数学最新文献

英文中文

IF： -

Existence of bounded asymptotic solutions of autonomous differential equations

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-14 DOI: 10.1016/j.jde.2025.113320

Vu Trong Luong , William Barker , Nguyen Duc Huy , Nguyen Van Minh

We study the existence of bounded asymptotic mild solutions to evolution equations of the form

u^{'} (t) = A u (t) + f (t), t \geq 0

in a Banach space

X

, where A generates an (analytic)

C_{0}

-semigroup and f is bounded. We find spectral conditions on A and f for the existence and uniqueness of asymptotic mild solutions with the same “profile” as that of f. In the resonance case, a sufficient condition of Massera type theorem is found for the existence of bounded solutions with the same profile as f. The obtained results are stated in terms of spectral properties of A and f, and they are analogs of classical results of Katznelson-Tzafriri and Massera for the evolution equations on the half line. Applications from PDE are given.

{"title":"Existence of bounded asymptotic solutions of autonomous differential equations","authors":"Vu Trong Luong , William Barker , Nguyen Duc Huy , Nguyen Van Minh","doi":"10.1016/j.jde.2025.113320","DOIUrl":"10.1016/j.jde.2025.113320","url":null,"abstract":"<div><div>We study the existence of bounded asymptotic mild solutions to evolution equations of the form <math><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>A</mi><mi>u</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>,</mo><mi>t</mi><mo>≥</mo><mn>0</mn></math> in a Banach space <math><mi>X</mi></math>, where A generates an (analytic) <math><msub><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msub></math>-semigroup and f is bounded. We find spectral conditions on A and f for the existence and uniqueness of asymptotic mild solutions with the same “profile” as that of f. In the resonance case, a sufficient condition of Massera type theorem is found for the existence of bounded solutions with the same profile as f. The obtained results are stated in terms of spectral properties of A and f, and they are analogs of classical results of Katznelson-Tzafriri and Massera for the evolution equations on the half line. Applications from PDE are given.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"434 ","pages":"Article 113320"},"PeriodicalIF":2.4,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An example of A 2 $A_2$ Rogers–Ramanujan bipartition identities of level 3

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-04-14 DOI: 10.1112/jlms.70152

Shunsuke Tsuchioka

We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type $� � �_{A}^{�} � �$ . We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a $� � q � �$ -version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.

{"title":"An example of \u0000 \u0000 \u0000 A\u0000 2\u0000 \u0000 $A_2$\u0000 Rogers–Ramanujan bipartition identities of level 3","authors":"Shunsuke Tsuchioka","doi":"10.1112/jlms.70152","DOIUrl":"https://doi.org/10.1112/jlms.70152","url":null,"abstract":"We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type <math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>A</mi>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <annotation>$A^{(1)}_2$</annotation>\u0000 </semantics></math>. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a <math>\u0000 <semantics>\u0000 <mi>q</mi>\u0000 <annotation>$q$</annotation>\u0000 </semantics></math>-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel numerical scheme for Black-Scholes PDEs modeling pricing securities

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications

Pub Date : 2025-04-14 DOI: 10.1016/j.camwa.2025.04.003

Sachin Kumar, Srinivasan Natesan

This article introduces an efficient numerical method for solving the Black-Scholes partial differential equation (PDE) that governs European options. The methodology employs the backward Euler scheme to discretize the time derivative and incorporates the non-symmetric interior penalty Galerkin method for handling the spatial derivatives. The study aims to determine optimal order error estimates in the

L^{2}

-norm and discrete energy norm. In addition, the proposed method is used to determine Greeks in option pricing. We validate the theoretical results presented in this work with numerical experiments.

引用次数: 0

The inviscid inflow-outflow problem via analyticity

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis

Pub Date : 2025-04-14 DOI: 10.1007/s00205-025-02095-y

Igor Kukavica, Wojciech Ożański, Marco Sammartino

We consider the incompressible Euler equations on an analytic domain (Omega ) with a nonhomogeneous boundary condition (ucdot {textsf{n}} = {overline{u}}cdot {textsf{n}}) on (partial Omega ), where ({overline{u}}) is a given divergence-free analytic vector field. We establish the local well-posedness for u in analytic spaces without any compatibility conditions in all space dimensions. We also prove the global well-posedness in the 2D case if ({overline{u}}) decays in time sufficiently fast.

引用次数: 0

Stationary distribution and extinction of a stochastic HIV/AIDS model with screened disease carriers, standard incidence rate and Ornstein–Uhlenbeck process

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters

Pub Date : 2025-04-14 DOI: 10.1016/j.aml.2025.109575

Wenjie Zuo, Shengnan Jiang

This paper proposes a stochastic HIV/AIDS model that includes screening for virus carriers and infected individuals actively seeking treatment, with the average number of sexual partners

\bar{k}

controlled by a log-normal Ornstein–Uhlenbeck process. By constructing appropriate Lyapunov functions, the existence of a stationary distribution is obtained. Additionally, we establish sufficient condition for the extinction of the diseases, thereby offering valuable insights into AIDS control and policy decisions.

引用次数: 0

Conical diffraction and Floquet edge states in an electromagnetically induced Lieb lattice

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals

Pub Date : 2025-04-14 DOI: 10.1016/j.chaos.2025.116423

Zijing Wang , Sheng Xu , ZhenkunWu , Peng Li , Feng Wen , Yuzong Gu , Yanbo Zhang

we investigate conical diffraction and Floquet edge states in a Lieb photonic lattice induced in a Λ-type atomic system with electromagnetically induced transparency. By tuning frequency detuning and coupling field intensity, we demonstrate significant modifications to both the Bloch structure and the resulting diffraction patterns. Furthermore, we theoretically model a helical Floquet modulation to break time-reversal symmetry, resulting in a photonic topological insulator. Through detailed theoretical and numerical analyses, including calculations of Berry curvature and Chern numbers, we verify the emergence of unidirectional edge states and their robustness against defects. These findings highlight the potential for dynamically controlling beam propagation in atomic lattices and open promising avenues for designing advanced photonic devices with topological protection.

引用次数: 0

Global viscosity solutions to Lorentzian eikonal equation on globally hyperbolic space-times

IF 2.4 2区数学 Q1 MATHEMATICS

Journal of Differential Equations

Pub Date : 2025-04-14 DOI: 10.1016/j.jde.2025.113323

Siyao Zhu , Hongguang Wu , Xiaojun Cui

In this paper, we show that any globally hyperbolic space-time admits at least one globally defined locally semiconcave function, which is a viscosity solution to the Lorentzian eikonal equation. According to whether the time orientation is changed, we divide the set of viscosity solutions into some subclasses. We show if the time orientation is consistent, then a viscosity solution has a variational representation locally. As a result, such a viscosity solution is locally semiconcave and has some weak KAM properties, as the one in the Riemannian case. On the other hand, if the time orientation of a viscosity solution is non-consistent, it will exhibit some peculiar properties which makes this kind of viscosity solutions totally different from the ones in the Riemannian case.

引用次数: 0

Counting flows of b-compatible graphs 计算 b 兼容图的流量

IF 1 3区数学 Q3 MATHEMATICS, APPLIED

Advances in Applied Mathematics

Pub Date : 2025-04-14 DOI: 10.1016/j.aam.2025.102901

Houshan Fu , Xiangyu Ren , Suijie Wang

<div><div>Kochol introduced the assigning polynomial <math><mi>F</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>α</mi><mo>;</mo><mi>k</mi><mo>)</mo></math> to count nowhere-zero <math><mo>(</mo><mi>A</mi><mo>,</mo><mi>b</mi><mo>)</mo></math>-flows of a graph G, where A is a finite Abelian group and α is a <math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math>-assigning from a family <math><mi>Λ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math> of certain nonempty vertex subsets of G to <math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math>. We introduce the concepts of b-compatible graph and b-compatible broken bond to give an explicit formula for the assigning polynomials and to examine their coefficients. More specifically, for a function <math><mi>b</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mi>A</mi></math>, let <math><msub><mrow><mi>α</mi></mrow><mrow><mi>G</mi><mo>,</mo><mi>b</mi></mrow></msub></math> be a <math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math>-assigning of G such that for each <math><mi>X</mi><mo>∈</mo><mi>Λ</mi><mo>(</mo><mi>G</mi><mo>)</mo></math>, <math><msub><mrow><mi>α</mi></mrow><mrow><mi>G</mi><mo>,</mo><mi>b</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>0</mn></math> if and only if <math><msub><mrow><mo>∑</mo></mrow><mrow><mi>v</mi><mo>∈</mo><mi>X</mi></mrow></msub><mi>b</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>0</mn></math>. We show that for any <math><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></math>-assigning α of G, if there exists a function <math><mi>b</mi><mo>:</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>→</mo><mi>A</mi></math> such that G is b-compatible and <math><mi>α</mi><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mi>G</mi><mo>,</mo><mi>b</mi></mrow></msub></math>, then the assigning polynomial <math><mi>F</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>α</mi><mo>;</mo><mi>k</mi><mo>)</mo></math> has the b-compatible spanning subgraph expansion<math><mi>F</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>α</mi><mo>;</mo><mi>k</mi><mo>)</mo><mo>=</mo><munder><mo>∑</mo><mrow><mtable><mtr><mtd><mi>S</mi><mo>⊆</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo><mo>,</mo></mtd></mtr><mtr><mtd><mi>G</mi><mo>−</mo><mi>S</mi><mrow><mtext> is</mtext><mspace></mspace><mtext>b</mtext><mtext>-compatible</mtext></mrow></mtd></mtr></mtable></mrow></munder><msup><mrow><mo>(</mo><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow></msup><msup><mrow><mi>k</mi></mrow><mrow><mi>m</mi><mo>(</mo><mi>G</mi><mo>−</mo><mi>S</mi><mo>)</mo></mrow></msup><mo>,</mo></math> and is the following form<math><mi>F</mi>

引用次数: 0

A unified approach to the spectral radius, connectivity and edge-connectivity of graphs

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics

Pub Date : 2025-04-14 DOI: 10.1016/j.disc.2025.114544

Yu Wang , Dan Li , Huiqiu Lin

For two integers

r \geq 2

and

h \geq 0

, the h-extra r-component connectivity

κ_{r}^{h} (G)

of a graph G is defined as the minimum size of a subset S of vertices whose removal disconnects G, such that there are at least r connected components in

G - S

and each component has at least

h + 1

vertices. Denote by

G_{n, δ}^{κ_{r}^{h}}

the set of n-vertex graphs with h-extra r-component connectivity

κ_{r}^{h}

and minimum degree δ. The following problem concerning spectral radius was proposed by Brualdi and Solheid (1986) [2]: Given a set of graphs

S

, find an upper bound for the spectral radius of graphs in

S

and characterize the graphs in which the maximum spectral radius is attained. We study this question for

S = G_{n, δ}^{κ_{r}^{h}}

where

r \geq 2

and

h \geq 0

. Fan, Gu and Lin (2024) [7] answered the question for

r \geq 2

and

h = 0

. In this paper, we solve this problem completely for

r \geq 2

and

h \geq 1

. Moreover, we also investigate analogous problems for the edge version. This implies some previous results in connectivity and edge-connectivity.

{"title":"A unified approach to the spectral radius, connectivity and edge-connectivity of graphs","authors":"Yu Wang , Dan Li , Huiqiu Lin","doi":"10.1016/j.disc.2025.114544","DOIUrl":"10.1016/j.disc.2025.114544","url":null,"abstract":"<div><div>For two integers <math><mi>r</mi><mo>≥</mo><mn>2</mn></math> and <math><mi>h</mi><mo>≥</mo><mn>0</mn></math>, the h-extra r-component connectivity <math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow></msubsup><mo>(</mo><mi>G</mi><mo>)</mo></math> of a graph G is defined as the minimum size of a subset S of vertices whose removal disconnects G, such that there are at least r connected components in <math><mi>G</mi><mo>−</mo><mi>S</mi></math> and each component has at least <math><mi>h</mi><mo>+</mo><mn>1</mn></math> vertices. Denote by <math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow></msubsup></mrow></msubsup></math> the set of n-vertex graphs with h-extra r-component connectivity <math><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow></msubsup></math> and minimum degree δ. The following problem concerning spectral radius was proposed by Brualdi and Solheid (1986) [2]: Given a set of graphs <math><mi>S</mi></math>, find an upper bound for the spectral radius of graphs in <math><mi>S</mi></math> and characterize the graphs in which the maximum spectral radius is attained. We study this question for <math><mi>S</mi><mo>=</mo><msubsup><mrow><mi>G</mi></mrow><mrow><mi>n</mi><mo>,</mo><mi>δ</mi></mrow><mrow><msubsup><mrow><mi>κ</mi></mrow><mrow><mi>r</mi></mrow><mrow><mi>h</mi></mrow></msubsup></mrow></msubsup></math> where <math><mi>r</mi><mo>≥</mo><mn>2</mn></math> and <math><mi>h</mi><mo>≥</mo><mn>0</mn></math>. Fan, Gu and Lin (2024) [7] answered the question for <math><mi>r</mi><mo>≥</mo><mn>2</mn></math> and <math><mi>h</mi><mo>=</mo><mn>0</mn></math>. In this paper, we solve this problem completely for <math><mi>r</mi><mo>≥</mo><mn>2</mn></math> and <math><mi>h</mi><mo>≥</mo><mn>1</mn></math>. Moreover, we also investigate analogous problems for the edge version. This implies some previous results in connectivity and edge-connectivity.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"348 9","pages":"Article 114544"},"PeriodicalIF":0.7,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143825674","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The minima of the geodesic length functions of uniform filling curves

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series

Pub Date : 2025-04-14 DOI: 10.1112/jlms.70153

Ernesto Girondo, Gabino González-Diez, Rubén A. Hidalgo

There is a natural link between (multi-)curves that fill up a closed oriented surface and dessins d'enfants. We use this approach to exhibit explicitly the minima of the geodesic length function of filling curves that admit a self-transverse homotopy equivalent representative such that all self-intersection points, as well as all faces of the complement, have the same multiplicity. We show that these minima are attained at the Grothendieck–Belyi surfaces determined by the natural dessin d'enfants associated with these filling curves. In particular, they are all Riemann surfaces defined over number fields.

引用次数: 0

首页上一页

下一页尾页

类型

数学最新文献

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

全部 Dokl. Math. Funct. Anal. Appl. J. Homotopy Relat. Struct. J. Math. Fluid Mech. Math. Phys. Anal. Geom. ACTA MATH APPL SIN-E Adv. Nonlinear Stud. Adv. Appl. Clifford Algebras ADV GEOM ALGEBR LOG+ Am. J. Math. Am. Math. Mon. ANN I H POINCARE-PR APPL CATEGOR STRUCT ANN STAT ANN MATH Appl. Numer. Math. Ann. Mat. Pura Appl. Ann. Global Anal. Geom. Arch. Math. Archiv. Math. Logic BIOMETRICS BIOMETRIKA Bull. Math. Sci Bull. Math. Biol. B IRAN MATH SOC Calc. Var. Partial Differ. Equations Bull. Am. Math. Soc. CALCOLO CHAOS SOLITON FRACT CHAOS COMB PROBAB COMPUT COMMUN STAT-THEOR M Commun. Math. Stat. Commun. Pure Appl. Math. C.R. Math. Commun. Pure Appl. Anal. Demonstratio Mathematica Des. Codes Cryptogr. Duke Math. J. Electron. J. Comb. FILOMAT FORUM MATH Fractal and Fractional Geom. Funct. Anal. GRAPH COMBINATOR INTEGR EQUAT OPER TH INT J ALGEBR COMPUT Interfaces Free Boundaries Int. J. Comput. Math. INT J NUMBER THEORY INVENT MATH Int. Math. Res. Not. Int. Stat. Rev. Isr. J. Math. J. Algebra J ALGEBR COMB J. Appl. Math. Comput. J. Appl. Stat. J. Comb. Des. J. Comput. Graphical Stat. J. Complex Networks J. Differ. Equations Appl. J. Differ. Equations J. Dyn. Differ. Equations J. Differ. Geom. J. Funct. Anal. J. Funct. Spaces J. Global Optim. J.Fourier Anal. Appl. J. Graph Theory J. Inequal. Appl. J. Math. Imaging Vision J. Multivar. Anal. J. Symb. Log. Journal of Survey Statistics and Methodology J. Am. Stat. Assoc. Linear Algebra Appl. Math. Z. MATH SLOVACA Math. Modell. Nat. Phenom. Math. Notes Math. Program. MATHEMATICS-BASEL Math. Ann. Math. Proc. Cambridge Philos. Soc. METHODOL COMPUT APPL Math. Comput. MATHEMATIKA Numer. Methods Partial Differ. Equations PHYSICA D Probab. Theory Relat. Fields Proc. Edinburgh Math. Soc. Proc. Am. Math. Soc. Q. Appl. Math. Ric. Mat. Stochastic Models STAT COMPUT TAIWAN J MATH TOPOL METHOD NONL AN

﹀