI, Korea)
|
Detection of CFIRB with AKARI/FIS Deep Observations
|
The Cosmic Far-Infrared Background (CFIRB) contains information about the number and distribution of contributing sources and thus gives us an important key to understand the evolution of galaxies. Using a confusion study to set a fundamental limit to the observations, we investigate the potential to explore the CFIRB with AKARI/FIS deep observations. The Far-Infrared Surveyor (FIS) is one of the focal-plane instruments on the AKARI (formerly known as ASTRO-F) satellite, which was launched in early 2006. Based upon source distribution models assuming three different cosmological evolutionary scenarios (no evolution, weak evolution, and strong evolution), an extensive model for diffuse emission from infrared cirrus, and instrumental noise estimates, we present a comprehensive analysis for the determination of the confusion levels for deep far-infrared observations. We use our derived sensitivities to suggest the best observational strategy for the AKARI/FIS mission to detect the CFIRB fluctuations. If the source distribution follows the evolutionary models, observations will be mostly limited by source confusion. We find that we will be able to detect the CFIRB fluctuations and that these will in turn provide information to discriminate between the evolutionary scenarios of galaxies in most low-to-medium cirrus regions.
|
2025-08-26
| 2,025
|
cosmic far infrar background cfirb contain inform number distribut contribut sourc thu give us import key understand evolut galaxi use confus studi set fundament limit observ investig potenti explor cfirb akari fi deep observ far infrar surveyor fi one focal plane instrument akari formerli known astro f satellit launch earli base upon sourc distribut model assum three differ cosmolog evolutionari scenario evolut weak evolut strong evolut extens model diffus emiss infrar cirru instrument nois estim present comprehens analysi determin confus level deep far infrar observ use deriv sensit suggest best observ strategi akari fi mission detect cfirb fluctuat sourc distribut follow evolutionari model observ mostli limit sourc confus find abl detect cfirb fluctuat turn provid inform discrimin evolutionari scenario galaxi low medium cirru region
|
6
| 6
|
A. Eriksson, P. Fernstrom, B. Mehlig, and S. Sagitov
|
An accurate model for genetic hitch-hiking
|
We suggest a simple deterministic approximation for the growth of the favoured-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitch-hiking. Only when Ns < 10 (N is the population size and s denotes the selection coefficient), are discrepancies between our approximation and direct numerical simulations of a Moran model noticeable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.
|
2025-10-01
| 2,025
|
suggest simpl determinist approxim growth favour allel frequenc select sweep use approxim introduc accur model genet hitch hike ns n popul size denot select coeffici discrep approxim direct numer simul moran model notic model describ gene genealog contigu segment neutral loci close select one assum select sweep happen instantan enabl us comput snp distribut neutral segment without bia
|
7
| 7
|
Michael Frank and Kamran Sharifi
|
Adjointability of densely defined closed operators and the
Magajna-Schweizer Theorem
|
In this notes unbounded regular operators on Hilbert $C^*$-modules over
arbitrary $C^*$-algebras are discussed. A densely defined operator $t$
possesses an adjoint operator if the graph of $t$ is an orthogonal summand.
Moreover, for a densely defined operator $t$ the graph of $t$ is orthogonally
complemented and the range of $P_FP_{G(t)^\bot}$ is dense in its biorthogonal
complement if and only if $t$ is regular. For a given $C^*$-algebra $\mathcal
A$ any densely defined $\mathcal A$-linear closed operator $t$ between Hilbert
$C^*$-modules is regular, if and only if any densely defined $\mathcal
A$-linear closed operator $t$ between Hilbert $C^*$-modules admits a densely
defined adjoint operator, if and only if $\mathcal A$ is a $C^*$-algebra of
compact operators. Some further characterizations of closed and regular modular
operators are obtained.
Changes 1: Improved results, corrected misprints, added references. Accepted
by J. Operator Theory, August 2007 / Changes 2: Filled gap in the proof of Thm.
3.1, changes in the formulations of Cor. 3.2 and Thm. 3.4, updated references
and address of the second author.
|
2025-04-29
| 2,025
|
note unbound regular oper hilbert c modul arbitrari c algebra discuss dens defin oper possess adjoint oper graph orthogon summand moreov dens defin oper graph orthogon complement rang p fp g bot dens biorthogon complement regular given c algebra mathcal dens defin mathcal linear close oper hilbert c modul regular dens defin mathcal linear close oper hilbert c modul admit dens defin adjoint oper mathcal c algebra compact oper character close regular modular oper obtain chang improv result correct misprint ad refer accept j oper theori august chang fill gap proof thm chang formul cor thm updat refer address second author
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8
| 8
|
Gerald H\"ohn
|
Selbstduale Vertexoperatorsuperalgebren und das Babymonster (Self-dual Vertex Operator Super Algebras and the Baby Monster)
|
We investigate self-dual vertex operator algebras (VOAs) and super algebras (SVOAs). Using the genus one correlation functions, it is shown that self-dual SVOAs exist only for half-integral central charges. It is described how self-dual SVOAs can be constructed from self-dual VOAs of larger central charge. The analogy with integral lattices and binary codes is emphasized.
One main result is the construction of the shorter Moonshine module, a self-dual SVOA of central charge 23.5 on which the Baby monster - the second largest sporadic simple group - acts by automorphisms. The shorter Moonshine module has the character q^(-47/48)*(1+ 4371q^(3/2)+ 96256q^2+ 1143745q^(5/2) +...) and is the "shorter cousin" of the Moonshine module. Its lattice and code analog are the shorter Leech lattice and shorter Golay code. We conjecture that the shorter Moonshine module is the unique SVOA with this character.
The final chapter introduces the notion of extremal VOAs and SVOAs. These are self-dual (S)VOAs with character having the same first few coefficients as the vacuum representation of the Virasoro algebra of the same central charge. We show that extremal VOAs exist at least for the central charges 8, 16, 24, 32, 40 and that extremal SVOAs exist only for the central charges c=0.5, 1, ..., 7.5, 8, 12, 14, 15, 15.5, 23.5 and 24. Examples for c=24 (resp. 23.5) are the (shorter) Moonshine module. Again, our results are similar to results known for codes and lattices.
|
2025-10-13
| 2,025
|
investig self dual vertex oper algebra voa super algebra svoa use genu one correl function shown self dual svoa exist half integr central charg describ self dual svoa construct self dual voa larger central charg analog integr lattic binari code emphas one main result construct shorter moonshin modul self dual svoa central charg babi monster second largest sporad simpl group act automorph shorter moonshin modul charact q q q q shorter cousin moonshin modul lattic code analog shorter leech lattic shorter golay code conjectur shorter moonshin modul uniqu svoa charact final chapter introduc notion extrem voa svoa self dual voa charact first coeffici vacuum represent virasoro algebra central charg show extrem voa exist least central charg extrem svoa exist central charg c exampl c resp shorter moonshin modul result similar result known code lattic
|
9
| 9
|
Hisanobu Shinya
|
A new result under the negation of the Riemann hypothesis
|
Suppose that the Riemann hypothesis for the Riemann $\zeta$-function is false. There have yet been no workable results that the falsity of the Riemann hypothesis implies. The result of this article may be considered as more workable for the sake of deducing other new results on the Riemann hypothesis.
|
2025-12-04
| 2,025
|
suppos riemann hypothesi riemann zeta function fals yet workabl result falsiti riemann hypothesi impli result articl may consid workabl sake deduc new result riemann hypothesi
|
10
| 10
|
Jinzhu Han
|
Study on Hilbert's Eighth Problems
|
In this paper, we used the principle of sieve function transformation to improve sieve method and the prime number theorem in the arithmetic sequence.For this, we proved General Riemann Hypothesis and Riemann Hypothesis to be true. further, we improved Selberg's line sieve method and proved Goldbach Conjecture and Twin Prime Conjecture to be true. However, we basically solved Hilbert's eighth problems.
|
2025-06-09
| 2,025
|
paper use principl siev function transform improv siev method prime number theorem arithmet sequenc prove gener riemann hypothesi riemann hypothesi true improv selberg line siev method prove goldbach conjectur twin prime conjectur true howev basic solv hilbert eighth problem
|
11
| 11
|
Hiroki Ohta and Shin-ichi Sasa
|
Critical fluctuations of time-dependent magnetization in a random-field
Ising model
|
Cooperative behaviors near the disorder-induced critical point in a random
field Ising model are numerically investigated by analyzing time-dependent
magnetization in ordering processes from a special initial condition. We find
that the intensity of fluctuations of time-dependent magnetization, $\chi(t)$,
attains a maximum value at a time $t=\tau$ in a normal phase and that
$\chi(\tau)$ and $\tau$ exhibit divergences near the disorder-induced critical
point. Furthermore, spin configurations around the time $\tau$ are
characterized by a length scale, which also exhibits a divergence near the
critical point. We estimate the critical exponents that characterize these
power-law divergences by using a finite-size scaling method.
|
2025-01-06
| 2,025
|
cooper behavior near disord induc critic point random field ise model numer investig analyz time depend magnet order process special initi condit find intens fluctuat time depend magnet chi attain maximum valu time tau normal phase chi tau tau exhibit diverg near disord induc critic point furthermor spin configur around time tau character length scale also exhibit diverg near critic point estim critic expon character power law diverg use finit size scale method
|
12
| 12
|
Yuri Neretin
|
Gauss--Berezin integral operators and spinors over supergroups
$\mathrm{OSp}(2p|2q)$, and Lagrangian super-Grasmannians
|
We obtain explicit formulas for the spinor representation $\rho$ of the real
orthosymplectic supergroup $\mathrm{OSp}(2p|2q,\mathbb{R})$ by integral
'Gauss--Berezin' operators. Next, we extend $\rho$ to a complex domain and get
a representation of a larger semigroup, which is a counterpart of Olshanski
subsemigroups in semisimple Lie groups. Further, we show that $\rho$ can be
extended to an operator-valued function on a certain domain in the Lagrangian
super-Grassmannian (graphs of elements of the supergroup
$\mathrm{OSp}(2p|2q,\mathbb{C})$ are Lagrangian super-subspaces) and show that
this function is a 'representation' in the following sense: we consider
Lagrangian subspaces as linear relations and composition of two Lagrangian
relations in general position corresponds to a product of Gauss--Berezin
operators
|
2025-02-11
| 2,025
|
obtain explicit formula spinor represent rho real orthosymplect supergroup mathrm osp p q mathbb r integr gauss berezin oper next extend rho complex domain get represent larger semigroup counterpart olshanski subsemigroup semisimpl lie group show rho extend oper valu function certain domain lagrangian super grassmannian graph element supergroup mathrm osp p q mathbb c lagrangian super subspac show function represent follow sens consid lagrangian subspac linear relat composit two lagrangian relat gener posit correspond product gauss berezin oper
|
13
| 13
|
Jerrold Franklin
|
The nature of electromagnetic energy
|
We study the nature and location of electromagetic energy for two cases. The energy density for electromagnetic radiation is shown to be $\frac{1}{8\pi}(E^2+B^2)$, with the energy contained in the electromagnet fields. For a static charge distribution, the electromagnet energy is contained in the charge, with an energy density, $\frac{1}{2}\rho\phi$, There is no energy outside the charge distribution. The electromagnetic fields do not contain the energy, and $\frac{1}{8\pi}(E^2+B^2)$ cannot be considered an energy density in this case. There is no ambiguity in either case as to where the energy is located.
|
2025-05-16
| 2,025
|
studi natur locat electromaget energi two case energi densiti electromagnet radiat shown frac pi e b energi contain electromagnet field static charg distribut electromagnet energi contain charg energi densiti frac rho phi energi outsid charg distribut electromagnet field contain energi frac pi e b cannot consid energi densiti case ambigu either case energi locat
|
14
| 14
|
Vikram H. Zaveri
|
Periodic relativity: the theory of gravity in flat space time
|
Periodic relativity (PR), uses a flat metric without weak field
approximation. PR satisfies Einstein's field equations. PR proposes a definite
connection between the proper time interval of an object and Doppler frequency
shift of its constituent particles. This is because fundamentally time is
periodic in nature. Periodic time of PR is the key parameter in development of
quantum gravity theory in which the universe begins with a quantum fluctuation
in the fundamental substance of the universe which is infinite, motionless and
indivisible. PR is based on the dynamic weak equivalence principle which
equates the gravitational mass with the relativistic mass. PR provides accurate
solutions for the rotation curves of galaxies and the energy levels of the
Hydrogen spectra including Lamb shift using common formalism. Flat space time
with Lorentz invariant acceleration presented here makes it possible to unite
PR with quantum mechanics. PR predicts limiting radius of the event horizon of
a black hole to be 1R_g and the shadow of a black hole to be due to frequency
shift of visible light into ultraviolet and higher range. PR equations can
probe inside the event horizon. Mathematical proof of periodic nature of time
is presented by way of introducing gravity into the electromagnetic wave
formalism. Theory shows that the electromagnetic wave is held together by
gravitational forces. Theory explains the mechanism of gravitational redshift
predicted by general relativity and predicts powerful gravitational radiation
at Planck epoch. Gravitational-wave strain amplitude is derived using quantum
mechanical formalism. Bound on graviton mass is mg < 1.51 x 10^{-41}eV/c^2.
Mechanism that explains Gamma-ray burst associated with GW150914 is presented.
GRB can shrink the event horizon. Gravity assisted EM wave stacking creates
$\gamma$-rays in M87 BH.
|
2025-01-16
| 2,025
|
period rel pr use flat metric without weak field approxim pr satisfi einstein field equat pr propos definit connect proper time interv object doppler frequenc shift constitu particl fundament time period natur period time pr key paramet develop quantum graviti theori univers begin quantum fluctuat fundament substanc univers infinit motionless indivis pr base dynam weak equival principl equat gravit mass relativist mass pr provid accur solut rotat curv galaxi energi level hydrogen spectra includ lamb shift use common formal flat space time lorentz invari acceler present make possibl unit pr quantum mechan pr predict limit radiu event horizon black hole r g shadow black hole due frequenc shift visibl light ultraviolet higher rang pr equat probe insid event horizon mathemat proof period natur time present way introduc graviti electromagnet wave formal theori show electromagnet wave held togeth gravit forc theori explain mechan gravit redshift predict gener rel predict power gravit radiat planck epoch gravit wave strain amplitud deriv use quantum mechan formal bound graviton mass mg x ev c mechan explain gamma ray burst associ gw present grb shrink event horizon graviti assist em wave stack creat gamma ray bh
|
15
| 15
|
Woong-Seob Jeong, Takao Nakagawa, Issei Yamamura, Chris P. Pearson, Richard S. Savage, Hyung Mok Lee, Hiroshi Shibai, Sin'itirou Makiuti, Hajime Baba, Dave Clements, Yasuo Doi, Elysandora Figueredo, Tomotsugu Goto, Sunao Hasegawa, Mitsunobu Kawada, Akiko Kawamura, Do Kester, Suk Minn Kwon, Hideo Matsuhara, Shuji Matsuura, Hiroshi Murakami, Sang Hoon Oh, Soojong Pak, Yong-Sun Park, Michael Rowan-Robinson, Stephen Serjeant, Mai Shirahata, Jungjoo Sohn, Toshinobu Takagi, Lingyu Wang, Glenn J. White, Chisato Yamauchi
|
The Far-Infrared Properties of Spatially Resolved AKARI Observations
|
We present the spatially resolved observations of IRAS sources from the Japanese infrared astronomy satellite AKARI All-Sky Survey during the performance verification (PV) phase of the mission. We extracted reliable point sources matched with IRAS point source catalogue. By comparing IRAS and AKARI fluxes, we found that the flux measurements of some IRAS sources could have been over or underestimated and affected by the local background rather than the global background. We also found possible candidates for new AKARI sources and confirmed that AKARI observations resolved IRAS sources into multiple sources. All-Sky Survey observations are expected to verify the accuracies of IRAS flux measurements and to find new extragalactic point sources.
|
2025-08-26
| 2,025
|
present spatial resolv observ ira sourc japanes infrar astronomi satellit akari sky survey perform verif pv phase mission extract reliabl point sourc match ira point sourc catalogu compar ira akari flux found flux measur ira sourc could underestim affect local background rather global background also found possibl candid new akari sourc confirm akari observ resolv ira sourc multipl sourc sky survey observ expect verifi accuraci ira flux measur find new extragalact point sourc
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16
| 16
|
F.A. Gareev, G.F. Gareeva, I.E. Zhidkova
|
Quantization of Atomic and Nuclear Rest Masses
|
We were able to quantize phenomenologically the first time the atomic and
nuclear rest masses. Note that this quantization rule is justified for atoms
and nuclei with different A, N and Z and the nuclei and atoms represent a
coherent synchronized systems -- a complex of coupled oscillators (resonators).
The cooperative resonance synchronization mechanisms are responsible for
explanation of how the electron volt world can influence the nuclear mega
electron volt world. It means that we created new possibilities for inducing
and controlling nuclear reactions by atomic processes.
|
2025-02-08
| 2,025
|
abl quantiz phenomenolog first time atom nuclear rest mass note quantiz rule justifi atom nuclei differ n z nuclei atom repres coher synchron system complex coupl oscil reson cooper reson synchron mechan respons explan electron volt world influenc nuclear mega electron volt world mean creat new possibl induc control nuclear reaction atom process
|
17
| 17
|
Vladislav V. Kravchenko
|
Solution of the equation d/dx(pdu/dx)+qu=cu by a solution of the
equation d/dx(pdu/dx)+qu=0
|
We give a simple solution of the equation d/dx(pdu/dx)+qu=cu whenever a
nontrivial solution of d/dx(pdu/dx)+qu=0 is known. The method developed for
obtaining this result is based on the theory of pseudoanalytic functions and
their relationship with solutions of the stationary two-dimensional Schrodinger
equation. The final result, that is the formula for the general solution of the
equation d/dx(pdu/dx)+qu=cu has a simple and easily verifiable form.
|
2025-05-06
| 2,025
|
give simpl solut equat dx pdu dx qu cu whenev nontrivi solut dx pdu dx qu known method develop obtain result base theori pseudoanalyt function relationship solut stationari two dimension schroding equat final result formula gener solut equat dx pdu dx qu cu simpl easili verifi form
|
18
| 18
|
S.V. Goloskokov (JINR) and P. Kroll (Wuppertal Univ.)
|
The role of the quark and gluon GPDs in hard vector-meson
electroproduction
|
Electroproduction of light vector mesons is analyzed on the basis of handbag
factorization. The required generalized parton distributions are constructed
from the CTEQ6 parton distributions with the help of double distributions. The
partonic subprocesses are calculated within the modified perturbative approach.
The present work extends our previous analysis of the longitudinal cross
section to the transverse one and other observables related to both the
corresponding amplitudes. Our results are compared to recent experimental
findings in detail.
|
2025-01-22
| 2,025
|
electroproduct light vector meson analyz basi handbag factor requir gener parton distribut construct cteq parton distribut help doubl distribut parton subprocess calcul within modifi perturb approach present work extend previou analysi longitudin cross section transvers one observ relat correspond amplitud result compar recent experiment find detail
|
19
| 19
|
Johannes Huisman and Fr\'ed\'eric Mangolte
|
The group of automorphisms of a real rational surface is n-transitive
|
Let X be a rational nonsingular compact connected real algebraic surface. Denote by Aut(X) the group of real algebraic automorphisms of X. We show that the group Aut(X) acts n-transitively on X, for all natural integers n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebraic surfaces are isomorphic if and only if they are homeomorphic as topological surfaces.
|
2025-05-23
| 2,025
|
let x ration nonsingular compact connect real algebra surfac denot aut x group real algebra automorph x show group aut x act n transit x natur integ n applic give new simpler proof fact two ration nonsingular compact connect real algebra surfac isomorph homeomorph topolog surfac
|
20
| 20
|
Mariko Ninomiya, Syoiti Ninomiya
|
A new weak approximation scheme of stochastic differential equations and
the Runge-Kutta method
|
In this paper, authors successfully construct a new algorithm for the new
higher order scheme of weak approximation of SDEs. The algorithm presented here
is based on [1][2]. Although this algorithm shares some features with the
algorithm presented by [3], algorithms themselves are completely different and
the diversity is not trivial. They apply this new algorithm to the problem of
pricing Asian options under the Heston stochastic volatility model and obtain
encouraging results.
[1] Shigeo Kusuoka, "Approximation of Expectation of Diffusion Process and
Mathematical Finance," Advanced Studies in Pure Mathematics, Proceedings of
Final Taniguchi Symposium, Nara 1998 (T. Sunada, ed.), vol. 31 2001, pp.
147--165. [2] Terry Lyons and Nicolas Victoir, "Cubature on Wiener Space,"
Proceedings of the Royal Society of London. Series A. Mathematical and Physical
Sciences 460 (2004), pp. 169--198. [3] Syoiti Ninomiya, Nicolas Victoir, "Weak
approximation of stochastic differential equations and application to
derivative pricing," Applied Mathematical Finance, Volume 15, Issue 2 April
2008, pages 107--121
|
2025-04-28
| 2,025
|
paper author success construct new algorithm new higher order scheme weak approxim sde algorithm present base although algorithm share featur algorithm present algorithm complet differ divers trivial appli new algorithm problem price asian option heston stochast volatil model obtain encourag result shigeo kusuoka approxim expect diffus process mathemat financ advanc studi pure mathemat proceed final taniguchi symposium nara sunada ed vol pp terri lyon nicola victoir cubatur wiener space proceed royal societi london seri mathemat physic scienc pp syoiti ninomiya nicola victoir weak approxim stochast differenti equat applic deriv price appli mathemat financ volum issu april page
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21
| 21
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Michael Frank, Alexander A. Pavlov
|
Strict essential extensions of C*-algebras and Hilbert C*-modules
|
In the present paper we develop both ideas of D. Baki\'c and B. Gulja{\v{s}}
and the categorical approach to multipliers from E.C. Lance's book and
publications of the second author, for the introduction and study of left
multipliers of Hilbert $C^*$-modules. Some properties and, in particular, the
property of maximality among all strictly essential extensions of a Hilbert
$C^*$-module for left multipliers are proved. Also relations between left
essential and left strictly essential extensions in different contexts are
obtained. Left essential and left strictly essential extensions of matrix
algebras are considered. In the final paragraph the topological approach to the
left multiplier theory of Hilbert $C^*$-modules is worked out.
|
2025-04-29
| 2,025
|
present paper develop idea baki c b gulja v categor approach multipli e c lanc book public second author introduct studi left multipli hilbert c modul properti particular properti maxim among strictli essenti extens hilbert c modul left multipli prove also relat left essenti left strictli essenti extens differ context obtain left essenti left strictli essenti extens matrix algebra consid final paragraph topolog approach left multipli theori hilbert c modul work
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22
| 22
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B. C. Sanctuary
|
Rationalization of EPR Coincidence Experiments
|
Coincidence experiments on EPR pairs show strong violations of Bell's
Inequalities at certain filter settings which is widely believed to mean that
local hidden variable models cannot explain these results. In this paper it is
shown that the 'non-separable' singlet density matrix can be represented as a
sum of separable density matrices which are products of individual
non-hermitian spin operator states. This decomposition is consistent with the
intuitive notion that after separation from the singlet the two physical
systems should be described by a product state. In spite of the
non-hermiticity, the values of the relevant spin observables are real. A new
local hidden variable model inspired by this decomposition is discussed.
|
2025-04-03
| 2,025
|
coincid experi epr pair show strong violat bell inequ certain filter set wide believ mean local hidden variabl model cannot explain result paper shown non separ singlet densiti matrix repres sum separ densiti matric product individu non hermitian spin oper state decomposit consist intuit notion separ singlet two physic system describ product state spite non hermit valu relev spin observ real new local hidden variabl model inspir decomposit discuss
|
23
| 23
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P. Kroll (Wuppertal Univ.)
|
Hard exclusive scattering at Jlab
|
The various factorization schemes for hard exclusive processes and the status
of their applications is briefly reviewed.
|
2025-01-22
| 2,025
|
variou factor scheme hard exclus process statu applic briefli review
|
24
| 24
|
Youssef Alaoui
|
On $q$-complete and $q$-concave with corners complex manifolds
|
It is proved that if there exists a positive and continuous function $f$ on an $n$-dimensional complex manifold $X$, $q$-convex with corners outside a compact set $K\subset X$ and which exhausts $X$ from below, then $dim_{\mathbb{C}}H^{p}(X,{\mathcal{F}})<+\infty$ for any coherent analytic sheaf ${\mathcal{F}}$ on $X$ if $p<n-q$. It is known from the theory of Andreotti and Grauert that if a complex space $X$ is $q$-complete, then $X$ is cohomoloogically $q$-complete. Until now it is not known in general if these two conditions are equivalent. The aim of section $4$ of this article is to provide a counterexample to the conjecture posed by Andreotti and Grauert ~\cite{ref2} to show that a cohomologically $q$-complete space is not necessarily $q$-complete. In section $5$ of this article, we will prove that there exist for each pair of integers $(n,q)$ with $2\leq q\leq n-1$ a $q$-complete with corners open subset $D$ of $\mathbb{P}^{n}$ and $\mathcal{F}\in coh(\mathbb{P}^{n})$ such that $D$ is not cohomologically $\hat{q}$-complete with respect to ${\mathcal{F}}$. Here $\hat{q}=n-[\frac{n-1}{q}]$, where $[x]$ denotes the integral part of $x$.
|
2025-10-09
| 2,025
|
prove exist posit continu function f n dimension complex manifold x q convex corner outsid compact set k subset x exhaust x dim mathbb c h p x mathcal f infti coher analyt sheaf mathcal f x p n q known theori andreotti grauert complex space x q complet x cohomoloog q complet known gener two condit equival aim section articl provid counterexampl conjectur pose andreotti grauert cite ref show cohomolog q complet space necessarili q complet section articl prove exist pair integ n q leq q leq n q complet corner open subset mathbb p n mathcal f coh mathbb p n cohomolog hat q complet respect mathcal f hat q n frac n q x denot integr part x
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25
| 25
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Jean-Paul Doeraene, Enrique Macias-Virg\'os, Daniel Tanr\'e
|
Ganea and Whitehead definitions for the tangential
Lusternik-Schnirelmann category of foliations
|
This work solves the problem of elaborating Ganea and Whitehead definitions
for the tangential category of a foliated manifold. We develop these two
notions in the category $\Tops$ of stratified spaces, that are topological
spaces $X$ endowed with a partition $\cF$ and compare them to a third invariant
defined by using open sets. More precisely, these definitions apply to an
element $(X,\cF)$ of $\Tops$ together with a class $\cA$ of subsets of $X$;
they are similar to invariants introduced by M. Clapp and D. Puppe.
If $(X,\cF)\in\Tops$, we define a transverse subset as a subspace $A$ of $X$
such that the intersection $S\cap A$ is at most countable for any $S\in \cF$.
Then we define the Whitehead and Ganea LS-categories of the stratified space by
taking the infimum along the transverse subsets. When we have a closed
manifold, endowed with a $C^1$-foliation, the three previous definitions, with
$\cA$ the class of transverse subsets, coincide with the tangential category
and are homotopical invariants.
|
2025-03-11
| 2,025
|
work solv problem elabor ganea whitehead definit tangenti categori foliat manifold develop two notion categori top stratifi space topolog space x endow partit cf compar third invari defin use open set precis definit appli element x cf top togeth class ca subset x similar invari introduc clapp pupp x cf top defin transvers subset subspac x intersect cap countabl cf defin whitehead ganea ls categori stratifi space take infimum along transvers subset close manifold endow c foliat three previou definit ca class transvers subset coincid tangenti categori homotop invari
|
26
| 26
|
Jan Snellman
|
Generating functions for borders
|
We give the generating function for the index of integer lattice points,
relative to a finite order ideal. The index is an important concept in the
theory of border bases, an alternative to Gr\"obner bases.
Equivalently, we explicitly solve a class of difference equations where the
right-hand side is the minimum of a number of affine forms.
|
2025-03-04
| 2,025
|
give gener function index integ lattic point rel finit order ideal index import concept theori border base altern gr obner base equival explicitli solv class differ equat right hand side minimum number affin form
|
27
| 27
|
D. Le Bolloc'h, V.L.R. Jacques, N. Kirova, J. Dumas, S. Ravy, J.
Marcus, F. Livet
|
Observation of correlations up to the micrometer scale in sliding
charge-density waves
|
High-resolution coherent x-ray diffraction experiment has been performed on
the charge density wave (CDW) system K$_{0.3}$MoO$_3$. The $2k_F$ satellite
reflection associated with the CDW has been measured with respect to external
dc currents. In the sliding regime, the $2k_F$ satellite reflection displays
secondary satellites along the chain axis which corresponds to correlations up
to the micrometer scale. This super long range order is 1500 times larger than
the CDW period itself. This new type of electronic correlation seems inherent
to the collective dynamics of electrons in charge density wave systems. Several
scenarios are discussed.
|
2025-01-08
| 2,025
|
high resolut coher x ray diffract experi perform charg densiti wave cdw system k moo k f satellit reflect associ cdw measur respect extern dc current slide regim k f satellit reflect display secondari satellit along chain axi correspond correl micromet scale super long rang order time larger cdw period new type electron correl seem inher collect dynam electron charg densiti wave system sever scenario discuss
|
28
| 28
|
M. Diehl (DESY Hamburg), Th. Feldmann (Univ. Siegen), P. Kroll (Univ.
Wuppertal)
|
Form factors and other measures of strangeness in the nucleon
|
We discuss the phenomenology of strange-quark dynamics in the nucleon, based
on experimental and theoretical results for electroweak form factors and for
parton densities. In particular, we construct a model for the generalized
parton distribution that relates the asymmetry s(x)-sbar(x) between the
longitudinal momentum distributions of strange quarks and antiquarks with the
form factor F1^s(t), which describes the distribution of strangeness in
transverse position space.
|
2025-01-22
| 2,025
|
discuss phenomenolog strang quark dynam nucleon base experiment theoret result electroweak form factor parton densiti particular construct model gener parton distribut relat asymmetri x sbar x longitudin momentum distribut strang quark antiquark form factor f describ distribut strang transvers posit space
|
29
| 29
|
Greg J. Stephens and William Bialek
|
Toward a statistical mechanics of four letter words
|
We consider words as a network of interacting letters, and approximate the
probability distribution of states taken on by this network. Despite the
intuition that the rules of English spelling are highly combinatorial (and
arbitrary), we find that maximum entropy models consistent with pairwise
correlations among letters provide a surprisingly good approximation to the
full statistics of four letter words, capturing ~92% of the multi-information
among letters and even "discovering" real words that were not represented in
the data from which the pairwise correlations were estimated. The maximum
entropy model defines an energy landscape on the space of possible words, and
local minima in this landscape account for nearly two-thirds of words used in
written English.
|
2025-02-13
| 2,025
|
consid word network interact letter approxim probabl distribut state taken network despit intuit rule english spell highli combinatori arbitrari find maximum entropi model consist pairwis correl among letter provid surprisingli good approxim full statist four letter word captur multi inform among letter even discov real word repres data pairwis correl estim maximum entropi model defin energi landscap space possibl word local minima landscap account nearli two third word use written english
|
30
| 30
|
Alan Kostelecky and Neil Russell
|
Data Tables for Lorentz and CPT Violation
|
This work tabulates measured and derived values of coefficients for Lorentz
and CPT violation in the Standard-Model Extension. Summary tables are extracted
listing maximal attained sensitivities in the matter, photon, neutrino, and
gravity sectors. Tables presenting definitions and properties are also
compiled.
|
2025-01-14
| 2,025
|
work tabul measur deriv valu coeffici lorentz cpt violat standard model extens summari tabl extract list maxim attain sensit matter photon neutrino graviti sector tabl present definit properti also compil
|
31
| 31
|
Irina Kmit
|
Classical solvability of nonlinear initial-boundary problems for first-order hyperbolic systems
|
We prove the global classical solvability of initial-boundary problems for semilinear first-order hyperbolic systems subjected to local and nonlocal nonlinear boundary conditions. We also establish lower bounds for the order of nonlinearity demarkating a frontier between regular cases (classical solvability) and singular cases (blow-up of solutions).
|
2025-12-10
| 2,025
|
prove global classic solvabl initi boundari problem semilinear first order hyperbol system subject local nonloc nonlinear boundari condit also establish lower bound order nonlinear demark frontier regular case classic solvabl singular case blow solut
|
32
| 32
|
L. D. Marks and D. R. Luke
|
Robust Mixing for Ab-Initio Quantum Mechanical Calculations
|
We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broydens second method for solving the self-consistent field equations of Kohn-Sham density functional theory. The algorithm is robust, requires relatively little finetuning and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.
|
2025-06-05
| 2,025
|
studi gener problem mix ab initio quantum mechan problem guid gener mathemat principl underli physic propos multisec form broyden second method solv self consist field equat kohn sham densiti function theori algorithm robust requir rel littl finetun appear outperform current state art converg case defeat mani method compar techniqu convent method problem rang simpl nearli patholog
|
33
| 33
|
Irina Kmit
|
On the Fredholm Solvability for a Class of Multidimensional Hyperbolic Problems
|
We prove the Fredholm alternative for a class of two-dimensional first-order hyperbolic systems with periodic-Dirichlet boundary conditions. Our approach is based on a regularization via a right parametrix.
|
2025-12-10
| 2,025
|
prove fredholm altern class two dimension first order hyperbol system period dirichlet boundari condit approach base regular via right parametrix
|
34
| 34
|
Derong Qiu
|
On Some Diophantine Parameters of the Cyclic Torsion Subgroups of Odd Order of Elliptic Curves over $\mathbb{Q}$
|
In this paper, we give some explicit Diophantine parameters of the cyclic torsion subgroups of odd order of elliptic curves over $\mathbb{Q}$.
|
2025-08-26
| 2,025
|
paper give explicit diophantin paramet cyclic torsion subgroup odd order ellipt curv mathbb q
|
35
| 35
|
Fabrizio Catanese and Frederic Mangolte
|
Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II
|
Let W -> X be a real smooth projective 3-fold fibred by rational curves. J. Koll\'ar proved that, if W(R) is orientable, then a connected component N of W(R) is essentially either a Seifert fibred manifold or a connected sum of lens spaces. Our Main Theorem, answering in the affirmative three questions of Koll\'ar, gives sharp estimates on the number and the multiplicities of the Seifert fibres and on the number and the torsions of the lens spaces when X is a geometrically rational surface. When N is Seifert fibred over a base orbifold F, our result generalizes Comessatti's theorem on smooth real rational surfaces: F cannot be simultaneously orientable and of hyperbolic type. We show as a surprise that, unlike in Comessatti's theorem, there are examples where F is non orientable, of hyperbolic type, and X is minimal. The technique we use is to construct Seifert fibrations as projectivized tangent bundles of Du Val surfaces.
|
2025-05-26
| 2,025
|
let w x real smooth project fold fibr ration curv j koll ar prove w r orient connect compon n w r essenti either seifert fibr manifold connect sum len space main theorem answer affirm three question koll ar give sharp estim number multipl seifert fibr number torsion len space x geometr ration surfac n seifert fibr base orbifold f result gener comessatti theorem smooth real ration surfac f cannot simultan orient hyperbol type show surpris unlik comessatti theorem exampl f non orient hyperbol type x minim techniqu use construct seifert fibrat projectiv tangent bundl du val surfac
|
36
| 36
|
Matthew Perlmutter, Miguel Rodriguez-Olmos
|
On Singular Poisson Sternberg Spaces
|
We obtain a theory of stratified Sternberg spaces thereby extending the
theory of cotangent bundle reduction for free actions to the singular case
where the action on the base manifold consists of only one orbit type. We find
that the symplectic reduced spaces are stratified topological fiber bundles
over the cotangent bundle of the orbit space. We also obtain a Poisson
stratification of the Sternberg space. To construct the singular Poisson
Sternberg space we develop an appropriate theory of singular connections for
proper group actions on a single orbit type manifold including a theory of
holonomy extending the usual Ambrose-Singer theorem for principal bundles.
|
2025-01-23
| 2,025
|
obtain theori stratifi sternberg space therebi extend theori cotang bundl reduct free action singular case action base manifold consist one orbit type find symplect reduc space stratifi topolog fiber bundl cotang bundl orbit space also obtain poisson stratif sternberg space construct singular poisson sternberg space develop appropri theori singular connect proper group action singl orbit type manifold includ theori holonomi extend usual ambros singer theorem princip bundl
|
37
| 37
|
Igor Kondrashuk and Anatoly Kotikov
|
Triangle UD integrals in the position space
|
We investigate triangle UD ladder integrals in the position space. The investigation is necessary to find an all-order in loop solution for an auxiliary Lcc correlator in Wess-Zumino-Landau gauge of the maximally supersymmetric Yang-Mills theory and to present correlators of dressed mean gluons in terms of it in all loops. We show that triangle UD ladder diagrams in the position space can be expressed in terms of the same UD functions Phi^(L) in terms of which they were represented in the momentum space, for an arbitrary number of rungs.
|
2025-09-05
| 2,025
|
investig triangl ud ladder integr posit space investig necessari find order loop solut auxiliari lcc correl wess zumino landau gaug maxim supersymmetr yang mill theori present correl dress mean gluon term loop show triangl ud ladder diagram posit space express term ud function phi l term repres momentum space arbitrari number rung
|
38
| 38
|
Mikhail Khovanov and Aaron D. Lauda
|
A diagrammatic approach to categorification of quantum groups I
|
To each graph without loops and multiple edges we assign a family of rings.
Categories of projective modules over these rings categorify
$U^-_q(\mathfrak{g})$, where $\mathfrak{g}$ is the Kac-Moody Lie algebra
associated with the graph.
|
2025-01-23
| 2,025
|
graph without loop multipl edg assign famili ring categori project modul ring categorifi u q mathfrak g mathfrak g kac moodi lie algebra associ graph
|
39
| 39
|
Fawei Zheng, Gang Zhou, Zhirong Liu, Jian Wu, Wenhui Duan, Bing-Lin Gu, and S. B. Zhang
|
Prediction of Half Metallicity along the Edge of Boron Nitride Zigzag Nanoribbons
|
First-principles calculations reveal half metallicity in zigzag boron nitride (BN) nanoribbons (ZBNNRs). When the B edge, but not the N edge, of the ZBNNR is passivated, despite being a pure $sp$-electron system, the ribbon shows a giant spin splitting. The electrons at the Fermi level are 100% spin polarized with a half-metal gap of 0.38 eV and its conductivity is dominated by metallic single-spin states. The two states across at the Dirac point have different molecular origins, which signals a switch of carrier velocity. The ZBNNR should be a good potential candidate for widegap spintronics.
|
2025-09-10
| 2,025
|
first principl calcul reveal half metal zigzag boron nitrid bn nanoribbon zbnnr b edg n edg zbnnr passiv despit pure sp electron system ribbon show giant spin split electron fermi level spin polar half metal gap ev conduct domin metal singl spin state two state across dirac point differ molecular origin signal switch carrier veloc zbnnr good potenti candid widegap spintron
|
40
| 40
|
Mireille Bousquet-M\'elou (LaBRI)
|
Families of prudent self-avoiding walks
|
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that have been counted so far in that they can wind around their starting point. Their enumeration was first addressed by Pr\'ea in 1997. He defined 4 classes of prudent walks, of increasing generality, and wrote a system of recurrence relations for each of them . However, these relations involve more and more parameters as the generality of the class increases. The first class actually consists of partially directed walks, and its generating function is well-known to be rational. The second class was proved to have an algebraic (quadratic) generating function by Duchi (2005). Here, we solve exactly the third class, which turns out to be much more complex: its generating function is not algebraic, nor even D-finite. The fourth class -- general prudent walks -- is the only isotropic one, and still defeats us. However, we design an isotropic family of prudent walks on the triangular lattice, which we count exactly. Again, the generating function is proved to be non-D-finite. We also study the asymptotic properties of these classes of walks, with the (somewhat disappointing) conclusion that their endpoint moves away from the origin at a positive speed. This is confirmed visually by the random generation procedures we have designed.
|
2025-09-26
| 2,025
|
self avoid walk saw squar lattic prudent never take step toward vertex alreadi visit prudent walk differ class saw count far wind around start point enumer first address pr ea defin class prudent walk increas gener wrote system recurr relat howev relat involv paramet gener class increas first class actual consist partial direct walk gener function well known ration second class prove algebra quadrat gener function duchi solv exactli third class turn much complex gener function algebra even finit fourth class gener prudent walk isotrop one still defeat us howev design isotrop famili prudent walk triangular lattic count exactli gener function prove non finit also studi asymptot properti class walk somewhat disappoint conclus endpoint move away origin posit speed confirm visual random gener procedur design
|
41
| 41
|
Mireille Bousquet-M\'elou (LaBRI)
|
Rational and algebraic series in combinatorial enumeration
|
Let A be a class of objects, equipped with an integer size such that for all n the number a(n) of objects of size n is finite. We are interested in the case where the generating fucntion sum_n a(n) t^n is rational, or more generally algebraic. This property has a practical interest, since one can usually say a lot on the numbers a(n), but also a combinatorial one: the rational or algebraic nature of the generating function suggests that the objects have a (possibly hidden) structure, similar to the linear structure of words in the rational case, and to the branching structure of trees in the algebraic case. We describe and illustrate this combinatorial intuition, and discuss its validity. While it seems to be satisfactory in the rational case, it is probably incomplete in the algebraic one. We conclude with open questions.
|
2025-09-26
| 2,025
|
let class object equip integ size n number n object size n finit interest case gener fucntion sum n n n ration gener algebra properti practic interest sinc one usual say lot number n also combinatori one ration algebra natur gener function suggest object possibl hidden structur similar linear structur word ration case branch structur tree algebra case describ illustr combinatori intuit discuss valid seem satisfactori ration case probabl incomplet algebra one conclud open question
|
42
| 42
|
Miklos Bona
|
On Two Related Questions of Wilf Concerning Standard Young Tableaux
|
We consider two questions of Wilf related to Standard Young Tableaux. We
provide a partial answer to one question, and that will lead us to a more
general answer to the other question. Our answers are purely combinatorial.
|
2025-04-30
| 2,025
|
consid two question wilf relat standard young tableaux provid partial answer one question lead us gener answer question answer pure combinatori
|
43
| 43
|
A.E. Brouwer and W.H. Haemers
|
Algebraic Graph Theory (a short course for postgraduate students and researchers)
|
This submission has been withdrawn by arXiv administration.
|
2025-07-10
| 2,025
|
submiss withdrawn arxiv administr
|
44
| 44
|
Michael Frank, Kamran Sharifi
|
Generalized inverses and polar decomposition of unbounded regular
operators on Hilbert $C^*$-modules
|
In this note we show that an unbounded regular operator $t$ on Hilbert
$C^*$-modules over an arbitrary $C^*$ algebra $ \mathcal{A}$ has polar
decomposition if and only if the closures of the ranges of $t$ and $|t|$ are
orthogonally complemented, if and only if the operators $t$ and $t^*$ have
unbounded regular generalized inverses. For a given $C^*$-algebra $
\mathcal{A}$ any densely defined $\mathcal A$-linear closed operator $t$
between Hilbert $C^*$-modules has polar decomposition, if and only if any
densely defined $\mathcal A$-linear closed operator $t$ between Hilbert
$C^*$-modules has generalized inverse, if and only if $\mathcal A$ is a
$C^*$-algebra of compact operators.
|
2025-04-29
| 2,025
|
note show unbound regular oper hilbert c modul arbitrari c algebra mathcal polar decomposit closur rang orthogon complement oper unbound regular gener invers given c algebra mathcal dens defin mathcal linear close oper hilbert c modul polar decomposit dens defin mathcal linear close oper hilbert c modul gener invers mathcal c algebra compact oper
|
45
| 45
|
Mireille Bousquet-M\'elou, Anders Claesson, Mark Dukes and Sergey Kitaev
|
(2+2)-free posets, ascent sequences and pattern avoiding permutations
|
We present bijections between four classes of combinatorial objects. Two of them, the class of unlabeled (2+2)-free posets and a certain class of involutions (or chord diagrams), already appeared in the literature, but were apparently not known to be equinumerous. We present a direct bijection between them. The third class is a family of permutations defined in terms of a new type of pattern. An attractive property of these patterns is that, like classical patterns, they are closed under the action of $D_8$, the symmetry group of the square. The fourth class is formed by certain integer sequences, called ascent sequences, which have a simple recursive structure and are shown to encode (2+2)-free posets and permutations. Our bijections preserve numerous statistics.
We determine the generating function of these classes of objects, thus recovering a non-D-finite series obtained by Zagier for the class of chord diagrams. Finally, we characterize the ascent sequences that correspond to permutations avoiding the barred pattern $3{\bar 1}52{\bar 4}$ and use this to enumerate those permutations, thereby settling a conjecture of Pudwell.
|
2025-09-26
| 2,025
|
present biject four class combinatori object two class unlabel free poset certain class involut chord diagram alreadi appear literatur appar known equinumer present direct biject third class famili permut defin term new type pattern attract properti pattern like classic pattern close action symmetri group squar fourth class form certain integ sequenc call ascent sequenc simpl recurs structur shown encod free poset permut biject preserv numer statist determin gener function class object thu recov non finit seri obtain zagier class chord diagram final character ascent sequenc correspond permut avoid bar pattern bar bar use enumer permut therebi settl conjectur pudwel
|
46
| 46
|
Andreea C. Nicoara
|
The Kohn Algorithm on Denjoy-Carleman Classes
|
The equivalence of the Kohn finite ideal type and the D'Angelo finite type with the subellipticity of the $\bar\partial$-Neumann problem is extended to pseudoconvex domains in $C^n$ whose defining function is in a Denjoy-Carleman quasianalytic class closed under differentiation. The proof involves algebraic geometry over a ring of germs of Denjoy-Carleman quasianalytic functions that is not known to be Noetherian and that is intermediate between the ring of germs of real-analytic functions and the ring of germs of smooth functions. It is also shown that this type of ring of germs of Denjoy-Carleman functions satisfies the $\sqrt{acc}$ property, one of the strongest properties a non-Noetherian ring could possess.
|
2025-11-11
| 2,025
|
equival kohn finit ideal type angelo finit type subellipt bar partial neumann problem extend pseudoconvex domain c n whose defin function denjoy carleman quasianalyt class close differenti proof involv algebra geometri ring germ denjoy carleman quasianalyt function known noetherian intermedi ring germ real analyt function ring germ smooth function also shown type ring germ denjoy carleman function satisfi sqrt acc properti one strongest properti non noetherian ring could possess
|
47
| 47
|
L.T. Vuong, A.J.L. Adam, J.M. Brok, M. A. Seo, D. S. Kim, P.C.M. Planken, H.P. Urbach
|
Electromagnetic Spin-Orbit Interactions via Scattering
|
The longitudinal components of orthogonal-circularly polarized fields carry a phase singularity that changes sign depending on the polarization handedness. The addition of orbital angular momentum adds to or cancels this singularity and results in polarization-dependent scattering through round and square apertures, which we demonstrate analytically, numerically, and experimentally. By preparing the incident polarization and arranging the configuration of sub-wavelength apertures, we produce shadow-side scattered fields with arbitrary phase vorticity.
|
2025-07-01
| 2,025
|
longitudin compon orthogon circularli polar field carri phase singular chang sign depend polar handed addit orbit angular momentum add cancel singular result polar depend scatter round squar apertur demonstr analyt numer experiment prepar incid polar arrang configur sub wavelength apertur produc shadow side scatter field arbitrari phase vortic
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48
| 48
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Xian-Jin Li
|
A proof of the Riemann hypothesis
|
In this paper we study traces of an integral operator on two orthogonal subspaces of a $L^2$ space. One of the two traces is shown to be zero. Also, we prove that the trace of the operator on the second subspace is nonnegative. Hence, the operator has a nonnegative trace on the $L^2$ space. This implies the positivity of Li's criterion. By Li's criterion, all nontrivial zeros of the Riemann zeta-function lie on the critical line.
|
2025-10-14
| 2,025
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paper studi trace integr oper two orthogon subspac l space one two trace shown zero also prove trace oper second subspac nonneg henc oper nonneg trace l space impli posit li criterion li criterion nontrivi zero riemann zeta function lie critic line
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49
| 49
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E. Lopez Sandoval
|
Static Universe: Infinite, Eternal and Self-Sustainable
|
In this paper, we present a "stellar dynamics" model of an infinite Universe, where matter distribution follows an inverse proportionality squared relationship with respect to the distance from the rotation center of galaxy clusters and superclusters (which share a common rotation center). We assume the Universe has infinite similar centers in terms of structure and dynamic equilibrium. We consider stars in galaxies to be homogeneously distributed with spherical symmetry and average radius, and the same applies to galaxies in the Universe. We study the smoothed potential of this universe and examine the effect of gravity on starlight: by applying the equivalence principle, we derive a mathematical expression for Hubble's law and a formula for its redshift, potentially explaining this phenomenon as a gravitational effect. We also provide an approximate calculation of Cosmic Background Radiation (CBR), assuming this radiation is the light from all the universe's stars reaching us with an extreme redshift caused by gravity. theory, postulating in consequence a new theory about the structure of the Universe: static, infinite, eternal and self-sustainable.
|
2025-07-10
| 2,025
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paper present stellar dynam model infinit univers matter distribut follow invers proportion squar relationship respect distanc rotat center galaxi cluster superclust share common rotat center assum univers infinit similar center term structur dynam equilibrium consid star galaxi homogen distribut spheric symmetri averag radiu appli galaxi univers studi smooth potenti univers examin effect graviti starlight appli equival principl deriv mathemat express hubbl law formula redshift potenti explain phenomenon gravit effect also provid approxim calcul cosmic background radiat cbr assum radiat light univers star reach us extrem redshift caus graviti theori postul consequ new theori structur univers static infinit etern self sustain
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50
| 50
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Stefan Schwede
|
Algebraic versus topological triangulated categories
|
The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such examples are called `algebraic' because they originate from abelian (or at least additive) categories. Stable homotopy theory produces examples of triangulated categories by quite different means, and in this context the source categories are usually very `non-additive' before passing to homotopy classes of morphisms. Because of their origin I refer to these examples as `topological triangulated categories'.
In these extended talk notes I explain some systematic differences between these two kinds of triangulated categories. There are certain properties -- defined entirely in terms of the triangulated structure -- which hold in all algebraic examples, but which fail in some topological ones. These differences are all torsion phenomena, and rationally there is no difference between algebraic and topological triangulated categories.
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2025-11-05
| 2,025
|
commonli known triangul categori aris chain complex abelian categori pass chain homotopi class invert quasi isomorph exampl call algebra origin abelian least addit categori stabl homotopi theori produc exampl triangul categori quit differ mean context sourc categori usual non addit pass homotopi class morphism origin refer exampl topolog triangul categori extend talk note explain systemat differ two kind triangul categori certain properti defin entir term triangul structur hold algebra exampl fail topolog one differ torsion phenomena ration differ algebra topolog triangul categori
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51
| 51
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Brendan Guilfoyle and Wilhelm Klingenberg
|
Proof of the Caratheodory Conjecture
|
A well-known conjecture of Caratheodory states that the number of umbilic
points on a closed convex surface in ${\mathbb E}^3$ must be greater than one.
In this paper we prove this for $C^{3+\alpha}$-smooth surfaces. The Conjecture
is first reformulated in terms of complex points on a Lagrangian surface in
$TS^2$, viewed as the space of oriented geodesics in ${\mathbb E}^3$. Here
complex and Lagrangian refer to the canonical neutral Kaehler structure on
$TS^2$. We then prove that the existence of a closed convex surface with only
one umbilic point implies the existence of a totally real Lagrangian hemisphere
in $TS^2$, to which it is not possible to attach the edge of a holomorphic
disc. The main step in the proof is to establish the existence of a holomorphic
disc with edge contained on any given totally real Lagrangian hemisphere. To
construct the holomorphic disc we utilize mean curvature flow with respect to
the neutral metric. Long-time existence of this flow is proven by a priori
estimates and we show that the flowing disc is asymptotically holomorphic.
Existence of a holomorphic disc is then deduced from Schauder estimates.
|
2025-01-20
| 2,025
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well known conjectur caratheodori state number umbil point close convex surfac mathbb e must greater one paper prove c alpha smooth surfac conjectur first reformul term complex point lagrangian surfac ts view space orient geodes mathbb e complex lagrangian refer canon neutral kaehler structur ts prove exist close convex surfac one umbil point impli exist total real lagrangian hemispher ts possibl attach edg holomorph disc main step proof establish exist holomorph disc edg contain given total real lagrangian hemispher construct holomorph disc util mean curvatur flow respect neutral metric long time exist flow proven priori estim show flow disc asymptot holomorph exist holomorph disc deduc schauder estim
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52
| 52
|
Mikhail Skopenkov
|
Embedding products of graphs into Euclidean spaces
|
For any collection of graphs we find the minimal dimension d such that the product of these graphs is embeddable into the d-dimensional Euclidean space. In particular, we prove that the n-th powers of the Kuratowsky graphs are not embeddable into the 2n-dimensional Euclidean space. This is a solution of a problem of Menger from 1929. The idea of the proof is the reduction to a problem from so-called Ramsey link theory: we show that any embedding of L into the (2n-1)-dimensional sphere, where L is the join of n copies of a 4-point set, has a pair of linked (n-1)-dimensional spheres.
|
2025-07-18
| 2,025
|
collect graph find minim dimens product graph embedd dimension euclidean space particular prove n th power kuratowski graph embedd n dimension euclidean space solut problem menger idea proof reduct problem call ramsey link theori show embed l n dimension sphere l join n copi point set pair link n dimension sphere
|
53
| 53
|
S. Ferrara, A. Marrani
|
Symmetric Spaces in Supergravity
|
We exploit the relation among irreducible Riemannian globally symmetric
spaces (IRGS) and supergravity theories in 3, 4 and 5 space-time dimensions.
IRGS appear as scalar manifolds of the theories, as well as moduli spaces of
the various classes of solutions to the classical extremal black hole Attractor
Equations. Relations with Jordan algebras of degree three and four are also
outlined.
|
2025-02-06
| 2,025
|
exploit relat among irreduc riemannian global symmetr space irg supergrav theori space time dimens irg appear scalar manifold theori well moduli space variou class solut classic extrem black hole attractor equat relat jordan algebra degre three four also outlin
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54
| 54
|
Zosia A. C. Krusberg
|
Physics education research: Resources for graduate student instructors
|
This resource letter intends to provide physics instructors - particularly graduate student teaching assistants - at the introductory university level with a small but representative collection of resources to acquire a familiarity with research in physics education for guidance in everyday instruction. The resources are in the form of books, articles, websites, journals, and organizations.
|
2025-05-29
| 2,025
|
resourc letter intend provid physic instructor particularli graduat student teach assist introductori univers level small repres collect resourc acquir familiar research physic educ guidanc everyday instruct resourc form book articl websit journal organ
|
55
| 55
|
Yale Fan
|
Applications of Multi-Valued Quantum Algorithms
|
This paper generalizes both the binary Deutsch-Jozsa and Grover algorithms to
$n$-valued logic using the quantum Fourier transform. Our extended
Deutsch-Jozsa algorithm is not only able to distinguish between constant and
balanced Boolean functions in a single query, but can also find closed
expressions for classes of affine logical functions in quantum oracles,
accurate to a constant term. Furthermore, our multi-valued extension of the
Grover algorithm for quantum database search requires fewer qudits and hence a
substantially smaller memory register, as well as fewer wasted information
states, to implement. We note several applications of these algorithms and
their advantages over the binary cases.
|
2025-02-18
| 2,025
|
paper gener binari deutsch jozsa grover algorithm n valu logic use quantum fourier transform extend deutsch jozsa algorithm abl distinguish constant balanc boolean function singl queri also find close express class affin logic function quantum oracl accur constant term furthermor multi valu extens grover algorithm quantum databas search requir fewer qudit henc substanti smaller memori regist well fewer wast inform state implement note sever applic algorithm advantag binari case
|
56
| 56
|
Andrzej Karbowski
|
Amdahl's and Gustafson-Barsis laws revisited
|
The paper presents a simple derivation of the Gustafson-Barsis law from the Amdahl's law. In the computer literature these two laws describing the speedup limits of parallel applications are derived separately. It is shown, that treating the time of the execution of the sequential part of the application as a constant, in few lines the Gustafson-Barsis law can be obtained from the Amdahl's law and that the popular claim, that Gustafson-Barsis law overthrows Amdahl's law is a mistake.
|
2025-12-12
| 2,025
|
paper present simpl deriv gustafson barsi law amdahl law comput literatur two law describ speedup limit parallel applic deriv separ shown treat time execut sequenti part applic constant line gustafson barsi law obtain amdahl law popular claim gustafson barsi law overthrow amdahl law mistak
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57
| 57
|
Alexander Perepechko
|
Affine algebraic monoids as endomorphisms' monoids of finite-dimensional
algebras
|
In this note we prove that any affine algebraic monoid can be obtained as the
endomorphisms' monoid of a finite-dimensional (nonassociative) algebra.
|
2025-03-06
| 2,025
|
note prove affin algebra monoid obtain endomorph monoid finit dimension nonassoci algebra
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58
| 58
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J. Ciston, A. Subramanian, L. D. Marks
|
Hydroxylated MgO (111) reconstructions: why the case for clean surfaces does not hold water
|
We report an experimental and theoretical analysis of the root(3)xroot(3)-R30 and 2x2 reconstructions on the MgO (111) surface combining transmission electron microscopy, x-ray photoelectron spectroscopy, and reasonably accurate density functional calculations using the meta-GGA functional TPSS. The experimental data clearly shows that the surfaces contain significant coverages of hydroxyl terminations, even after UHV annealing, and as such cannot be the structures which have been previously reported. For the 2x2 surfaces a relatively simple structural framework is detailed which fits all the experimental and theoretical data. For the root(3)xroot(3) there turn out to be two plausible structures and neither the experimental nor theoretical results can differentiate between the two within error. However, by examining the conditions under which the surface is formed we describe a kinetic route for the transformation between the different reconstructions that involves mobile hydroxyl groups and protons, and relatively immobile cations, which strongly suggests only one of the two root(3)xroot(3) structures.
|
2025-09-22
| 2,025
|
report experiment theoret analysi root xroot r x reconstruct mgo surfac combin transmiss electron microscopi x ray photoelectron spectroscopi reason accur densiti function calcul use meta gga function tpss experiment data clearli show surfac contain signific coverag hydroxyl termin even uhv anneal cannot structur previous report x surfac rel simpl structur framework detail fit experiment theoret data root xroot turn two plausibl structur neither experiment theoret result differenti two within error howev examin condit surfac form describ kinet rout transform differ reconstruct involv mobil hydroxyl group proton rel immobil cation strongli suggest one two root xroot structur
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59
| 59
|
Cyril Houdayer
|
Free Araki-Woods factors and Connes' bicentralizer problem
|
We show that for any free Araki-Woods factor $\mathcal{M} = \Gamma(H_\R, U_t)"$ of type ${\rm III_1}$, the bicentralizer of the free quasi-free state $\varphi_U$ is trivial. Using Haagerup's Theorem, it follows that there always exists a faithful normal state $\psi$ on $\mathcal{M}$ such that $(\mathcal{M}^\psi)' \cap \mathcal{M} = \C$.
|
2025-07-17
| 2,025
|
show free araki wood factor mathcal gamma h r u type rm iii bicentr free quasi free state varphi u trivial use haagerup theorem follow alway exist faith normal state psi mathcal mathcal psi cap mathcal c
|
60
| 60
|
S.V. Goloskokov and P. Kroll
|
The target asymmetry in hard vector-meson electroproduction and parton
angular momenta
|
The target asymmetry for electroproduction of vector mesons is investigated
within the handbag approach. While the generalized parton distribution (GPD) H
is taken from a previous analysis of the elctroproduction cross section, we
here construct the GPD E from double distributions and constrain it by the
Pauli form factors of the nucleon, positivity bounds and sum rules. Predictions
for the target asymmetry are given for various vector mesons and discussed how
experimental data on the asymmetry will further constrain E and what we may
learn about the angular momenta the partons carry.
|
2025-01-22
| 2,025
|
target asymmetri electroproduct vector meson investig within handbag approach gener parton distribut gpd h taken previou analysi elctroproduct cross section construct gpd e doubl distribut constrain pauli form factor nucleon posit bound sum rule predict target asymmetri given variou vector meson discuss experiment data asymmetri constrain e may learn angular momenta parton carri
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61
| 61
|
Martijn Kool
|
Fixed point loci of moduli spaces of sheaves on toric varieties
|
Extending work of Klyachko and Perling, we develop a combinatorial description of pure equivariant sheaves of any dimension on an arbitrary nonsingular toric variety $X$. Using geometric invariant theory (GIT), this allows us to construct explicit moduli spaces of pure equivariant sheaves on $X$ corepresenting natural moduli functors (similar to work of Payne in the case of equivariant vector bundles). The action of the algebraic torus on $X$ lifts to the moduli space of all Gieseker stable sheaves on $X$ and we express its fixed point locus explicitly in terms of moduli spaces of pure equivariant sheaves on $X$. One of the problems arising is to find an equivariant line bundle on the side of the GIT problem, which precisely recovers Gieseker stability. In the case of torsion free equivariant sheaves, we can always construct such equivariant line bundles. As a by-product, we get a combinatorial description of the fixed point locus of the moduli space of $\mu$-stable reflexive sheaves on $X$. As an application, we show in a sequel how these methods can be used to compute generating functions of Euler characteristics of moduli spaces of $\mu$-stable torsion free sheaves on nonsingular complete toric surfaces.
|
2025-10-02
| 2,025
|
extend work klyachko perl develop combinatori descript pure equivari sheav dimens arbitrari nonsingular toric varieti x use geometr invari theori git allow us construct explicit moduli space pure equivari sheav x corepres natur moduli functor similar work payn case equivari vector bundl action algebra toru x lift moduli space giesek stabl sheav x express fix point locu explicitli term moduli space pure equivari sheav x one problem aris find equivari line bundl side git problem precis recov giesek stabil case torsion free equivari sheav alway construct equivari line bundl product get combinatori descript fix point locu moduli space mu stabl reflex sheav x applic show sequel method use comput gener function euler characterist moduli space mu stabl torsion free sheav nonsingular complet toric surfac
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62
| 62
|
Mireille Bousquet-M\'elou (LaBRI), Marni Mishna
|
Walks with small steps in the quarter plane
|
Let S be a subset of {-1,0,1}^2 not containing (0,0). We address the enumeration of plane lattice walks with steps in S, that start from (0,0) and always remain in the first quadrant. A priori, there are 2^8 problems of this type, but some are trivial. Some others are equivalent to a model of walks confined to a half-plane: such models can be solved systematically using the kernel method, which leads to algebraic generating functions. We focus on the remaining cases, and show that there are 79 inherently different problems to study. To each of them, we associate a group G of birational transformations. We show that this group is finite in exactly 23 cases. We present a unified way of solving 22 of the 23 models associated with a finite group. For each of them, the generating function is found to be D-finite. The 23rd model, known as Gessel's walks, has recently been proved by Bostan et al. to have an algebraic (and hence D-finite) solution. We conjecture that the remaining 56 models, associated with an infinite group, have a non-D-finite generating function. Our approach allows us to recover and refine some known results, and also to obtain new results. For instance, we prove that walks with N, E, W, S, SW and NE steps have an algebraic generating function.
|
2025-09-26
| 2,025
|
let subset contain address enumer plane lattic walk step start alway remain first quadrant priori problem type trivial other equival model walk confin half plane model solv systemat use kernel method lead algebra gener function focu remain case show inher differ problem studi associ group g birat transform show group finit exactli case present unifi way solv model associ finit group gener function found finit rd model known gessel walk recent prove bostan et al algebra henc finit solut conjectur remain model associ infinit group non finit gener function approach allow us recov refin known result also obtain new result instanc prove walk n e w sw ne step algebra gener function
|
63
| 63
|
Amod Agashe
|
The Modular number, Congruence number, and Multiplicity One
|
Let N be a positive integer and let f be a newform of weight 2 on \Gamma_0(N). In earlier joint work with K. Ribet and W. Stein, we introduced the notions of the modular number and the congruence number of the quotient abelian variety A_f of J_0(N) associated to the newform f. These invariants are analogs of the notions of the modular degree and congruence primes respectively associated to elliptic curves. We show that if p is a prime such that every maximal ideal of the Hecke algebra of characteristic p that contains the annihilator ideal of f satisfies multiplicity one, then the modular number and the congruence number have the same p-adic valuation.
|
2025-10-07
| 2,025
|
let n posit integ let f newform weight gamma n earlier joint work k ribet w stein introduc notion modular number congruenc number quotient abelian varieti f j n associ newform f invari analog notion modular degre congruenc prime respect associ ellipt curv show p prime everi maxim ideal heck algebra characterist p contain annihil ideal f satisfi multipl one modular number congruenc number p adic valuat
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64
| 64
|
Cyril Houdayer
|
Structural results for free Araki-Woods factors and their continuous cores
|
We show that for any type ${\rm III_1}$ free Araki-Woods factor $\mathcal{M} = \Gamma(H_\R, U_t)"$ associated with an orthogonal representation $(U_t)$ of $\R$ on a separable real Hilbert space $H_\R$, the continuous core $M = \mathcal{M} \rtimes_\sigma \R$ is a semisolid ${\rm II_\infty}$ factor, i.e. for any non-zero finite projection $q \in M$, the ${\rm II_1}$ factor $qMq$ is semisolid. If the representation $(U_t)$ is moreover assumed to be mixing, then we prove that the core $M$ is solid. As an application, we construct an example of a non-amenable solid ${\rm II_1}$ factor $N$ with full fundamental group, i.e. $\mathcal{F}(N) = \R^*_+$, which is not isomorphic to any interpolated free group factor $L(\F_t)$, for $1 < t \leq +\infty$.
|
2025-07-17
| 2,025
|
show type rm iii free araki wood factor mathcal gamma h r u associ orthogon represent u r separ real hilbert space h r continu core mathcal rtime sigma r semisolid rm ii infti factor e non zero finit project q rm ii factor qmq semisolid represent u moreov assum mix prove core solid applic construct exampl non amen solid rm ii factor n full fundament group e mathcal f n r isomorph interpol free group factor l f leq infti
|
65
| 65
|
S.A. Moiseev, and W. Tittel
|
Optical quantum memory with generalized time-reversible atom-light
interactions
|
We examine a quantum memory scheme based on controllable dephasing of atomic
coherence of a non-resonant, inhomogeneously broadened Raman transition. We
show that it generalizes the physical conditions for time-reversible
interaction between light and atomic ensembles from weak to strong fields and
from linear to non-linear interactions. We also develop a unified framework for
different realizations exploiting either controlled reversible inhomogeneous
broadening or atomic frequency combs, and discuss new aspects related to
storage and manipulation of quantum states.
|
2025-02-06
| 2,025
|
examin quantum memori scheme base control dephas atom coher non reson inhomogen broaden raman transit show gener physic condit time revers interact light atom ensembl weak strong field linear non linear interact also develop unifi framework differ realiz exploit either control revers inhomogen broaden atom frequenc comb discuss new aspect relat storag manipul quantum state
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66
| 66
|
A.A. Reshetnyak
|
Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian
Description of Mixed-symmetry HS Fields in AdS Spaces
|
We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras
$\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of
relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$
in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and
$\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic,
$s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young
tableaux with two rows. We consider a method of constructing the Verma modules
$V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ and
establish a possibility of their Fock-space realizations in terms of formal
power series in oscillator operators which serve to realize an additive
conversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$,
containing a set of 2nd-class constraints, into a converted (super)algebra
$\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ =
$\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraints
only. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotent
BFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powers
of ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangian
formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and
generalized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic
constraints are examined as well.
|
2025-03-20
| 2,025
|
studi properti nonlinear superalgebra mathcal algebra mathcal b aris one one correspond set relat extract ad group irreduc represent e ad space set oper form mathcal mathcal b respect fermion n boson n n mathbb n hs field character young tableaux two row consid method construct verma modul v mathcal v mathcal b mathcal mathcal b establish possibl fock space realiz term formal power seri oscil oper serv realiz addit convers super algebra mathcal mathcal b contain set nd class constraint convert super algebra mathcal b c mathcal b mathcal b mathcal c mathcal mathcal contain set st class constraint algebra mathcal b c construct exact nilpot bfv brst oper q nonvanish term rd degre power ghost coordin use q construct gaug invari lagrangian formul lf hs field given mass energi e gener spin mathbf lf shell algebra constraint examin well
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67
| 67
|
Yu.V. Andreyev, M.V. Koroteev
|
On chaotic nature of speech signals
|
Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparatively small dimension and the positive largest Lyapunov exponent
|
2025-06-03
| 2,025
|
variou phonem consid term nonlinear dynam phase portrait signal embed space correl dimens estim largest lyapunov expon analyz shown speech signal compar small dimens posit largest lyapunov expon
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68
| 68
|
J. Christopher Kops
|
Weak convergence of the periodic multiplicative Selmer algorithm
|
In order to prove weak convergence of the periodic multiplicative Selmer algorithm we ensure that the periodicity matrix is positive and establish a relation between its entries and eigenvalues. Since we can imply that the limit of these relations exist, we arrive at the desired result.
|
2025-11-18
| 2,025
|
order prove weak converg period multipl selmer algorithm ensur period matrix posit establish relat entri eigenvalu sinc impli limit relat exist arriv desir result
|
69
| 69
|
Francesco Bartolucci and Ivonne L. Solis-Trapala
|
Multidimensional latent Markov models in a developmental study of
inhibitory control and attentional flexibility in early childhood
|
We demonstrate the use of a multidimensional extension of the latent Markov
model to analyse data from studies with correlated binary responses in
developmental psychology. In particular, we consider an experiment based on a
battery of tests which was administered to pre-school children, at three time
periods, in order to measure their inhibitory control and attentional
flexibility abilities. Our model represents these abilities by two latent
traits which are associated to each state of a latent Markov chain. The
conditional distribution of the tests outcomes given the latent process depends
on these abilities through a multidimensional two-parameter logistic
parameterisation. We outline an EM algorithm to conduct likelihood inference on
the model parameters; we also focus on likelihood ratio testing of hypotheses
on the dimensionality of the model and on the transition matrices of the latent
process. Through the approach based on the proposed model, we find evidence
that supports that inhibitory control and attentional flexibility can be
conceptualised as distinct constructs. Furthermore, we outline developmental
aspects of participants' performance on these abilities based on inspection of
the estimated transition matrices.
|
2025-01-08
| 2,025
|
demonstr use multidimension extens latent markov model analys data studi correl binari respons development psycholog particular consid experi base batteri test administ pre school children three time period order measur inhibitori control attent flexibl abil model repres abil two latent trait associ state latent markov chain condit distribut test outcom given latent process depend abil multidimension two paramet logist parameteris outlin em algorithm conduct likelihood infer model paramet also focu likelihood ratio test hypothes dimension model transit matric latent process approach base propos model find evid support inhibitori control attent flexibl conceptualis distinct construct furthermor outlin development aspect particip perform abil base inspect estim transit matric
|
70
| 70
|
Alexey G. Gorinov, Isaac C. Kalinkin
|
Combinatorics of double cosets and fundamental domains for the subgroups of the modular group
|
As noticed by R.~Kulkarni, the conjugacy classes of subgroups of the modular group correspond bijectively to bipartite cuboid graphs. We'll explain how to recover the graph corresponding to a subgroup $G$ of $\mathrm{PSL}_2(\mathbb{Z})$ from the combinatorics of the right action of $\mathrm{PSL}_2(\mathbb{Z})$ on the right cosets $G\setminus\mathrm{PSL}_2(\mathbb{Z})$. This gives a method of constructing nice fundamental domains (which Kulkarni calls "special polygons") for the action of $G$ on the upper half plane.
For the classical congruence subgroups $\Gamma_0(N)$, $\Gamma_1(N)$, $\Gamma(N)$ etc. the number of operations the method requires is the index times something that grows not faster than a polynomial in $\log N$. This is roughly the square root of the number of operations required by the naive procedure. We give algorithms to locate an element of the upper half-plane on the fundamental domain and to write a given element of $G$ as a product of independent generators. We also (re)prove a few related results about the automorphism groups of modular curves. For example, we give a simple proof that the automorphism group of $X(N)$ is $\mathrm{SL}_2(\mathbb{Z}/N)/\{\pm I\}$.
|
2025-05-14
| 2,025
|
notic r kulkarni conjugaci class subgroup modular group correspond biject bipartit cuboid graph explain recov graph correspond subgroup g mathrm psl mathbb z combinator right action mathrm psl mathbb z right coset g setminu mathrm psl mathbb z give method construct nice fundament domain kulkarni call special polygon action g upper half plane classic congruenc subgroup gamma n gamma n gamma n etc number oper method requir index time someth grow faster polynomi log n roughli squar root number oper requir naiv procedur give algorithm locat element upper half plane fundament domain write given element g product independ gener also prove relat result automorph group modular curv exampl give simpl proof automorph group x n mathrm sl mathbb z n pm
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71
| 71
|
A. Eriksson, B. Mahjani, and B. Mehlig
|
Sequential Markov coalescent algorithms for population models with demographic structure
|
We analyse sequential Markov coalescent algorithms for populations with demographic structure: for a bottleneck model, a population-divergence model, and for a two-island model with migration. The sequential Markov coalescent method is an approximation to the coalescent suggested by McVean and Cardin, and Marjoram and Wall. Within this algorithm we compute, for two individuals randomly sampled from the population, the correlation between times to the most recent common ancestor and the linkage probability corresponding to two different loci with recombination rate R between them. We find that the sequential Markov coalescent method approximates the coalescent well in general in models with demographic structure. An exception is the case where individuals are sampled from populations separated by reduced gene flow. In this situation, the gene-history correlations may be significantly underestimated. We explain why this is the case.
|
2025-10-01
| 2,025
|
analys sequenti markov coalesc algorithm popul demograph structur bottleneck model popul diverg model two island model migrat sequenti markov coalesc method approxim coalesc suggest mcvean cardin marjoram wall within algorithm comput two individu randomli sampl popul correl time recent common ancestor linkag probabl correspond two differ loci recombin rate r find sequenti markov coalesc method approxim coalesc well gener model demograph structur except case individu sampl popul separ reduc gene flow situat gene histori correl may significantli underestim explain case
|
72
| 72
|
Laurence D. Marks, Ann N. Chiaramonti, Fabien Tran and Peter Blaha
|
The Small Unit Cell Reconstructions of SrTiO3 (111)
|
We analyze the basic structural units of simple reconstructions of the (111) surface of SrTiO3 using density functional calculations. The prime focus is to answer three questions: what is the most appropriate functional to use; how accurate are the energies; what are the dominant low-energy structures and where do they lie on the surface phase diagram. Using test calculations of representative small molecules we compare conventional GGA with higher-order methods such as the TPSS meta-GGA and on-site hybrid methods PBE0 and TPSSh, the later being the most accurate. There are large effects due to reduction of the metal d oxygen sp hybridization when using the hybrid methods which are equivalent to a dynamical GGA+U, which leads to rather substantial improvements in the atomization energies of simple calibration molecules, even though the d-electron density for titanium compounds is rather small. By comparing the errors of the different methods we are able to generate an estimate of the theoretical error, which is about 0.25eV per 1x1 unit cell, with changes of 0.5-1.0 eV per 1x1 cell with the more accurate method relative to conventional GGA. An analysis of the plausible structures reveals an unusual low-energy TiO2-rich configuration with an unexpected distorted trigonal biprismatic structure. This structure can act as a template for layers of either TiO or Ti2O3, consistent with experimental results as well as, in principle, Magnelli phases. The results also suggest that both the fracture surface and the stoichiometric SrTiO3 (111) surface should spontaneously disproportionate into SrO and TiO2 rich domains, and show that there are still surprises to be found for polar oxide surfaces.
|
2025-09-22
| 2,025
|
analyz basic structur unit simpl reconstruct surfac srtio use densiti function calcul prime focu answer three question appropri function use accur energi domin low energi structur lie surfac phase diagram use test calcul repres small molecul compar convent gga higher order method tpss meta gga site hybrid method pbe tpssh later accur larg effect due reduct metal oxygen sp hybrid use hybrid method equival dynam gga u lead rather substanti improv atom energi simpl calibr molecul even though electron densiti titanium compound rather small compar error differ method abl gener estim theoret error ev per x unit cell chang ev per x cell accur method rel convent gga analysi plausibl structur reveal unusu low energi tio rich configur unexpect distort trigon biprismat structur structur act templat layer either tio ti consist experiment result well principl magnelli phase result also suggest fractur surfac stoichiometr srtio surfac spontan disproportion sro tio rich domain show still surpris found polar oxid surfac
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73
| 73
|
Cyril Houdayer
|
Strongly solid group factors which are not interpolated free group factors
|
We give examples of non-amenable ICC groups $\Gamma$ with the Haagerup property, weakly amenable with constant $\Lambda_{\cb}(\Gamma) = 1$, for which we show that the associated ${\rm II_1}$ factors $L(\Gamma)$ are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra $P \subset L(\Gamma)$ generates an amenable von Neumann algebra. Nevertheless, for these examples of groups $\Gamma$, $L(\Gamma)$ is not isomorphic to any interpolated free group factor $L(\F_t)$, for $1 < t \leq \infty$.
|
2025-07-17
| 2,025
|
give exampl non amen icc group gamma haagerup properti weakli amen constant lambda cb gamma show associ rm ii factor l gamma strongli solid e normal diffus amen subalgebra p subset l gamma gener amen von neumann algebra nevertheless exampl group gamma l gamma isomorph interpol free group factor l f leq infti
|
74
| 74
|
Yale Fan
|
Quantum Simulation of Simple Many-Body Dynamics
|
Quantum computers could potentially simulate the dynamics of systems such as
polyatomic molecules on a much larger scale than classical computers. We
investigate a general quantum computational algorithm that simulates the time
evolution of an arbitrary non-relativistic, Coulombic many-body system in three
dimensions, considering only spatial degrees of freedom. We use a simple
discretized model of Schrodinger evolution and discuss detailed constructions
of the operators necessary to realize the scheme of Wiesner and Zalka. The
algorithm is simulated numerically for small test cases, and its outputs are
found to be in good agreement with analytical solutions.
|
2025-02-18
| 2,025
|
quantum comput could potenti simul dynam system polyatom molecul much larger scale classic comput investig gener quantum comput algorithm simul time evolut arbitrari non relativist coulomb mani bodi system three dimens consid spatial degre freedom use simpl discret model schroding evolut discuss detail construct oper necessari realiz scheme wiesner zalka algorithm simul numer small test case output found good agreement analyt solut
|
75
| 75
|
Valery Alexeev and Rita Pardini
|
Explicit compactifications of moduli spaces of Campedelli and Burniat surfaces
|
We describe explicitly the geometric compactifications, obtained by adding slc surfaces $X$ with ample canonical class, for two connected components in the moduli space of surfaces of general type: Campedelli surfaces with $\pi_1(X)=\mathbb Z_2^3$ and Burniat surfaces with $K^2=6$.
|
2025-05-15
| 2,025
|
describ explicitli geometr compactif obtain ad slc surfac x ampl canon class two connect compon moduli space surfac gener type campedelli surfac pi x mathbb z burniat surfac k
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76
| 76
|
Xing M. Wang
|
From Dirac Notation to Probability Bracket Notation: Time Evolution and
Path Integral under Wick Rotations
|
In this work, we advance the development of the Probability Bracket Notation
(PBN), a formalism inspired by Dirac's notation in quantum mechanics, to
provide a unified framework for probability modeling. We demonstrate that under
a Special Wick Rotation (SWR), an imaginary-time map, the Schr\"odinger
equation, the transition amplitude, and its associated path integral in Dirac
notation transform into the master equation, the transition probability, and
its Euclidean path integral in the PBN, from which we can reproduce the master
equation, representing induced micro-diffusion processes. By extending this
approach through a General Wick Rotation (GWR) and employing an anti-Hermitian
wave-number operator, we perform parallel derivations of path integrals in both
the Dirac and PBN frameworks. This leads to the formulation of the Euclidean
Lagrangian for induced diffusions and the strong-damping harmonic oscillator
(described by the Smoluchowski diffusion equation). Our findings highlight the
versatility of the PBN in bridging quantum mechanics and stochastic processes,
offering a coherent notation system for analyzing time evolution and path
integrals across these domains.
|
2025-05-07
| 2,025
|
work advanc develop probabl bracket notat pbn formal inspir dirac notat quantum mechan provid unifi framework probabl model demonstr special wick rotat swr imaginari time map schr oding equat transit amplitud associ path integr dirac notat transform master equat transit probabl euclidean path integr pbn reproduc master equat repres induc micro diffus process extend approach gener wick rotat gwr employ anti hermitian wave number oper perform parallel deriv path integr dirac pbn framework lead formul euclidean lagrangian induc diffus strong damp harmon oscil describ smoluchowski diffus equat find highlight versatil pbn bridg quantum mechan stochast process offer coher notat system analyz time evolut path integr across domain
|
77
| 77
|
Mikhail Tyaglov
|
On the number of real critical points of logarithmic derivatives and the Hawaii conjecture
|
For a given real entire function $\phi$ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions $Q=(\phi'/\phi)'$ and $Q_1=(\phi''/\phi')'$. This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W.Smith, The zeros of derivatives of entire functions and the P\'olya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405--431] stating that the number of real zeros of $Q$ does not exceed the number of nonreal zeros of $\phi$.
|
2025-07-01
| 2,025
|
given real entir function phi finit mani nonreal zero establish connect number real zero function q phi phi q phi phi connect lead proof hawaii conjectur craven g csorda w smith zero deriv entir function p olya wiman conjectur ann math state number real zero q exceed number nonreal zero phi
|
78
| 78
|
Simeon Hellerman
|
A Universal Inequality for CFT and Quantum Gravity
|
We prove that every unitary two-dimensional conformal field theory (with no extended chiral algebra, and with central charges $c_L, c_R > 1$) contains a primary operator with dimension $\Delta_1$ that satisfies $0 < \Delta_1 < (c_L + c_R)/12 + 0.473695$. Translated into gravitational language using the AdS_3 /CFT_2 dictionary, our result proves rigorously that the lightest massive excitation in any theory of 3D gravity with cosmological constant $\Lambda < 0$ can be no heavier than $1/(4 G_N) + o(|\Lambda|^(1/2))$. In the flat-space approximation, this limiting mass is twice that of the lightest BTZ black hole. The derivation of the bound applies at finite central charge for the CFT, and does not rely on an asymptotic expansion at large central charge. Neither does our proof rely on any special property of the CFT such as supersymmetry or holomorphic factorization, nor on any bulk interpretation in terms of string theory or semiclassical gravity. Our only assumptions are unitarity and modular invariance of the dual CFT. Our proof demonstrates for the first time that there exists a universal center-of-mass energy beyond which a theory of "pure" quantum gravity can never consistently be extended.
|
2025-06-10
| 2,025
|
prove everi unitari two dimension conform field theori extend chiral algebra central charg c l c r contain primari oper dimens delta satisfi delta c l c r translat gravit languag use ad cft dictionari result prove rigor lightest massiv excit theori graviti cosmolog constant lambda heavier g n lambda flat space approxim limit mass twice lightest btz black hole deriv bound appli finit central charg cft reli asymptot expans larg central charg neither proof reli special properti cft supersymmetri holomorph factor bulk interpret term string theori semiclass graviti assumpt unitar modular invari dual cft proof demonstr first time exist univers center mass energi beyond theori pure quantum graviti never consist extend
|
79
| 79
|
Louis E. Labuschagne and Wladyslaw A. Majewski
|
Maps on noncommutative Orlicz spaces
|
A generalization of the Pistone-Sempi argument, demonstrating the utility of
non-commutative Orlicz spaces, is presented. The question of lifting positive
maps defined on von Neumann algebra to maps on corresponding noncommutative
Orlicz spaces is discussed. In particular, we describe those Jordan *-morphisms
on semifinite von Neumann algebras which in a canonical way induce quantum
composition operators on noncommutative Orlicz spaces. Consequently, it is
proved that the framework of noncommutative Orlicz spaces is well suited for an
analysis of large class of interesting noncommutative dynamical systems.
|
2025-03-19
| 2,025
|
gener piston sempi argument demonstr util non commut orlicz space present question lift posit map defin von neumann algebra map correspond noncommut orlicz space discuss particular describ jordan morphism semifinit von neumann algebra canon way induc quantum composit oper noncommut orlicz space consequ prove framework noncommut orlicz space well suit analysi larg class interest noncommut dynam system
|
80
| 80
|
A.T.Goritschnig, P.Kroll, W.Schweiger
|
$p\bar{p} \to \Lambda_c \bar{\Lambda}_c$ within a Handbag Picture --
Cross Section and Spin Observables
|
We study the process $p\bar{p} \to \Lambda_c \bar{\Lambda}_c$ within the
generalized parton picture. Our starting point is the double handbag diagram
which factorizes into soft generalized parton distributions and a hard
subprocess amplitude for $u \bar{u} \to c \bar{c}$. Our cross-section
predictions may become interesting in view of forthcoming experiments at FAIR
in Darmstadt.
|
2025-01-22
| 2,025
|
studi process p bar p lambda c bar lambda c within gener parton pictur start point doubl handbag diagram factor soft gener parton distribut hard subprocess amplitud u bar u c bar c cross section predict may becom interest view forthcom experi fair darmstadt
|
81
| 81
|
Ralf Greve, Luca Placidi, Hakime Seddik
|
A continuum-mechanical model for the flow of anisotropic polar ice
|
In order to study the mechanical behaviour of polar ice masses, the method of continuum mechanics is used. The newly developed CAFFE model (Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor) is described, which comprises an anisotropic flow law as well as a fabric evolution equation. The flow law is an extension of the isotropic Glen's flow law, in which anisotropy enters via an enhancement factor that depends on the deformability of the polycrystal. The fabric evolution equation results from an orientational mass balance and includes constitutive relations for grain rotation and recrystallization. The CAFFE model fulfills all the fundamental principles of classical continuum mechanics, is sufficiently simple to allow numerical implementations in ice-flow models and contains only a limited number of free parameters. The applicability of the CAFFE model is demonstrated by a case study for the site of the EPICA (European Project for Ice Coring in Antarctica) ice core in Dronning Maud Land, East Antarctica.
|
2025-11-10
| 2,025
|
order studi mechan behaviour polar ice mass method continuum mechan use newli develop caff model continuum mechan anisotrop flow model base anisotrop flow enhanc factor describ compris anisotrop flow law well fabric evolut equat flow law extens isotrop glen flow law anisotropi enter via enhanc factor depend deform polycryst fabric evolut equat result orient mass balanc includ constitut relat grain rotat recrystal caff model fulfil fundament principl classic continuum mechan suffici simpl allow numer implement ice flow model contain limit number free paramet applic caff model demonstr case studi site epica european project ice core antarctica ice core dron maud land east antarctica
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82
| 82
|
Zosia A. C. Krusberg
|
Physics education research: Resources for middle school science teachers
|
This resource letter intends to provide middle school science teachers with a collection of resources to aid them in planning and implementing a physical science curriculum. The resources are in the form of books, websites, journals, and organizations.
|
2025-05-29
| 2,025
|
resourc letter intend provid middl school scienc teacher collect resourc aid plan implement physic scienc curriculum resourc form book websit journal organ
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83
| 83
|
H. Aratyn, J.F. Gomes and A.H. Zimerman
|
Darboux-Backlund Derivation of Rational Solutions of the Painleve IV
Equation
|
Rational solutions of the Painleve IV equation are constructed in the setting
of pseudo-differential Lax formalism describing AKNS hierarchy subject to the
additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian
representations for rational solutions are obtained by successive actions of
the Darboux-Backlund transformations.
|
2025-02-18
| 2,025
|
ration solut painlev iv equat construct set pseudo differenti lax formal describ akn hierarchi subject addit non isospectr virasoro symmetri constraint conveni wronskian represent ration solut obtain success action darboux backlund transform
|
84
| 84
|
Michael Edmund Tobar, Toshikazu Suzuki, Kazuaki Kuroda
|
Detecting Free-Mass Common-Mode Motion Induced by Incident Gravitational
Waves: Testing General Relativity and Source Direction via Fox-Smith and
Michelson Interferometers
|
In this paper we show that information on both the differential and common
mode free-mass response to a gravitational wave can provide important
information on discriminating the direction of the gravitational wave source
and between different theories of gravitation. The conventional Michelson
interferometer scheme only measures the differential free-mass response. By
changing the orientation of the beam splitter, it is possible to configure the
detector so it is sensitive to the common-mode of the free-mass motion. The
proposed interferometer is an adaptation of the Fox-Smith interferometer. A
major limitation to the new scheme is its enhanced sensitivity to laser
frequency fluctuations over the conventional, and we propose a method of
canceling these fluctuations. The configuration could be used in parallel to
the conventional differential detection scheme with a significant sensitivity
and bandwidth.
|
2025-04-08
| 2,025
|
paper show inform differenti common mode free mass respons gravit wave provid import inform discrimin direct gravit wave sourc differ theori gravit convent michelson interferomet scheme measur differenti free mass respons chang orient beam splitter possibl configur detector sensit common mode free mass motion propos interferomet adapt fox smith interferomet major limit new scheme enhanc sensit laser frequenc fluctuat convent propos method cancel fluctuat configur could use parallel convent differenti detect scheme signific sensit bandwidth
|
85
| 85
|
Shinichiro Yamato
|
The Laue pattern and the Rydberg formula in classical soliton models
|
In recent researches of the dynamics of solitons, it is gradually revealed that oscillation modes play a crucial role when we analyze the dynamics of solitons. Some dynamical properties of solitons on external potentials are studied with both numerical methods and analytical methods. In this paper, we propose a method to deal with such oscillation modes of solitons in potential wells. We show that oscillations of a soliton is described by the Klein-Gordon equation with an external potential. Although this analysis does not seems to give quantitative scattering amplitude of a soliton itself, it explains qualitative pictures of scattering. As a result of our analysis, when a soliton is scattered in a cyclic potential, the Laue pattern emerges. Furthermore, since our analysis is based on the Klein-Gordon equation, a discrete frequency spectrum of a soliton is obtained when it is bounded by some potentials. What is especially important is that this analysis predicts a frequency spectrum of a soliton in the Coulomb potential and then we find that this system absorbs external waves with specific frequencies described by the Rydberg formula.
|
2025-08-19
| 2,025
|
recent research dynam soliton gradual reveal oscil mode play crucial role analyz dynam soliton dynam properti soliton extern potenti studi numer method analyt method paper propos method deal oscil mode soliton potenti well show oscil soliton describ klein gordon equat extern potenti although analysi seem give quantit scatter amplitud soliton explain qualit pictur scatter result analysi soliton scatter cyclic potenti laue pattern emerg furthermor sinc analysi base klein gordon equat discret frequenc spectrum soliton obtain bound potenti especi import analysi predict frequenc spectrum soliton coulomb potenti find system absorb extern wave specif frequenc describ rydberg formula
|
86
| 86
|
Cyril Houdayer, Dimitri Shlyakhtenko
|
Strongly solid ${\rm II_1}$ factors with an exotic MASA
|
Using an extension of techniques of Ozawa and Popa, we give an example of a non-amenable strongly solid $\rm{II}_1$ factor $M$ containing an "exotic" maximal abelian subalgebra $A$: as an $A$,$A$-bimodule, $L^2(M)$ is neither coarse nor discrete. Thus we show that there exist $\rm{II}_1$ factors with such property but without Cartan subalgebras. It also follows from Voiculescu's free entropy results that $M$ is not an interpolated free group factor, yet it is strongly solid and has both the Haagerup property and the complete metric approximation property.
|
2025-07-17
| 2,025
|
use extens techniqu ozawa popa give exampl non amen strongli solid rm ii factor contain exot maxim abelian subalgebra bimodul l neither coars discret thu show exist rm ii factor properti without cartan subalgebra also follow voiculescu free entropi result interpol free group factor yet strongli solid haagerup properti complet metric approxim properti
|
87
| 87
|
Indira Chatterji and T.N.Venkataramana
|
Discrete Linear Groups containing Arithmetic Groups
|
We prove in a large number of cases, that a Zariski dense discrete subgroup of a simple real algebraic group $G$ which contains a higher rank lattice is a lattice in the group $G$. For example, we show that a Zariski dense subgroup of $SL_n({\mathbb R})$ which contains $SL_3({\mathbb Z})$ in the top left hand corner, is conjugate to $SL_n({\mathbb Z})$ .
|
2025-10-07
| 2,025
|
prove larg number case zariski dens discret subgroup simpl real algebra group g contain higher rank lattic lattic group g exampl show zariski dens subgroup sl n mathbb r contain sl mathbb z top left hand corner conjug sl n mathbb z
|
88
| 88
|
H. Razmi and A. MohammadKazemi
|
On the Relativistic Origin of spin: A Case for the "Rest Angular Momentum"
|
The intrinsic angular momentum, or spin, is a cornerstone of modern physics with profound applications from nuclear magnetic resonance to spintronics. While its mathematical structure within quantum theory is well-defined, its fundamental origin is often less emphasized. This paper revisits the genesis of spin by examining its emergence in relativistic wave equations, its role in the Thomas precession, and its formulation for massless photons in electrodynamics. It is argued that these foundational elements collectively demonstrate that spin is inherently a consequence of relativistic spacetime symmetry, rather than a purely quantum mechanical property. Consequently, the term "rest angular momentum" offers a more conceptually accurate description, highlighting its origin as an intrinsic property manifest even in an object's rest frame, as dictated by the Poincar\'e group.
|
2025-09-30
| 2,025
|
intrins angular momentum spin cornerston modern physic profound applic nuclear magnet reson spintron mathemat structur within quantum theori well defin fundament origin often less emphas paper revisit genesi spin examin emerg relativist wave equat role thoma precess formul massless photon electrodynam argu foundat element collect demonstr spin inher consequ relativist spacetim symmetri rather pure quantum mechan properti consequ term rest angular momentum offer conceptu accur descript highlight origin intrins properti manifest even object rest frame dictat poincar e group
|
89
| 89
|
I. Neri and D. Boll\'e
|
The Cavity Approach to Parallel Dynamics of Ising Spins on a Graph
|
We use the cavity method to study parallel dynamics of disordered Ising
models on a graph. In particular, we derive a set of recursive equations in
single site probabilities of paths propagating along the edges of the graph.
These equations are analogous to the cavity equations for equilibrium models
and are exact on a tree. On graphs with exclusively directed edges we find an
exact expression for the stationary distribution of the spins. We present the
phase diagrams for an Ising model on an asymmetric Bethe lattice and for a
neural network with Hebbian interactions on an asymmetric scale-free graph. For
graphs with a nonzero fraction of symmetric edges the equations can be solved
for a finite number of time steps. Theoretical predictions are confirmed by
simulation results. Using a heuristic method, the cavity equations are extended
to a set of equations that determine the marginals of the stationary
distribution of Ising models on graphs with a nonzero fraction of symmetric
edges. The results of this method are discussed and compared with simulations.
|
2025-04-23
| 2,025
|
use caviti method studi parallel dynam disord ise model graph particular deriv set recurs equat singl site probabl path propag along edg graph equat analog caviti equat equilibrium model exact tree graph exclus direct edg find exact express stationari distribut spin present phase diagram ise model asymmetr beth lattic neural network hebbian interact asymmetr scale free graph graph nonzero fraction symmetr edg equat solv finit number time step theoret predict confirm simul result use heurist method caviti equat extend set equat determin margin stationari distribut ise model graph nonzero fraction symmetr edg result method discuss compar simul
|
90
| 90
|
Anton Petrunin
|
PIGTIKAL (puzzles in geometry that I know and love)
|
Problems for the graduate students who want to improve problem-solving skills
in geometry. Every problem has a short elegant solution -- this gives a hint
which was not available when the problem was discovered.
|
2025-02-04
| 2,025
|
problem graduat student want improv problem solv skill geometri everi problem short eleg solut give hint avail problem discov
|
91
| 91
|
S.V. Goloskokov (JINR) and P. Kroll (Wuppertal Univ.)
|
An attempt to understand exclusive pi+ electroproduction
|
Hard exclusive pi+ electroproduction is investigated within the handbag
approach. The prominent role of the pion-pole contribution is demonstrated. It
is also shown that the experimental data require a twist-3 effect which ensues
from the helicity-flip generalized parton distribution H_T and the twist-3 pion
wave function. The results calculated from this handbag approach are compared
in detail with the experimental data on cross sections and spin asymmetries
measured with a polarized target. It is also commented on consequences of this
approach for exclusive \pi^0 and vector-meson electroproduction.
|
2025-01-22
| 2,025
|
hard exclus pi electroproduct investig within handbag approach promin role pion pole contribut demonstr also shown experiment data requir twist effect ensu helic flip gener parton distribut h twist pion wave function result calcul handbag approach compar detail experiment data cross section spin asymmetri measur polar target also comment consequ approach exclus pi vector meson electroproduct
|
92
| 92
|
Axel van de Walle
|
Multicomponent multisublattice alloys, nonconfigurational entropy and other additions to the Alloy Theoretic Automated Toolkit
|
A number of new functionalities have been added to the Alloy Theoretic Automated Toolkit (ATAT) since it was last reviewed in this journal in 2002. ATAT can now handle multicomponent multisublattice alloy systems, nonconfigurational sources of entropy (e.g. vibrational and electronic entropy), Special Quasirandom Structures (SQS) generation, tensorial cluster expansion construction and includes interfaces for multiple atomistic or ab initio codes. This paper presents an overview of these features geared towards the practical use of the code. The extensions to the cluster expansion formalism needed to cover multicomponent multisublattice alloys are also formally demonstrated.
|
2025-06-11
| 2,025
|
number new function ad alloy theoret autom toolkit atat sinc last review journal atat handl multicompon multisublattic alloy system nonconfigur sourc entropi e g vibrat electron entropi special quasirandom structur sq gener tensori cluster expans construct includ interfac multipl atomist ab initio code paper present overview featur gear toward practic use code extens cluster expans formal need cover multicompon multisublattic alloy also formal demonstr
|
93
| 93
|
Laurent Bienvenu, Alexander Shen
|
Algorithmic information theory and martingales
|
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s (Solomonov, Kolmogorov, Martin-Lof, Levin, Chaitin, Schnorr and others). We conclude with some remarks about the use of the algorithmic information theory in the foundations of probability theory.
|
2025-08-27
| 2,025
|
notion individu random sequenc goe back von mise describ evolut notion especi use martingal suggest vill develop algorithm inform theori solomonov kolmogorov martin lof levin chaitin schnorr other conclud remark use algorithm inform theori foundat probabl theori
|
94
| 94
|
Niurka R.Quintero, Jos'e A. Cuesta, and Renato Alvarez-Nodarse
|
Symmetries shape the current in ratchets induced by a bi-harmonic force
|
Equations describing the evolution of particles, solitons, or localized structures, driven by a zero-average, periodic, external force, and invariant under time reversal and a half-period time shift, exhibit a ratchet current when the driving force breaks these symmetries. The bi-harmonic force $f(t)=\epsilon_1\cos(q \omega t+\phi_1)+\epsilon_2\cos(p\omega t+\phi_2)$ does it for almost any choice of $\phi_{1}$ and $\phi_{2}$, provided $p$ and $q$ are two co-prime integers such that $p+q$ is odd. It has been widely observed, in experiments in Josephson-junctions, photonic crystals, etc., as well as in simulations, that the ratchet current induced by this force has the shape $v\propto\epsilon_1^p\epsilon_2^q\cos(p \phi_{1} - q \phi_{2} + \theta_0)$ for small amplitudes, where $\theta_0$ depends on the damping ($\theta_0=\pi/2$ if there is no damping, and $\theta_0=0$ for overdamped systems). We rigorously prove that this precise shape can be obtained solely from the broken symmetries of the system and is independent of the details of the equation describing the system.
|
2025-11-11
| 2,025
|
equat describ evolut particl soliton local structur driven zero averag period extern forc invari time revers half period time shift exhibit ratchet current drive forc break symmetri bi harmon forc f epsilon co q omega phi epsilon co p omega phi almost choic phi phi provid p q two co prime integ p q odd wide observ experi josephson junction photon crystal etc well simul ratchet current induc forc shape v propto epsilon p epsilon q co p phi q phi theta small amplitud theta depend damp theta pi damp theta overdamp system rigor prove precis shape obtain sole broken symmetri system independ detail equat describ system
|
95
| 95
|
Edwin Hammerich
|
Design of Pulse Shapes Based on Sampling with Gaussian Prefilter
|
Two new pulse shapes for communications are presented. The first pulse shape generates a set of pulses without intersymbol interference (ISI) or ISI-free for short. In the neighborhood of the origin it is similar in shape to the classical cardinal sine function but is of exponential decay at infinity. This pulse shape is identical to the interpolating function of a generalized sampling theorem with Gaussian prefilter. The second pulse shape is obtained from the first pulse shape by spectral factorization. Besides being also of exponential decay at infinity, it has a causal appearance since it is of superexponential decay for negative times. It is closely related to the orthonormal generating function considered earlier by Unser in the context of shift-invariant spaces. This pulse shape is not ISI-free but it generates a set of orthonormal pulses. The second pulse shape may also be used to define a receive matched filter so that at the filter output the ISI-free pulses of the first kind are recovered.
|
2025-09-25
| 2,025
|
two new puls shape commun present first puls shape gener set puls without intersymbol interfer isi isi free short neighborhood origin similar shape classic cardin sine function exponenti decay infin puls shape ident interpol function gener sampl theorem gaussian prefilt second puls shape obtain first puls shape spectral factor besid also exponenti decay infin causal appear sinc superexponenti decay neg time close relat orthonorm gener function consid earlier unser context shift invari space puls shape isi free gener set orthonorm puls second puls shape may also use defin receiv match filter filter output isi free puls first kind recov
|
96
| 96
|
Luca Ghislanzoni
|
Partial Sums of the Series for the Dirichlet Eta Function, their Peculiar Convergence, the Simple Zeros Conjecture, and the RH
|
For any $s \in \mathbb{C}$ with $\Re(s)>0$, denote by $\eta_{n-1}(s)$ the $(n-1)^{th}$ partial sum of the Dirichlet series for the eta function $\eta(s)=1-2^{-s}+3^{-s}-\cdots \;$, and by $R_n(s)$ the corresponding remainder. Denoting by $u_n(s)$ the segment starting at $\eta_{n-1}(s)$ and ending at $\eta_n(s)$, we first show how, for sufficiently large $n$ values, the circle of diameter $u_{n+2}(s)$ lies strictly inside the circle of diameter $u_n(s)$, to then derive the asymptotic relationship $R_n(s) \sim (-1)^{n-1}/n^s$, as $n \rightarrow \infty$. Denoting by $D=\left\{s \in \mathbb{C}: \; 0< \Re(s) < \frac{1}{2}\right\}$ the open left half of the critical strip, define for all $s\in D$ the ratio $\chi_n^{\pm}(s) = \eta_n(1-s) / \eta_n(s)$. We then prove that the limit $L(s)=\lim_{N(s)<n\to\infty} \chi_n^{\pm}(s)$ exists at every point $s$ of the domain $D$. The function $L(s)$ is continuous on $D$ if and only if the Riemann Hypothesis is true. Finally, we remark how the asymptotic behaviour of $R_n(s)$ can also provide insights substantiating the so called Simple Zeros Conjecture.
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2025-08-08
| 2,025
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mathbb c denot eta n n th partial sum dirichlet seri eta function eta cdot r n correspond remaind denot u n segment start eta n end eta n first show suffici larg n valu circl diamet u n lie strictli insid circl diamet u n deriv asymptot relationship r n sim n n n rightarrow infti denot left mathbb c frac right open left half critic strip defin ratio chi n pm eta n eta n prove limit l lim n n infti chi n pm exist everi point domain function l continu riemann hypothesi true final remark asymptot behaviour r n also provid insight substanti call simpl zero conjectur
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97
| 97
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Franz G. Mertens, Niurka R. Quintero and A. R. Bishop
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Nonlinear Schr\"odinger Equation with Spatio-Temporal Perturbations
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We investigate the dynamics of solitons of the cubic Nonlinear Schr\"odinger Equation (NLSE) with the following perturbations: non-parametric spatio-temporal driving of the form $f(x,t) = a \exp[i K(t) x]$, damping, and a linear term which serves to stabilize the driven soliton. Using the time evolution of norm, momentum and energy, or, alternatively, a Lagrangian approach, we develop a Collective-Coordinate-Theory which yields a set of ODEs for our four collective coordinates. These ODEs are solved analytically and numerically for the case of a constant, spatially periodic force $f(x)$. The soliton position exhibits oscillations around a mean trajectory with constant velocity. This means that the soliton performs, on the average, a unidirectional motion although the spatial average of the force vanishes. The amplitude of the oscillations is much smaller than the period of $f(x)$. In order to find out for which regions the above solutions are stable, we calculate the time evolution of the soliton momentum $P(t)$ and soliton velocity $V(t)$: This is a parameter representation of a curve $P(V)$ which is visited by the soliton while time evolves. Our conjecture is that the soliton becomes unstable, if this curve has a branch with negative slope. This conjecture is fully confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the soliton lives longer, the shorter the branch with negative slope is.
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2025-11-11
| 2,025
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investig dynam soliton cubic nonlinear schr oding equat nlse follow perturb non parametr spatio tempor drive form f x exp k x damp linear term serv stabil driven soliton use time evolut norm momentum energi altern lagrangian approach develop collect coordin theori yield set ode four collect coordin ode solv analyt numer case constant spatial period forc f x soliton posit exhibit oscil around mean trajectori constant veloc mean soliton perform averag unidirect motion although spatial averag forc vanish amplitud oscil much smaller period f x order find region solut stabl calcul time evolut soliton momentum p soliton veloc v paramet represent curv p v visit soliton time evolv conjectur soliton becom unstabl curv branch neg slope conjectur fulli confirm simul perturb nlse moreov curv also yield good estim soliton lifetim soliton live longer shorter branch neg slope
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98
| 98
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Michael Frank, Alexander S. Mishchenko, Alexander A. Pavlov
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Orthogonality-preserving, C*-conformal and conformal module mappings on
Hilbert C*-modules
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We investigate orthonormality-preserving, C*-conformal and conformal module
mappings on Hilbert C*-modules to obtain their general structure.
Orthogonality-preserving bounded module maps T act as a multiplication by an
element \lambda of the center of the multiplier algebra of the C*-algebra of
coefficients combined with an isometric module operator as long as some polar
decomposition conditions for the specific element \lambda are fulfilled inside
that multiplier algebra. Generally, T always fulfils the equality $<T(x),T(y) >
= | \lambda |^2 < x,y>$ for any elements x,y of the Hilbert C*-module. At the
contrary, C*-conformal and conformal bounded C*-linear mappings are shown to be
only the positive real multiples of isometric module operators.
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2025-04-29
| 2,025
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investig orthonorm preserv c conform conform modul map hilbert c modul obtain gener structur orthogon preserv bound modul map act multipl element lambda center multipli algebra c algebra coeffici combin isometr modul oper long polar decomposit condit specif element lambda fulfil insid multipli algebra gener alway fulfil equal x lambda x element x hilbert c modul contrari c conform conform bound c linear map shown posit real multipl isometr modul oper
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99
| 99
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Alexander I. Efimov
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Homological mirror symmetry for curves of higher genus
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Katzarkov has proposed a generalization of Kontsevich's mirror symmetry
conjecture, covering some varieties of general type. Seidel \cite{Se} has
proved a version of this conjecture in the simplest case of the genus two
curve. Basing on the paper of Seidel, we prove the conjecture (in the same
version) for curves of genus $g\geq 3,$ relating the Fukaya category of a genus
$g$ curve to the category of Landau-Ginzburg branes on a certain singular
surface. We also prove a kind of reconstruction theorem for hypersurface
singularities. Namely, formal type of hypersurface singularity (i.e. a formal
power series up to a formal change of variables) can be reconstructed, with
some technical assumptions, from its D$(\Z/2)$-G category of Landau-Ginzburg
branes. The precise statement is Theorem 1.2.
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2025-02-07
| 2,025
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katzarkov propos gener kontsevich mirror symmetri conjectur cover varieti gener type seidel cite se prove version conjectur simplest case genu two curv base paper seidel prove conjectur version curv genu g geq relat fukaya categori genu g curv categori landau ginzburg brane certain singular surfac also prove kind reconstruct theorem hypersurfac singular name formal type hypersurfac singular e formal power seri formal chang variabl reconstruct technic assumpt z g categori landau ginzburg brane precis statement theorem
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