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Sharp Isolated Toughness Bound for Fractional (k, m)-Deleted Graphs 分数(k, m)-删除图的尖锐孤立韧性界
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1067-x
Wei Gao, Wei-fan Wang, Yao-jun Chen
{"title":"Sharp Isolated Toughness Bound for Fractional (k, m)-Deleted Graphs","authors":"Wei Gao,&nbsp;Wei-fan Wang,&nbsp;Yao-jun Chen","doi":"10.1007/s10255-024-1067-x","DOIUrl":"10.1007/s10255-024-1067-x","url":null,"abstract":"<div><p>A graph <i>G</i> is a fractional (<i>k, m</i>)-deleted graph if removing any <i>m</i> edges from <i>G</i>, the resulting subgraph still admits a fractional <i>k</i>-factor. Let <i>k</i> ≥ 2 and <i>m</i> ≥ 1 be integers. Denote <span>(lfloor{2m over k}rfloor^{ast}=lfloor{2m over k}rfloor)</span> if <span>(2m over k)</span> is not an integer, and <span>(lfloor{2m over k}rfloor^{ast}=lfloor{2m over k}rfloor - 1)</span> if <span>(2m over k)</span> is an integer. In this paper, we prove that <i>G</i> is a fractional (<i>k, m</i>)-deleted graph if <i>δ</i>(<i>G</i>) ≥ <i>k</i> + <i>m</i> and isolated toughness meets </p><div><div><span>$$Ileft( G right) &gt; left{ {matrix{{3 - {1 over m},,,,,,,,,,,,,,,,,,,,,,,,,} &amp; {{text{if}},k = 2,{text{and}},m ge 3,} cr {k + {{{{leftlfloor {{{2m} over k}} rightrfloor }^*}} over {m + 1 - {{leftlfloor {{{2m} over k}} rightrfloor }^*}}},} &amp; {{text{otherwise}}.,,,,,,,,,,,,,,,,,,,,,} cr } } right.$$</span></div></div><p>Furthermore, we show that the isolated toughness bound is tight.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"252 - 269"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889739","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
Riemann-Hilbert Problem and Multiple High-order Poles Solutions of the Focusing mKdV Equation with Nonzero Boundary Conditions 具有非零边界条件的聚焦mKdV方程的Riemann-Hilbert问题和多高阶解
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1037-3
Zi-yi Wang, Shou-fu Tian, Jin-jie Yang
{"title":"Riemann-Hilbert Problem and Multiple High-order Poles Solutions of the Focusing mKdV Equation with Nonzero Boundary Conditions","authors":"Zi-yi Wang,&nbsp;Shou-fu Tian,&nbsp;Jin-jie Yang","doi":"10.1007/s10255-024-1037-3","DOIUrl":"10.1007/s10255-024-1037-3","url":null,"abstract":"<div><p>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/<i>S</i><sub>11</sub>(<i>k</i>) 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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"234 - 251"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889741","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
Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors 具有自回归误差的多函数线性模型的最小二乘估计
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1143-2
Meng Wang, Ming-liang Shu, Jian-jun Zhou, Si-xin Wu, Min Chen
{"title":"Least Square Estimation for Multiple Functional Linear Model with Autoregressive Errors","authors":"Meng Wang,&nbsp;Ming-liang Shu,&nbsp;Jian-jun Zhou,&nbsp;Si-xin Wu,&nbsp;Min Chen","doi":"10.1007/s10255-024-1143-2","DOIUrl":"10.1007/s10255-024-1143-2","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"84 - 98"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889709","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
A Dive Into the Asymptotic Analysis Theory: a Short Review from Fluids to Financial Markets 渐近分析理论的深入：从流体到金融市场的简短回顾
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-12-26 DOI: 10.1007/s10255-024-1144-1
Gabriele Sbaiz
{"title":"A Dive Into the Asymptotic Analysis Theory: a Short Review from Fluids to Financial Markets","authors":"Gabriele Sbaiz","doi":"10.1007/s10255-024-1144-1","DOIUrl":"10.1007/s10255-024-1144-1","url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":"41 1","pages":"152 - 161"},"PeriodicalIF":0.9,"publicationDate":"2024-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142889713","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
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
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