Article
Mathematics, Applied
Yi-Fen Ke
Summary: Novel observations for SDLCPs are presented in this paper, leading to the establishment of modulus-based matrix splitting iteration methods. The convergence of these methods has been analyzed and numerical experiments have shown their effectiveness in solving SDLCPs.
NUMERICAL ALGORITHMS
(2021)
Article
Mathematics
Yongkun Li, Mei Huang, Bing Li
Summary: In this paper, the definition of Besicovitch almost periodic functions is given using the Bohr property and the Bochner property, and their basic properties, including composition theorem, are studied. The equivalence of the Bohr definition and the Bochner definition is proved. Then, using the contraction fixed point theorem, the existence and uniqueness of Besicovitch almost periodic solutions for a class of abstract semi-linear delay differential equations are studied, even if the equation degenerates into ordinary differential equations, the result is new.
Article
Mechanics
S. K. Singh, A. Baxy, A. Banerjee, D. Bhattacharya, R. K. Varma
Summary: This research proposes a perspective on the dispersion relation of flexural waves on periodic structures, and validates the theory through models and methods. The results show the favorable impact of size effect and rotational theory on structures. Additionally, the geometric shape and material properties of the structure significantly affect the location and width of the attenuation band.
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS
(2023)
Article
Mathematics
A. N. Malyshev, M. Sadkane
Summary: This paper investigates the periodic Lyapunov matrix equations for a general discrete-time linear periodic system, where the matrix coefficients can be singular. New decay estimates of the Green matrices are derived in terms of the spectral norms of special solutions to the periodic Lyapunov matrix equations, based on the periodic Schur decomposition of matrices. The results are of great significance for stability and control problems in discrete-time linear periodic systems.
LINEAR & MULTILINEAR ALGEBRA
(2023)
Article
Engineering, Multidisciplinary
Christopher Jelich, Mahmoud Karimi, Nicole Kessissoglou, Steffen Marburg
Summary: This paper presents an efficient computational approach to solve a sequence of block Toeplitz systems using global and block variants of the GMRES method. The performance is assessed in terms of wall clock time, number of multiplications, and peak memory usage. Two numerical examples demonstrate the effectiveness of the proposed method.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2021)
Article
Acoustics
Kenneth E. E. Gilbert
Summary: This paper presents a wide-angle formulation of the Beilis-Tappert method for wave propagation over irregular terrain, along with numerical examples. The study reveals the need for a slope-dependent filter for selecting the physical vertical wave numbers in the method. The importance of the filter is demonstrated through theoretical and numerical analysis of propagation over steep and shallow hills.
JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA
(2022)
Article
Multidisciplinary Sciences
Lyonell Boulton, George Farmakis, Beatrice Pelloni
Summary: The study investigates the phenomenon of revivals for the linear Schrodinger and Airy equations over a finite interval with various non-periodic boundary conditions. It is found that the Airy equation does not generally exhibit revivals even for boundary conditions very close to periodic, in contrast to the linear Schrodinger equation. A new, weaker form of revival phenomena is also described in the case of certain Robin-type boundary conditions for the linear Schrodinger equation.
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2021)
Article
Mathematics, Applied
Hojjat Farzadfard
Summary: The conditions mentioned above are necessary and sufficient for the Poincare functional equation to have a cosine-like solution.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Anna Bahyrycz, Justyna Sikorska
Summary: This passage discusses equations between linear spaces and linear mappings, and obtains the general solution and results for specific cases.
RESULTS IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Rinko Miyazaki, Dohan Kim, Jong Son Shin
Summary: In this paper, criteria for the uniform boundedness of solutions to linear difference equations (LEs) with periodic forcing functions are provided. Firstly, a necessary and sufficient condition for the boundedness of the sequence {Ln} of a square matrix L is derived, leading to a criterion for the uniform boundedness of solutions to LEs. Secondly, a criterion for the uniform boundedness of solutions to LEs with periodic forcing functions is obtained by utilizing a certain representation of solutions. Additionally, the characteristic equation of a matrix under the commuting condition is presented in relation to LEs with delay.
Article
Mathematics, Interdisciplinary Applications
Dilek Varol
Summary: This article introduces the improved Kawahara equation, which is one of the most significant nonlinear evolution equations in mathematical physics. The analytical solutions of the conformable fractional extended Kawahara equation were obtained using the Jacobi elliptic function expansion method. By changing variables, this extended equation can be applied to different fractional forms in time, space, or both. Various types of fractional problems are illustrated to demonstrate the practical application of the given method, and some of the obtained solutions are presented in two- or three-dimensional graphics as visual proof.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Applied
A. Mouzoun, D. Zeglami, Y. Aissi
Summary: This paper provides an explicit description of the solutions to parametric functional equations in number theory, as well as different methods for solving these equations based on the value of beta. Solutions to a matrix multiplicative Cauchy functional equation on abelian regular semigroups are also presented, with implications for more general equations.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jiansheng Geng, Xiufang Ren, Yingfei Yi
Summary: In this paper, we study the one-dimensional, quasi-periodically forced, linear KdV equations and obtain results on the reducibility of the equations and the existence and stability of solutions.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Hojjat Farzadfard
Summary: This paper generalizes the results of Alexander Sarkovskii and explores the relationship between continuous periodic functions that satisfy a specific functional equation.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Materials Science, Multidisciplinary
Adil Jhangeer, Muhammad Muddassar, Zia Ur Rehman, Jan Awrejcewicz, Muhmmad Bilal Riaz
Summary: This study measures the multistability and dynamic behavior of non-linear wave solutions of the unperturbed and perturbed FitzHugh-Nagumo (FHN) equation using analytical and numerical methods. Various solitonic structures are calculated for the unperturbed model, and bifurcation behavior is reported after transforming the model into a dynamic system with the Galilean transformation. Sensitivity analysis is used to analyze periodic and quasi-periodic behavior under different initial values.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Peter Frolkovic, Nikola Gajdosova
Summary: This paper presents compact semi-implicit finite difference schemes for solving advection problems using level set methods. Through numerical tests and stability analysis, the accuracy and stability of the proposed schemes are verified.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Md. Rajib Arefin, Jun Tanimoto
Summary: Human behaviors are strongly influenced by social norms, and this study shows that injunctive social norms can lead to bi-stability in evolutionary games. Different games exhibit different outcomes, with some showing the possibility of coexistence or a stable equilibrium.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Dingyi Du, Chunhong Fu, Qingxiang Xu
Summary: A correction and improvement are made on a recent joint work by the second and third authors. An optimal perturbation bound is also clarified for certain 2 x 2 Hermitian matrices.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Pingrui Zhang, Xiaoyun Jiang, Junqing Jia
Summary: In this study, improved uniform error bounds are developed for the long-time dynamics of the nonlinear space fractional Dirac equation in two dimensions. The equation is discretized in time using the Strang splitting method and in space using the Fourier pseudospectral method. The major local truncation error of the numerical methods is established, and improved uniform error estimates are rigorously demonstrated for the semi-discrete scheme and full-discretization. Numerical investigations are presented to verify the error bounds and illustrate the long-time dynamical behaviors of the equation with honeycomb lattice potentials.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kuan Zou, Wenchen Han, Lan Zhang, Changwei Huang
Summary: This research extends the spatial PGG on hypergraphs and allows cooperators to allocate investments unevenly. The results show that allocating more resources to profitable groups can effectively promote cooperation. Additionally, a moderate negative value of investment preference leads to the lowest level of cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Kui Du
Summary: This article introduces two new regularized randomized iterative algorithms for finding solutions with certain structures of a linear system ABx = b. Compared to other randomized iterative algorithms, these new algorithms can find sparse solutions and have better performance.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Shadi Malek Bagomghaleh, Saeed Pishbin, Gholamhossein Gholami
Summary: This study combines the concept of vanishing delay arguments with a linear system of integral-algebraic equations (IAEs) for the first time. The piecewise collocation scheme is used to numerically solve the Hessenberg type IAEs system with vanishing delays. Well-established results regarding regularity, existence, uniqueness, and convergence of the solution are presented. Two test problems are studied to verify the theoretical achievements in practice.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Qi Hu, Tao Jin, Yulian Jiang, Xingwen Liu
Summary: Public supervision plays an important role in guiding and influencing individual behavior. This study proposes a reputation incentives mechanism with public supervision, where each player has the authority to evaluate others. Numerical simulations show that reputation provides positive incentives for cooperation.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Werner M. Seiler, Matthias Seiss
Summary: This article proposes a geometric approach for the numerical integration of (systems of) quasi-linear differential equations with singular initial and boundary value problems. It transforms the original problem into computing the unstable manifold at a stationary point of an associated vector field, allowing efficient and robust solutions. Additionally, the shooting method is employed for boundary value problems. Examples of (generalized) Lane-Emden equations and the Thomas-Fermi equation are discussed.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Lisandro A. Raviola, Mariano F. De Leo
Summary: We evaluated the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations and showed that the proposed methods are effective in terms of accuracy and computational cost. They can be applied to both irreversible models and dissipative solitons, offering a promising alternative for solving a wide range of evolutionary partial differential equations.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Yong Wang, Jie Zhong, Qinyao Pan, Ning Li
Summary: This paper studies the set stability of Boolean networks using the semi-tensor product of matrices. It introduces an index-vector and an algorithm to verify and achieve set stability, and proposes a hybrid pinning control technique to reduce computational complexity. The issue of synchronization is also discussed, and simulations are presented to demonstrate the effectiveness of the results obtained.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Ling Cheng, Sirui Zhang, Yingchun Wang
Summary: This paper considers the optimal capacity allocation problem of integrated energy systems (IESs) with power-gas systems for clean energy consumption. It establishes power-gas network models with equality and inequality constraints, and designs a novel full distributed cooperative optimal regulation scheme to tackle this problem. A distributed projection operator is developed to handle the inequality constraints in IESs. The simulation demonstrates the effectiveness of the distributed optimization approach.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Abdurrahim Toktas, Ugur Erkan, Suo Gao, Chanil Pak
Summary: This study proposes a novel image encryption scheme based on the Bessel map, which ensures the security and randomness of the ciphered images through the chaotic characteristics and complexity of the Bessel map.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Xinjie Fu, Jinrong Wang
Summary: In this paper, we establish an SAIQR epidemic network model and explore the global stability of the disease in both disease-free and endemic equilibria. We also consider the control of epidemic transmission through non-instantaneous impulsive vaccination and demonstrate the sustainability of the model. Finally, we validate the results through numerical simulations using a scale-free network.
APPLIED MATHEMATICS AND COMPUTATION
(2024)
Article
Mathematics, Applied
Maria Han Veiga, Lorenzo Micalizzi, Davide Torlo
Summary: The paper focuses on the iterative discretization of weak formulations in the context of ODE problems. Several strategies to improve the accuracy of the method are proposed, and the method is combined with a Deferred Correction framework to introduce efficient p-adaptive modifications. Analytical and numerical results demonstrate the stability and computational efficiency of the modified methods.
APPLIED MATHEMATICS AND COMPUTATION
(2024)