WSEAS Transactions on Mathematics最新文献_第5页

On a Derivative-free Optimization Approach to Some Problems of Civil Engineering 土木工程若干问题的无导数优化方法

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI: 10.37394/23206.2023.22.71

Jiří Vala, Petra Jarošová

{"title":"On a Derivative-free Optimization Approach to Some Problems of Civil Engineering","authors":"Jiří Vala, Petra Jarošová","doi":"10.37394/23206.2023.22.71","DOIUrl":"https://doi.org/10.37394/23206.2023.22.71","url":null,"abstract":"Development of advanced materials and structures for civil engineering, due to the requirements of green and sustainable building, including the reduction of energy consumption and the balance between occupant comfort and environmental friendliness, needs proper analysis of related physical, chemical, etc. processes, whose mathematical description leads to direct, sensitivity and inverse initial and boundary value problems for nonlinear partial differential equations, analysed numerically using finite element, difference and similar techniques. Design optimization requires to implement a set of additional variable parameters into all related computations, which is very expensive or quite impossible in most cases. Thus realistic computational strategies work with the minimizations of some cost functions with unknown parameters using certain kind of numerical differentiation, like quasi-Newton, inexact Newton or conjugate gradient methods, some derivative-free approach, or, as a much-favoured alternative, some heuristic soft-computing algorithm. A reasonable compromise seems to be the exploitation of an algorithm coming from the non-gradient Nelder-Mead simplex approach. In this paper, referring to the experience with i) the direct problem of thermal design of a residential building and ii) the inverse problem of identification of material characteristics as thermal conductivity and diffusivity from well-advised laboratory experiments, after several remarks to the history and progress of the Nelder-Mead method and its improvements, we shall demonstrate some convergence properties of such approach, regardless of the highly cited evaluation of the original Nelder-Mead algorithm: “Mathematicians hate it because you cannot prove convergence; engineers seem to love it because it often works.”","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Smooth Homotopy 4-Sphere 光滑同伦4球

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI: 10.37394/23206.2023.22.76

Akio Kawauchi

引用次数: 3

A Special Interval Newton Step for Solving Nonlinear Equations 求解非线性方程的特殊区间牛顿步

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI: 10.37394/23206.2023.22.74

Ioannis A. Nikas

{"title":"A Special Interval Newton Step for Solving Nonlinear Equations","authors":"Ioannis A. Nikas","doi":"10.37394/23206.2023.22.74","DOIUrl":"https://doi.org/10.37394/23206.2023.22.74","url":null,"abstract":"The problem of finding the zeros of a nonlinear equation has been extensively and thoroughly studied. Point methods constitute a significant and extensive category of techniques, allowing for the efficient finding of zeros with arbitrary precision under specific conditions. However, the limitation of these methods is that they typically yield a single zero. An alternative approach employs Interval Analysis, leveraging its properties to provide reliable and with certainty inclusions of all zeros within a given search interval. Interval methods, such as the Interval Newton method, exhibit quadratic convergence to the corresponding inclusions when monotonicity and simple zeros exist. Nonetheless, there exist pathological cases, like the existence of multiple zeros, where the obtained inclusions cannot be bounded with arbitrary precision, necessitating the adoption of bisection schemes to refine the search interval. These schemes not only increase computational time and cost but also result in a higher number of enclosures, enclosing sometimes the same zero more than once. The main objective of this work is to enhance the applicability of Interval Newton method in cases where no efficient alternative are available. Thus, in this paper, the Interval Newton method is studied and an adjusted perturbation technique is proposed to address the cases where multiple zeros exist. In particular, the given function is vertically shifted. Then, the Interval Newton operator is applied once to this shifted function. The resulting enclosures are then used to efficiently partition the search interval. The successful application of the Interval Newton method is expected to improve overall performance and reduce reliance on bisection schemes. Experimental results on a set of problems demonstrate the effectiveness of the proposed technique.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134957817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Asset Pricing Model and Economic Activity of Firms 资产定价模型与企业经济活动

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI: 10.37394/23206.2023.22.75

Pithak Srisuksai

引用次数: 0

Investigation of Affine Factorable Surfaces in Pseudo-Galilean Space 伪伽利略空间中仿射可因子曲面的研究

WSEAS Transactions on Mathematics Pub Date : 2023-09-26 DOI: 10.37394/23206.2023.22.73

Mohamed Saad, Hossam Abdel-Aziz, Haytham Ali

引用次数: 0

Uncertain Random Block Replacement Policy with No Replacement at Failure 失效不替换的不确定随机块替换策略

WSEAS Transactions on Mathematics Pub Date : 2023-09-20 DOI: 10.37394/23206.2023.22.69

Yury Alekseevich Malyukov, Alexey Olegovich Nedosekin, Zinaida Igorevna Abdoulaeva, Alexey Viktorovich Silakov

{"title":"Uncertain Random Block Replacement Policy with No Replacement at Failure","authors":"Yury Alekseevich Malyukov, Alexey Olegovich Nedosekin, Zinaida Igorevna Abdoulaeva, Alexey Viktorovich Silakov","doi":"10.37394/23206.2023.22.69","DOIUrl":"https://doi.org/10.37394/23206.2023.22.69","url":null,"abstract":"The classic block replacement problem assumes the lifetime of component as a random variable, and the downtime cost caused by failed component is a constant. However, when a new type of unit is used in a block replacement system, its lifetime is indeterminate and its distribution cannot be obtained by probability theory due to the lack of historical operational data. And if the component is not replaced immediately when it fails, the downtime cost per unit time is not fixed but always effected by some stochastic factors such as market. Thus, uncertainty and randomness coexist in a block replacement system of new components. In this paper, the lifetime of the component is regarded as an uncertain variable and the downtime cost per unit time is considered as a random variable, and an uncertain random programming model of block replacement with no replacement at failure is developed for a system composed of new type of components, and the formulated model aims to find an optimal replacement time to minimize the expected cost rate in one replacement cycle. An implicit solution of the optimal replacement time is obtained, and the condition ensuring the existence and uniqueness of the optimal replacement time is given. Finally, a numerical example is presented to prove feasibility of the proposed model.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the properties of Generalized Jacobsthal and Generalized Jacobsthal-Lucas sequences 关于广义Jacobsthal和广义Jacobsthal- lucas序列的性质

WSEAS Transactions on Mathematics Pub Date : 2023-09-20 DOI: 10.37394/23206.2023.22.70

Sukanya Somprom, Piyanut Puangjumpa, Aruntida Sichiangha

引用次数: 0

On Some New Uncertain Spaces using Generalized Difference Operator 用广义差分算子讨论一些新的不确定空间

WSEAS Transactions on Mathematics Pub Date : 2023-09-13 DOI: 10.37394/23206.2023.22.68

Dowlath Fathima

引用次数: 0

Investigating Stochastic Dynamics of the Gilpin-Ayala Model in Dispersed Polluted Environments 分散污染环境中Gilpin-Ayala模型的随机动力学研究

WSEAS Transactions on Mathematics Pub Date : 2023-09-13 DOI: 10.37394/23206.2023.22.67

A. Nait Brahim, B. Harchaoui, S. Boutouil, M. El Idrissi, S. Aznague, A. Settati, A. Lahrouz, M. El Jarroudi

{"title":"Investigating Stochastic Dynamics of the Gilpin-Ayala Model in Dispersed Polluted Environments","authors":"A. Nait Brahim, B. Harchaoui, S. Boutouil, M. El Idrissi, S. Aznague, A. Settati, A. Lahrouz, M. El Jarroudi","doi":"10.37394/23206.2023.22.67","DOIUrl":"https://doi.org/10.37394/23206.2023.22.67","url":null,"abstract":"This research delves into the analysis of a stochastic Gilpin-Ayala model operating within an anxious environment, encompassing the phenomenon of diffusion between two distinct and specified geographical regions that are the subjects of investigation. Initially, we rigorously formulate the essential criteria for ascertaining the survival or extinction of the species. Furthermore, we furnish empirical substantiation for the presence of a stable distribution. A significant milestone of our study involves the discernment and comprehensive delineation of the pivotal determinants that intricately regulate extinction dynamics and persistence within the framework of pollution parameters. This outcome underscores the pronounced impact of pollution on ecological dynamics and affirms the necessity of incorporating pollution parameters into the purview of environmental investigations. This revelation demonstrates that in the absence of pollution, the conventional criteria governing extinction and persistence closely parallel those witnessed in unpolluted environments, thus validating the robustness of our mathematical analysis. A series of numerical depictions are introduced to validate and provide empirical support for the acquired results.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of the Structure of Chaotic Solutions of Differential Equations 微分方程混沌解的结构分析

WSEAS Transactions on Mathematics Pub Date : 2023-07-27 DOI: 10.37394/23206.2023.22.66

Maryna Belova, Volodymyr Denysenko, S. Kartashova, V. Kotlyar, Stanislav Mikhailenko

引用次数: 0