Article
Mathematics, Applied
Taqi A. M. Shatnawi, Nadeem Abbas, Wasfi Shatanawi
Summary: This paper investigates the steady flow of incompressible hybrid Casson nanofluid over a vertical permeable exponential stretching sheet, exploring the influences of magnetic field, heat production, nonlinear radiation, and slip effects. It presents three hybrid nanofluidic models, discusses the impact on temperature profile and skin friction, and highlights the enhanced heat transfer rate in the Yamada-Ota model compared to other models.
Article
Mathematics
Wenbin Lyu, Zhi-An Wang
Summary: This paper investigates a class of reaction-diffusion system with density-suppressed motility. The paper proves the existence of a unique global classical solution for the system and shows that the solution is uniformly bounded in time under certain conditions.
ELECTRONIC RESEARCH ARCHIVE
(2022)
Article
Mathematics, Applied
Xin-Yi Gao, Yong-Jiang Guo, Wen-Rui Shan
Summary: This study conducts symbolic computation to analyze the nonlinear and dispersive long gravity waves propagating along two horizontal directions. It explores scaling transformations, hetero-Backlund transformations, and similarity reductions in the system, emphasizing the dependence on coefficients.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
(2023)
Article
Mathematics
Remi Gribonval, Gitta Kutyniok, Morten Nielsen, Felix Voigtlaender
Summary: This study focuses on the expressivity of deep neural networks, analyzing the complexity of networks based on the number of connections or neurons. The research investigates a class of functions whose error of best approximation decays at a certain rate with increasing complexity budget. The findings suggest that certain types of skip connections do not affect the resulting approximation spaces, and discuss the impact of network nonlinearity and depth on these spaces.
CONSTRUCTIVE APPROXIMATION
(2022)
Article
Mathematics
Pintu Bhunia, Kallol Paul
Summary: In this paper, we study the numerical radius of Hilbert space operators and propose improved upper bounds compared to the existing ones. By utilizing non-negative continuous functions, we generalize the numerical radius inequalities of n x n operator matrices. Additionally, we derive upper and lower bounds for the B-numerical radius of operator matrices, where B is a diagonal operator matrix with positive operator A in each diagonal entry. We show that these bounds generalize and improve upon existing results.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics
Si Luo
Summary: Based on the study of data from China's A-share listed companies, this paper finds that digital finance development plays a significant role in promoting the digital transformation of enterprises. Digital finance development can alleviate the financing constraint of enterprises and drive enterprise innovation, thus facilitating the digital transformation of enterprises.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics
Bo Zheng, Jia Li, Jianshe Yu
Summary: In this study, a delay differential equation model is used to investigate the suppression of wild mosquito populations by releasing Wolbachia-infected male mosquitoes. The research provides conditions for the nonexistence and existence of periodic solutions and proves the global asymptotic stability of the unique periodic solution. Furthermore, it demonstrates that one periodic solution is stable while the other is unstable when there are two periodic solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Qingqing Liu, Hongyun Peng, Zhi-An Wang
Summary: This paper investigates a quasi-linear hyperbolic-parabolic system modeling vasculogenesis, showing the existence of a nonlinear diffusion wave under suitable structural assumptions on the pressure function. The study demonstrates that the solution of the system will locally and asymptotically converge to this wave if the wave strength is small. Additionally, using time-weighted energy estimates, it is further proven that the convergence rate of the nonlinear diffusion wave is algebraic.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Christian Pinto-Gutierrez, Sandra Gaitan, Diego Jaramillo, Simon Velasquez
Summary: Non-fungible tokens (NFTs) represent ownership of digital art or unique digital items on a blockchain through smart contracts. NFTs have gained significant attention from cryptocurrency investors and the media, and research shows that Bitcoin and Ether returns greatly influence the popularity of NFTs.
Article
Mathematics, Applied
Sijia Du, Zhan Zhou
Summary: This paper focuses on a partial discrete Dirichlet boundary value problem involving the mean curvature operator. By making proper assumptions on the nonlinear term, the existence of multiple solutions is established using the critical point theory. Furthermore, the parameter intervals for obtaining at least two positive solutions and an unbounded sequence of positive solutions are separately determined with the help of the maximum principle.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Mathematics
Jin Tao, Dachun Yang, Wen Yuan, Yangyang Zhang
Summary: In this article, the authors prove that the commutator [b, T-Ω] is compact on X if and only if b is an element of CMO(R-n). The authors mainly employ three key tools: elaborate estimates, the complete John-Nirenberg inequality, and the generalized Fr 'echet-Kolmogorov theorem. These results have a wide range of applications.
POTENTIAL ANALYSIS
(2023)
Article
Mathematics
Hai-Yang Jin, Zhi-An Wang, Leyun Wu
Summary: In this paper, we study the initial-boundary value problem of a three-species spatial food chain model in a bounded domain. We establish the global existence of classical solutions and prove the global stability of prey-only steady state, semi-coexistence, and coexistence steady states.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Yanlin Li, Abimbola Abolarinwa, Ali H. Alkhaldi, Akram Ali
Summary: This paper generalizes some integral inequalities of the Hardy type to the setting of a complete non-compact smooth metric measure space without any geometric constraint on the potential function. The adopted approach highlights some criteria for a smooth metric measure space to admit Hardy inequalities related to Witten and Witten p-Laplace operators. The results in this paper complement in several aspects to those obtained recently in the non-compact setting.
Article
Mathematics, Applied
Qiao-Li Dong, Lulu Liu, Yonghong Yao
Summary: In this paper, new projection and contraction methods are introduced for solving the split feasibility problem with a self adaptive step size. The converging speed of the iterative methods is accelerated by using alternated inertial extrapolation. The weak convergence of the proposed methods is established under mild conditions. Preliminary numerical examples are provided to demonstrate the significant improvements of the proposed algorithms compared to those in [8].
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS
(2022)
Article
Mathematics, Applied
Ahmed M. Zidan, Adnan Khan, Rasool Shah, Mohammed Kbiri Alaoui, Wajaree Weera
Summary: This article demonstrates the solution to the time-fractional Fisher's equation using two well-known analytical methods. The proposed techniques, a modified form of the Adomian decomposition method and homotopy perturbation method with a Yang transform, show high accuracy and reliability through illustrative examples. The benefits of these techniques include a small number of calculations and applicability in various fields of applied sciences.
Article
Computer Science, Theory & Methods
Albert S. Berahas, Liyuan Cao, Krzysztof Choromanski, Katya Scheinberg
Summary: This paper analyzes several methods for approximating gradients of noisy functions using only function values, including finite differences, linear interpolation, Gaussian smoothing, and smoothing on a sphere. By deriving bounds on the number of samples and sampling radius, the paper ensures favorable convergence properties for line search or fixed step size descent methods. The paper also presents numerical results evaluating the quality of gradient approximations and their performance with a line search derivative-free optimization algorithm.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2022)
Article
Mathematics
Georgia Irina Oros, Luminita-Ioana Cotirla
Summary: This paper deals with the problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered to enhance novelty. Three new classes of bi-univalent functions are presented, and the relation between known results and the new ones is highlighted. Estimates on the Taylor-Maclaurin coefficients and the investigation of Fekete-Szego functional are also included for each of the new classes.
Article
Mathematics
Yanlin Li, Melek Erdogdu, Ayse Yavuz
Summary: In this paper, we investigate the differential geometric properties of the soliton surface associated with the Betchov-Da Rios equation. We provide derivative formulas for the Frenet frame of the unit speed curve and discuss the linear map of Weingarten type in the tangent space of the surface. We also obtain the necessary and sufficient conditions for the soliton surface to be a minimal surface and examine an application of the soliton surface associated with the Betchov-Da Rios equation.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
(2023)
Article
Mathematics
Juncheng Wei, Yuanze Wu
Summary: In this paper, we study the nonlinear Schrodinger equations with mixed nonlinearities. We establish the existence of solutions and investigate the existence and nonexistence of ground states in different parameter ranges. Additionally, we provide precise asymptotic behaviors of the ground states and mountain-pass solutions as the parameters approach specific values.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Yanlin Li, Kemal Eren, Kebire Hilal Ayvaci, Soley Ersoy
Summary: In this study, ruled developable surfaces with pointwise 1-type Gauss map of Frenet-type framed base (Ftfb) curve are presented in Euclidean 3-space. Tangent developable surfaces, focal developable surfaces, and rectifying developable surfaces with singular points are explored. The necessary conditions for the Gauss map of these surfaces to be pointwise 1-type are derived. Examples and graphics of each type of these surfaces are provided.
