Article
Mathematics
C. G. Karthick Babu, Anirban Mukhopadhyay, A. Sankaranarayanan
Summary: The paper discusses the asymptotic formula for the number of prime numbers p that have a residue pattern with a given finite set S. It also provides a similar formula for primes p that satisfy certain conditions involving an irrational number alpha and a real number beta. The author introduces a mapping function theta and auxiliary conditions to derive these formulas and extends the results under certain assumptions.
INTERNATIONAL JOURNAL OF NUMBER THEORY
(2023)
Article
Computer Science, Information Systems
Jing-Yu Ji, Man Leung Wong
Summary: This study attempts to solve nonlinear equation systems using decomposition-based multiobjective optimization. By transforming the system into a bi-objective optimization problem using reference points, an improved decomposition algorithm is applied for solving. Experimental results demonstrate the superior performance and shorter execution time of the proposed method compared to other algorithms.
INFORMATION SCIENCES
(2022)
Article
Mathematics
Umberto Guarnotta, Salvatore A. Marano
Summary: The study establishes an existence result for Neumann elliptic systems with singular, convective, sign-changing, arbitrarily growing reactions. The proofs are based on various techniques and theories, ultimately leading to the discovery of infinitely many solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Roger Casals, Honghao Gao
Summary: We prove that all maximal-tb positive Legendrian torus links (n, m) in the standard contact 3-sphere, except for (2, m), (3, 3), (3, 4) and (3, 5), admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances that induce faithful actions of the modular group PSL(2, Z) and the mapping class group M-0,M-4 into the coordinate rings of algebraic varieties associated to Legendrian links. In particular, our results imply that there exist Lagrangian concordance monoids with subgroups of exponential-growth, and yield Stein surfaces homotopic to a 2-sphere with infinitely many distinct exact Lagrangian surfaces of higher-genus. We also show that there exist infinitely many satellite and hyperbolic knots with Legendrian representatives admitting infinitely many exact Lagrangian fillings.
ANNALS OF MATHEMATICS
(2022)
Article
Mathematics, Applied
Shuai Jiang, Shibo Liu
Summary: This article obtains a sequence of solutions converging to zero for the Kirchhoff equation using truncating technique and a variant of Clark's theorem. The results are presented for both the Kirchhoff equation and the Schrödinger-Poisson system on a bounded smooth domain.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Interdisciplinary Applications
Erika Diz-Pita, Jaume Llibre, M. Victoria Otero-Espinar
Summary: This paper classifies the five-parameter planar Kolmogorov systems and provides a topological classification of their phase portraits on the Poincare disc. The study reveals that these systems have 13 topologically distinct global phase portraits.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Engineering, Mechanical
Roberto De Leo, James A. Yorke
Summary: Chaotic attractors, chaotic saddles, and periodic orbits are examples of chain-recurrent sets. The qualitative behavior of a dynamical system can be encapsulated in a graph, with nodes representing chain-recurrent sets. Physical systems can have infinitely many disjoint coexisting nodes, as seen in systems like the logistic map. Comparing the Lorenz system and the logistic map shows how similar their graph bifurcation diagrams are in certain parameter ranges.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Tomas Dutko, Carlo Mercuri, Teresa Megan Tyler
Summary: This study investigates a nonlinear Schrodinger-Poisson system, analyzing its properties and the existence of solutions with the critical Sobolev exponent being a key factor.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Sebastiano Peotta, Fredrik Brange, Aydin Deger, Teemu Ojanen, Christian Flindt
Summary: Dynamical phase transitions extend the concept of criticality to nonstationary settings, involving sudden changes in the macroscopic properties of time-evolving quantum systems. The research combines symmetry, topology, and nonequilibrium physics, utilizing Loschmidt cumulants to determine critical times of interacting many-body systems. Experimental prospects include predicting the first critical time of a quantum many-body system by measuring energy fluctuations in the initial state, with potential implementation on near-term quantum computers with a limited number of qubits.
Article
Management
Paulin Jacquot, Cheng Wan
Summary: This paper defines and analyzes the concept of variational Wardrop equilibrium for nonatomic aggregative games with an infinity of player types. These equilibria are characterized by an infinite-dimensional variational inequality. The paper presents a convergence theorem, under monotonicity conditions, for computing such an equilibrium with arbitrary precision. To achieve this, a sequence of nonatomic games with a finite number of player types is introduced to approximate the initial game. The paper proves the existence of a symmetric Wardrop equilibrium in each of these games, and shows that these symmetric equilibria converge to an equilibrium of the infinite game, which can be computed as solutions of finite dimensional variational inequalities. The model is illustrated through an example from smart grids, where a large population of electricity consumers is described by a parametric distribution, resulting in a nonatomic game with an infinity of different player types, with actions subject to coupling constraints.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Correction
Mathematics
U. Guarnotta, S. A. Marano
Summary: This paper provides a correct formulation of Theorems 4.2-4.3 in reference [1]. (C) 2020 Elsevier Inc. All rights reserved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Ky Ho, Patrick Winkert
Summary: In this paper, we study elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a locally defined right-hand side. By using an abstract critical point result and recent a priori bounds, we prove the existence of a sequence of nontrivial solutions whose L∞-norms converge to zero.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Fangyi Qin, Jun Wang, Jing Yang
Summary: The present paper discusses the existence of infinitely many positive solutions in a class of Schrdinger-poisson system, by making suitable assumptions on the decay rate of coefficients and using purely variational methods. Challenges arising from the nonlocal term are overcome through delicate estimates, leading to the discovery of infinitely many positive solutions.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Abdolrahman Razani, Giovany Figueiredo
Summary: Using genus theory, this paper proves the existence of infinitely many solutions for an anisotropic equation involving subcritical growth, as well as the existence of k-pairs of distinct solutions using Krasnoselskii genus and Clark's theorem. Furthermore, the existence of infinitely many solutions for an anisotropic equation involving critical growth is studied.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Erika Diz-Pita, Jaume Llibre, M. Victoria Otero-Espinar
Summary: The study provided a topological classification of the global phase portraits of Kolmogorov systems in the Poincare disc, revealing a total of 22 topologically distinct phase portraits.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics
Antal Balog, Andrew Granville, Jozsef Solymosi
QUARTERLY JOURNAL OF MATHEMATICS
(2017)
Article
Mathematics, Applied
Andrew Granville, Kannan Soundararajan
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2018)
Article
Mathematics
Andrew Granville
AMERICAN MATHEMATICAL MONTHLY
(2018)
Article
Mathematics, Applied
Jonathan Bober, Leo Goldmakher, Andrew Granville, Dimitris Koukoulopoulos
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY
(2018)
Article
Mathematics, Applied
Andrew Granville, Adam J. Harper, Kannan Soundararajan
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2018)
Article
Mathematics
I. P. Goulden, Andrew Granville, L. Bruce Richmond, Jeffrey Shallit
Article
Mathematics
Andrew Granville, Adam J. Harper, K. Soundararajan
COMPOSITIO MATHEMATICA
(2019)
Article
Mathematics
Andrew Granville, Dimitris Koukoulopoulos
Article
Mathematics
Andrew Granville, Xuancheng Shao
ADVANCES IN MATHEMATICS
(2019)
Article
Mathematics
A. Granville, G. Shakan
ACTA MATHEMATICA HUNGARICA
(2020)
Article
Mathematics, Applied
Andrew Granville, Aled Walker
Summary: The research proves that the set NA has a certain easily-described structure when N >= b - l, as recently conjectured. It also classifies sets A for which this bound cannot be improved.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics
Andrew Granville, Allysa Lumley
Summary: This article formulates conjectures for the number of primes in intervals of length y around x using heuristic reasoning. The maximum growth rate of the number of primes is found to be surprisingly slow as y ranges from log x to (log x)(2). The provided data somewhat supports these conjectures, but there may be room for modifications.
EXPERIMENTAL MATHEMATICS
(2023)
Article
Mathematics
Andrew Granville, Youness Lamzouri
Summary: This paper investigates the large deviations of sums of weighted random variables that are approximately independent, with examples from number theory.
LITHUANIAN MATHEMATICAL JOURNAL
(2021)
Article
Mathematics
Regis De La Bret Eche, Andrew Granville
Summary: We demonstrate that a large exponential sum with multiplicative coefficients implies the associated multiplicative function is pretentious. This finding has applications in the circle method and provides a natural interpretation of the local-global principle.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
