Acta Mathematicae Applicatae Sinica, English Series最新文献

For a graph G of order n and a positive integer k, a k-weak cycle partition of G, called k-WCP, is a sequence of vertex disjoint subgraphs H₁, H₂, ⋯, H_k of G with (bigcupnolimits_{i=1}^{k} V(H_{i})=V(G)), where H_i is isomorphic to K₁, K₂ or a cycle. Let σ₂(G) = min{d(x) + d(y): xy ∉ E(G), x, y ∈ V(G)}. Hu and Li [Discrete Math. 307(2007)] proved that if G is a graph of order n ≥ k + 12 with a k-WCP and (sigma_{2}(G) geq {{2n+k-4} over 3}), then G contains a k-WCP with at most one subgraph isomorphic to K₂. In this paper, we generalize their result on the analogy of Fan-type condition that (max{{d(x),d(y)}} geq {{2n+k-4} over 6}) for each pair of nonadjacent vertices x, y ∈ V(G).

This paper deals with numerical solutions for nonlinear first-order boundary value problems (BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta (ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν+1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

A graph G is a fractional (k, m)-deleted graph if removing any m edges from G, the resulting subgraph still admits a fractional k-factor. Let k ≥ 2 and m ≥ 1 be integers. Denote (lfloor{2m over k}rfloor^{ast}=lfloor{2m over k}rfloor) if (2m over k) is not an integer, and (lfloor{2m over k}rfloor^{ast}=lfloor{2m over k}rfloor - 1) if (2m over k) is an integer. In this paper, we prove that G is a fractional (k, m)-deleted graph if δ(G) ≥ k + m and isolated toughness meets

Furthermore, we show that the isolated toughness bound is tight.

The focusing modified Korteweg-de Vries (mKdV) equation with multiple high-order poles under the nonzero boundary conditions is first investigated via developing a Riemann-Hilbert (RH) approach. We begin with the asymptotic property, symmetry and analyticity of the Jost solutions, and successfully construct the RH problem of the focusing mKdV equation. We solve the RH problem when 1/S₁₁(k) has a single high-order pole and multiple high-order poles. Furthermore, we derive the soliton solutions of the focusing mKdV equation which corresponding with a single high-order pole and multiple high-order poles, respectively. Finally, the dynamics of one- and two-soliton solutions are graphically discussed.

The asymptotic analysis theory is a powerful mathematical tool employed in the study of complex systems. By exploring the behavior of mathematical models in the limit as certain parameters tend toward infinity or zero, the asymptotic analysis facilitates the extraction of simplified limit-equations, revealing fundamental principles governing the original complex dynamics. We will highlight the versatility of asymptotic methods in handling different scenarios, ranging from fluid mechanics to biological systems and economic mechanisms, with a greater focus on the financial markets models. This short overview aims to convey the broad applicability of the asymptotic analysis theory in advancing our comprehension of complex systems, making it an indispensable tool for researchers and practitioners across different disciplines. In particular, such a theory could be applied to reshape intricate financial models (e.g., stock market volatility models) into more manageable forms, which could be tackled with time-saving numerical implementations.

The multicolor Ramsey number r_k(C₄) is the smallest integer N such that any k-edge coloring of K_N contains a monochromatic C₄. The current best upper bound of r_k(C₄) was obtained by Chung (1974) and independently by Irving (1974), i.e., r_k(C₄) ≤ k² + k + 1 for all k ≥ 2. There is no progress on the upper bound since then. In this paper, we improve the upper bound of r_k(C₄) by showing that r_k(C₄) ≤ k² + k − 1 for even k ≥ 6. The improvement is based on the upper bound of the Turán number ex(n, C₄), in which we mainly use the double counting method and many novel ideas from Firke, Kosek, Nash, and Williford [J. Combin. Theory, Ser. B 103 (2013), 327–336].

As an extension of linear regression in functional data analysis, functional linear regression has been studied by many researchers and applied in various fields. However, in many cases, data is collected sequentially over time, for example the financial series, so it is necessary to consider the autocorrelated structure of errors in functional regression background. To this end, this paper considers a multiple functional linear model with autoregressive errors. Based on the functional principal component analysis, we apply the least square procedure to estimate the functional coefficients and autoregression coefficients. Under some regular conditions, we establish the asymptotic properties of the proposed estimators. A simulation study is conducted to investigate the finite sample performance of our estimators. A real example on China’s weather data is applied to illustrate the validity of our model.

Several eigenvalue properties of the third-order boundary value problems with distributional potentials are investigated. Firstly, we prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Next, the continuity and differential properties of the eigenvalues of the problems are given, especially we nd the differential expressions for the boundary conditions, the coefficient functions and the endpoints. Finally, we show a brief application to a kind of transmission boundary value problems of the problems studied here.

This article proves the existence and uniqueness conditions of the solution of two-dimensional time-space tempered fractional diffusion-wave equation. We find analytical solution of the equation via the two-step Adomian decomposition method (TSADM). The existence result is obtained with the help of some fixed point theorems, while the uniqueness of the solution is a consequence of the Banach contraction principle. Additionally, we study the stability via the Ulam-Hyers stability for the considered problem. The existing techniques use numerical algorithms for solving the two-dimensional time-space tempered fractional diffusion-wave equation, and thus, the results obtained from them are the approximate solution of the problem with high computational and time complexity. In comparison, our proposed method eliminates all the difficulties arising from numerical methods and gives an analytical solution with a straightforward process in just one iteration.

This research paper addresses a topic of interest to many researchers and engineers due to its effective applications in various industrial areas. It focuses on the thermoelastic laminated beam model with nonlinear structural damping, nonlinear time-varying delay, and microtemperature effects. Our primary goal is to establish the stability of the solution. To achieve this, and under suitable hypotheses, we demonstrate energy decay and construct a Lyapunov functional that leads to our results.