IF 3.4 2区数学

Applied Mathematics and Computation Pub Date : 2025-09-05 DOI: 10.1016/j.amc.2025.129708

Jia-Hao Syu, Yuh-Dauh Lyuu

{"title":"Trapezoid and trapezoidal prism for the maximum relative drawdown: Probability, crash options pricing, and risk","authors":"Jia-Hao Syu, Yuh-Dauh Lyuu","doi":"10.1016/j.amc.2025.129708","DOIUrl":"10.1016/j.amc.2025.129708","url":null,"abstract":"<div><div>Maximum drawdown (MDD) and maximum relative drawdown (MrDD) are well-known in portfolio management and performance evaluations. They can also form the basis of a stop-loss strategy. But there is no closed-form formula for the probability that the MrDD (MDD) ever reaches some positive threshold over a period of time. This paper focuses on MrDD and employs a random walk to approximate the underlying geometric Brownian motion (GBM) for the price, taking care to match the threshold for faster convergence. Let <span><math><mi>n</mi></math></span> be the number of time steps. This paper proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>1.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoid to calculate the above-mentioned probability. The trapezoid can price the crash option with a digital payoff accurately. This paper further proposes an <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mi>n</mi><mrow><mn>2.5</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span>-sized trapezoidal prism to price the crash option with a resetting payoff accurately and calculate the expected return rate and common risk measures of an MrDD-based stop-loss strategy.</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":"510 ","pages":"Article 129708"},"PeriodicalIF":3.4,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Minimum bisections of graphs without even cycles 无偶环图的最小等分

IF 0.7 3区数学

Discrete Mathematics Pub Date : 2025-09-05 DOI: 10.1016/j.disc.2025.114768

Mengjiao Rao , Qinghou Zeng

{"title":"Minimum bisections of graphs without even cycles","authors":"Mengjiao Rao , Qinghou Zeng","doi":"10.1016/j.disc.2025.114768","DOIUrl":"10.1016/j.disc.2025.114768","url":null,"abstract":"<div><div>A bisection of a graph <em>G</em> is a partition of <span><math><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> into two parts <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> satisfying <span><math><mo>|</mo><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>|</mo><mo>−</mo><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>|</mo><mo>|</mo><mo>≤</mo><mn>1</mn></math></span>, and its size is the number of edges that go across the two parts. The minimum bisection problem asks for a bisection in a given graph minimizing the size which is defined as the bisection width. We present some upper bounds on the bisection width for graphs with a perfect matching and without short even cycles. Let <em>G</em> be an <em>n</em>-vertex <span><math><mo>{</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>,</mo><msub><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msub><mo>}</mo></math></span>-free graph with <em>m</em> edges and a perfect matching. We first show that <em>G</em> has a bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mo>(</mo><mi>n</mi><mo>−</mo><mn>6</mn><mo>)</mo><mo>/</mo><mn>8</mn></math></span>. Together with probabilistic techniques, we show that there is a constant <span><math><mi>ζ</mi><mo>></mo><mn>0</mn></math></span> such that <em>G</em> has bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mi>ζ</mi><mspace></mspace><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msqrt><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow></msqrt></math></span> if <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, and this is tight up to the value of <em>ζ</em>. Furthermore, if <em>G</em> is <span><math><msub><mrow><mi>C</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msub></math></span>-free for some fixed integer <span><math><mi>k</mi><mo>≥</mo><mn>3</mn></math></span> and <span><math><mi>n</mi><mo>≥</mo><mn>8</mn></math></span>, then there is a constant <span><math><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>></mo><mn>0</mn></math></span> such that <em>G</em> has a bisection of size at most <span><math><mi>m</mi><mo>/</mo><mn>2</mn><mo>−</mo><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo><msup><mrow><mi>m</mi></mrow><mrow><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn><mo>)</mo></mrow></msup></math></span>. This is tight up to the value of <span><math><mi>c</mi><mo>(</mo><mi>k</mi><mo>)</mo></math></span> for <span><math><mn>2</mn><mi>k</mi><mo>∈</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>}</mo></math></span>.</div></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":"349 2","pages":"Article 114768"},"PeriodicalIF":0.7,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Convergence analysis of a fast ADI compact finite difference method for two-dimensional semi-linear time-fractional reaction-diffusion equations with weak initial singularity 具有弱初始奇异性的二维半线性时间分数阶反应扩散方程的快速ADI紧致有限差分法的收敛性分析

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-05 DOI: 10.1016/j.camwa.2025.08.028

Priyanka, Sunil Kumar

{"title":"Convergence analysis of a fast ADI compact finite difference method for two-dimensional semi-linear time-fractional reaction-diffusion equations with weak initial singularity","authors":"Priyanka, Sunil Kumar","doi":"10.1016/j.camwa.2025.08.028","DOIUrl":"10.1016/j.camwa.2025.08.028","url":null,"abstract":"<div><div>In this work, considering the solution's weak initial singularity, a rigorous error analysis of a finite difference method for simulating a two-dimensional semi-linear time-fractional reaction-diffusion equation (TFRDE) is presented. The recently introduced ADI method by Kumari and Roul (2024) <span><span>[31]</span></span> for solving a class of linear TFRDEs encounters with problematic mesh parameter adjustments and ignorance of the derivative bounds, potentially rendering the latest methodology deficient and erroneous. The present study aims to design a computationally efficient L1 ADI scheme for semi-linear TFRDEs and provide a comprehensive error analysis. To address intrinsically non-local characteristics of the solution, we employ sum-of-exponential approximation to the singular kernel of time-fractional derivative on a graded mesh with unequal time-steps that yield denser mesh near the initial point. As a result, we effectively mitigate the high storage and computational requirements and return the convergence point to its optimal state. The two spatial variables are treated with a fourth order compact finite difference operator. Moreover, an alternating direction implicit method is utilized to compute the solution of the derived two-dimensional system by splitting it into two separate one-dimensional problems. With the aid of local truncation error estimate and discrete fractional Grönwall inequality, the stability and convergence analysis of the scheme are carried out rigorously through the discrete energy approach. The numerical results corroborate the convergence analysis and highlight the computational efficacy of the numerical scheme. Numerical examples demonstrate the CPU performance of the fast compact ADI method, and presented comparisons distinctly showcases the effectiveness of the graded mesh enhancing convergence order to achieve optimal results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"199 ","pages":"Pages 1-21"},"PeriodicalIF":2.5,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144997863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Stacked pseudo-convergent sequences and polynomial Dedekind domains 叠置伪收敛序列与多项式Dedekind域

IF 1.3 1区数学

Algebra & Number Theory Pub Date : 2025-09-05 DOI: 10.2140/ant.2025.19.1947

Giulio Peruginelli

引用次数: 0

A New Approach for Homogeneity Pursuit in Short Panel Data Analysis 短面板数据分析中同质性追求的新方法

IF 3.7 1区数学

Journal of the American Statistical Association Pub Date : 2025-09-05 DOI: 10.1080/01621459.2025.2552513

Yang Han, Weichi Wu, Wenyang Zhang

引用次数: 0

Boosting AI-Generated Biomedical Images with Confidence through Advanced Statistical Inference 通过先进的统计推断，增强人工智能生成的生物医学图像的信心

IF 3.7 1区数学

Journal of the American Statistical Association Pub Date : 2025-09-05 DOI: 10.1080/01621459.2025.2552510

Zhiling Gu, Shan Yu, Guannan Wang, Lily Wang

引用次数: 0

Effect of host movement on the prevalence of vector-borne diseases. 宿主移动对媒介传播疾病流行的影响。

IF 2.3 4区数学

Journal of Mathematical Biology Pub Date : 2025-09-05 DOI: 10.1007/s00285-025-02254-5

Daozhou Gao, Yuan Lou

{"title":"Effect of host movement on the prevalence of vector-borne diseases.","authors":"Daozhou Gao, Yuan Lou","doi":"10.1007/s00285-025-02254-5","DOIUrl":"10.1007/s00285-025-02254-5","url":null,"abstract":"<p><p>Human movement plays a key role in spreading vector-borne diseases globally. Various spatial models of vector-borne diseases have been proposed and analyzed, mainly focusing on disease dynamics. In this paper, based on a multi-patch Ross-Macdonald model, we study the impact of host migration on the local and global host disease prevalences. Specifically, we find that the local disease prevalence of any patch is bounded by the minimum and maximum disease prevalences of all disconnected patches and establish a weak order-preserving property. For global disease prevalence, we derive its formula at both zero and infinite dispersal rates and compare them under certain conditions, and calculate the right derivative at no dispersal. In the case of two patches, we give two complete classifications of the model parameter space: one is to compare the host disease prevalences with and without host dispersal, and the other is to determine the monotonicity of host disease prevalence with respect to host dispersal rate. Numerical simulations confirm inconsistence between disease persistence and host disease prevalence, as well as between host prevalence and vector prevalence in response to host movement. In general, a more uneven distribution of hosts and vectors in a homogeneous environment leads to lower host prevalence but higher vector prevalence and stronger disease persistence.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":"91 3","pages":"33"},"PeriodicalIF":2.3,"publicationDate":"2025-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12413432/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145001859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Near-Peer Mentoring in Data Science: A Plot for Mutual Growth 数据科学中的近同伴指导：共同成长的情节

IF 1.8 4区数学

American Statistician Pub Date : 2025-09-04 DOI: 10.1080/00031305.2025.2550314

Chiara Sabatti, Qian Zhao

引用次数: 0

On new approximations of a functional equation having monomials 关于具有单项式的泛函方程的新近似

IF 1.2 3区数学

Journal of Mathematical Analysis and Applications Pub Date : 2025-09-04 DOI: 10.1016/j.jmaa.2025.130045

Hamid Khodaei

引用次数: 0

Natural convection resulting from exponentially varying wall heating in a square enclosure 方形围护结构中由指数变化的壁面加热引起的自然对流

IF 2.5 2区数学

Computers & Mathematics with Applications Pub Date : 2025-09-04 DOI: 10.1016/j.camwa.2025.08.024

Nagehan Alsoy-Akgün

{"title":"Natural convection resulting from exponentially varying wall heating in a square enclosure","authors":"Nagehan Alsoy-Akgün","doi":"10.1016/j.camwa.2025.08.024","DOIUrl":"10.1016/j.camwa.2025.08.024","url":null,"abstract":"<div><div>The numerical investigation in this study explores the effects of non-uniform wall heating in a square cavity and its influence on natural convection behavior. A non-uniform heat source is applied to the left vertical wall of the cavity, whereas the right vertical wall is uniformly cooled. The remaining horizontal walls are thermally isolated. The main focus is on the heat transfer and fluid mixing caused by the convection occurring within the cavity. The governing equations are tackled with the help of the Dual Reciprocity Boundary Element Method (DRBEM). In the DRBEM procedure, the fundamental solution of the Laplace equation is used for solving the stream function equation, while for the vorticity transport and temperature equations-initially converted into the modified Helmholtz form-the fundamental solution of the modified Helmholtz equation (MHD) is applied. In order to transform the equations into this form, a relaxation parameter is applied to the corresponding term within the Laplace terms, and a forward difference scheme is employed for the time derivatives. In addition to the benefit of solving smaller-sized systems resulting from the boundary discretization in DRBEM, there is no requirement for an additional time integration scheme for the vorticity transport and energy equations, thus removing any potential stability issues. Calculations were performed for Rayleigh numbers of 10<sup>3</sup>, 10<sup>4</sup>, 10<sup>5</sup> and 10<sup>6</sup> and beta parameters <span><math><mo>−</mo><mn>2</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span>. Obtained results show that the average Nusselt number was found to increase with increasing Ra and <em>β</em> parameter, indicating enhanced convective heat transfer. Thus, it has been concluded that the heater position is quite effective in heat transfer.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"197 ","pages":"Pages 235-258"},"PeriodicalIF":2.5,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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