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Upper Bounds on the Multicolor Ramsey Numbers rk(C4) 多色拉姆齐数rk（C4）的上界
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-023-1074-3
Tian-yu Li, Qi-zhong Lin
{"title":"Upper Bounds on the Multicolor Ramsey Numbers rk(C4)","authors":"Tian-yu Li,&nbsp;Qi-zhong Lin","doi":"10.1007/s10255-023-1074-3","DOIUrl":"10.1007/s10255-023-1074-3","url":null,"abstract":"<div><p>The multicolor Ramsey number <i>r</i><sub><i>k</i></sub>(<i>C</i><sub>4</sub>) is the smallest integer <i>N</i> such that any <i>k</i>-edge coloring of <i>K</i><sub><i>N</i></sub> contains a monochromatic <i>C</i><sub>4</sub>. The current best upper bound of <i>r</i><sub><i>k</i></sub>(<i>C</i><sub>4</sub>) was obtained by Chung (1974) and independently by Irving (1974), i.e., <i>r</i><sub><i>k</i></sub>(<i>C</i><sub>4</sub>) ≤ <i>k</i><sup>2</sup> + <i>k</i> + 1 for all <i>k</i> ≥ 2. There is no progress on the upper bound since then. In this paper, we improve the upper bound of <i>r</i><sub><i>k</i></sub>(<i>C</i><sub>4</sub>) by showing that <i>r</i><sub><i>k</i></sub>(<i>C</i><sub>4</sub>) ≤ <i>k</i><sup>2</sup> + <i>k</i> − 1 for even <i>k</i> ≥ 6. The improvement is based on the upper bound of the Turán number ex(<i>n, C</i><sub>4</sub>), 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].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"286 - 294"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889740","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Some Eigenvalue Properties of Third-order Boundary Value Problems with Distributional Potentials 具有分布势的三阶边值问题的若干特征值性质
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-023-1064-5
Hai-yan Zhang, Ji-jun Ao
{"title":"Some Eigenvalue Properties of Third-order Boundary Value Problems with Distributional Potentials","authors":"Hai-yan Zhang,&nbsp;Ji-jun Ao","doi":"10.1007/s10255-023-1064-5","DOIUrl":"10.1007/s10255-023-1064-5","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"179 - 199"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Solution of a Time-Space Tempered Fractional Diffusion-Wave Equation and its Theoretical Aspects 一个时空调质分数阶扩散波动方程的解及其理论问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1123-6
Pratibha Verma, Surabhi Tiwari
{"title":"Solution of a Time-Space Tempered Fractional Diffusion-Wave Equation and its Theoretical Aspects","authors":"Pratibha Verma,&nbsp;Surabhi Tiwari","doi":"10.1007/s10255-024-1123-6","DOIUrl":"10.1007/s10255-024-1123-6","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"1 - 26"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Exponential Decay of Laminated Beam with Nonlinear Time-varying Delay and Microtemperature Effect 非线性时变延迟层合梁的指数衰减和微温度效应
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1151-2
Imene Laribi, Ali Krelifa, Djamel Ouchenane, Fares Yazid, Salah Boulaaras, Salah Zitouni
{"title":"Exponential Decay of Laminated Beam with Nonlinear Time-varying Delay and Microtemperature Effect","authors":"Imene Laribi,&nbsp;Ali Krelifa,&nbsp;Djamel Ouchenane,&nbsp;Fares Yazid,&nbsp;Salah Boulaaras,&nbsp;Salah Zitouni","doi":"10.1007/s10255-024-1151-2","DOIUrl":"10.1007/s10255-024-1151-2","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"270 - 285"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Bifurcations and Spatiotemporal Patterns in the Diffusive Nutrient-Microorganism Model 营养物-微生物扩散模型的分岔与时空模式
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1079-6
Ya-di Wang, Hai-long Yuan, Yan-ling Li
{"title":"Bifurcations and Spatiotemporal Patterns in the Diffusive Nutrient-Microorganism Model","authors":"Ya-di Wang,&nbsp;Hai-long Yuan,&nbsp;Yan-ling Li","doi":"10.1007/s10255-024-1079-6","DOIUrl":"10.1007/s10255-024-1079-6","url":null,"abstract":"<div><p>In this paper, the diffusive nutrient-microorganism model subject to Neumann boundary conditions is considered. The Hopf bifurcations and steady state bifurcations which bifurcate from the positive constant equilibrium of the system are investigated in details. In addition, the formulae to determine the direction of Hopf and steady state bifurcations are derived. Our results show the existence of spatially homogeneous/nonhomogeneous periodic orbits and steady state solutions, which indicates the spatiotemporal dynamics of the system. Some numerical simulations are also presented to support the analytical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"162 - 178"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889712","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Efficient Hyperbolic Kernel Function Yielding the Best Known Iteration Bounds for Linear Programming 给出线性规划最优迭代界的有效双曲核函数
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1146-z
Imene Touil, Wided Chikouche, Djamel Benterki, Amina Zerari
{"title":"An Efficient Hyperbolic Kernel Function Yielding the Best Known Iteration Bounds for Linear Programming","authors":"Imene Touil,&nbsp;Wided Chikouche,&nbsp;Djamel Benterki,&nbsp;Amina Zerari","doi":"10.1007/s10255-024-1146-z","DOIUrl":"10.1007/s10255-024-1146-z","url":null,"abstract":"<div><p>Interior-point methods (IPMs) for linear programming (LP) are generally based on the logarithmic barrier function. Peng et al. (J. Comput. Technol. 6: 61–80, 2001) were the first to propose non-logarithmic kernel functions (KFs) for solving IPMs. These KFs are strongly convex and smoothly coercive on their domains. Later, Bai et al. (SIAM J. Optim. 15(1): 101–128, 2004) introduced the first KF with a trigonometric barrier term. Since then, no new type of KFs were proposed until 2020, when Touil and Chikouche (Filomat. 34(12): 3957–3969, 2020; Acta Math. Sin. (Engl. Ser.), 38(1): 44–67, 2022) introduced the first hyperbolic KFs for semidefinite programming (SDP). They established that the iteration complexities of algorithms based on their proposed KFs are <span>({cal O}(n^{2 over 3} log {n over epsilon}))</span> and <span>({cal O}(n^{3 over 4} log {n over epsilon}))</span> for large-update methods, respectively. The aim of this work is to improve the complexity result for large-update method. In fact, we present a new parametric KF with a hyperbolic barrier term. By simple tools, we show that the worst-case iteration complexity of our algorithm for the large-update method is <span>({cal O}({sqrt n} log n log{n over epsilon}))</span> iterations. This coincides with the currently best-known iteration bounds for IPMs based on all existing kind of KFs.</p><p>The algorithm based on the proposed KF has been tested. Extensive numerical simulations on test problems with different sizes have shown that this KF has promising results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"133 - 151"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889715","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Dynamics of a Stochastic SEITR Model for Tuberculosis with Incomplete Treatment 不完全治疗肺结核的随机SEITR模型动力学
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1147-y
Xiao-dong Wang, Kai Wang
{"title":"The Dynamics of a Stochastic SEITR Model for Tuberculosis with Incomplete Treatment","authors":"Xiao-dong Wang,&nbsp;Kai Wang","doi":"10.1007/s10255-024-1147-y","DOIUrl":"10.1007/s10255-024-1147-y","url":null,"abstract":"<div><p>In this paper, a stochastic SEITR model is formulated to describe the transmission dynamics of tuberculosis with incompletely treatment. Sufficient conditions for the existence of a stationary distribution and extinction are obtained. In addition, numerical simulations are given to illustrate these analytical results. Theoretical and numerical results show that large environmental perturbations can inhibit the spread of tuberculosis.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"99 - 113"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Hausdorff Measure of Space Anisotropic Gaussian Processes with Non-stationary Increments 具有非平稳增量的空间各向异性高斯过程的Hausdorff测度
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1051-5
Jun Wang, Zhen-long Chen, Wei-jie Yuan, Guang-jun Shen
{"title":"Hausdorff Measure of Space Anisotropic Gaussian Processes with Non-stationary Increments","authors":"Jun Wang,&nbsp;Zhen-long Chen,&nbsp;Wei-jie Yuan,&nbsp;Guang-jun Shen","doi":"10.1007/s10255-024-1051-5","DOIUrl":"10.1007/s10255-024-1051-5","url":null,"abstract":"<div><p>Let <i>X</i> = {<i>X</i>(<i>t</i>), <i>t</i> ∈ ℝ<sub>+</sub>} be a centered space anisotropic Gaussian process values in ℝ<sup><i>d</i></sup> with non-stationary increments, whose components are independent but may not be identically distributed. Under certain conditions, then almost surely <i>c</i><sub>1</sub> ≤ <i>ϕ</i> − <i>m</i>(<i>X</i>([0, 1])) ≤ <i>c</i><sub>2</sub>, where <i>ϕ</i> denotes the exact Hausdorff measure associated with function <span>(phi left( s right) = {s^{{1 over {{alpha _k}}} + sumlimits_{i = 1}^k {left( {1 - {{{alpha _i}} over {{alpha _k}}}} right)} }}log ,log,{1 over s})</span> for some 1 ≤ <i>k</i> ≤ <i>d</i>, (<i>α</i><sub>1</sub>,⋯, <i>α</i><sub><i>d</i></sub>) ∈ (0, 1]<sup><i>d</i></sup>. We also obtain the exact Hausdorff measure of the graph of <i>X</i> on [0, 1].</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"114 - 132"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Lp-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon 有限或无限时间水平线上多维斜反射 BSDE 的 Lp 解与最优切换问题
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1136-1
Xue-jun Shi, Qun Feng, Long Jiang
{"title":"Lp-solutions of Multi-dimensional Oblique Reflected BSDEs and Optimal Switching Problem on Finite or Infinite Time Horizon","authors":"Xue-jun Shi,&nbsp;Qun Feng,&nbsp;Long Jiang","doi":"10.1007/s10255-024-1136-1","DOIUrl":"10.1007/s10255-024-1136-1","url":null,"abstract":"<div><p>In this paper, we study mulit-dimensional oblique reflected backward stochastic differential equations (RBSDEs) in a more general framework over finite or infinite time horizon, corresponding to the pricing problem for a type of real option. We prove that the equation can be solved uniquely in <i>L</i><sup><i>p</i></sup>(1 &lt; <i>p</i> ≤ 2)-space, when the generators are uniformly continuous but each component taking values independently. Furthermore, if the generator of this equation fulfills the infinite time version of Lipschitzian continuity, we can also conclude that the solution to the oblique RBSDE exists and is unique, despite the fact that the values of some generator components may affect one another.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1127 - 1146"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Uniformity of Asymmetric Augmented Designs 不对称增强设计的均匀性
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-11-06 DOI: 10.1007/s10255-024-1135-2
Zhi-qing Wang, Xiang-yu Fang, Zu-jun Ou
{"title":"Uniformity of Asymmetric Augmented Designs","authors":"Zhi-qing Wang,&nbsp;Xiang-yu Fang,&nbsp;Zu-jun Ou","doi":"10.1007/s10255-024-1135-2","DOIUrl":"10.1007/s10255-024-1135-2","url":null,"abstract":"<div><p>Follow-up experimental designs are widely applied to explore the relationship between factors and responses step by step in various fields such as science and engineering. When some additional resources or information become available after the initial design of experiment is carried out, some additional runs and/or factors may be added in the follow-up stage. In this paper, the issue of the uniform row augmented designs and column augmented designs with mixed two-, three- and four-level is investigated. The uniformity of augmented designs is discussed under the wrap-around <i>L</i><sub>2</sub>-discrepancy. Some lower bounds of wrap-around <i>L</i><sub>2</sub>-discrepancy for the augmented designs are obtained, which can be used to assess uniformity of augmented design. Numerical results show that augmented designs have high efficiency, which have low discrepancy and close to the proposed lower bounds.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"40 4","pages":"1025 - 1044"},"PeriodicalIF":0.9,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587904","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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