WSEAS Transactions on Mathematics最新文献

{"title":"Application of the Bilateral Hybrid Methods to Solving Initial -Value Problems for the Volterra Integro-Differential Equations","authors":"Vagif Ibrahimov, Galina Mehdiyeva, Mehriban Imanova, Davron Aslonqulovich Juraev","doi":"10.37394/23206.2023.22.86","DOIUrl":"https://doi.org/10.37394/23206.2023.22.86","url":null,"abstract":"The many problems of natural sciences are reduced to solving integro-differential equations with variable boundaries. It is known that Vito Volterra, for the study of the memory of Earth, has constructed the integro-differential equations. As is known, there is a class of analytical and numerical methods for solving the Volterra integro-differential equation. Among them, the numerical methods are the most popular. For solving this equation Volterra himself used the quadrature methods. How known in solving the initial-value problem for the Volterra integro-differential equations, increases the volume of calculations, when moving from one point to another, which is the main disadvantage of the quadrature methods. Here the method is exempt from the specified shortcomings and has found the maximum value for the order of accuracy and also the necessary conditions imposed on the coefficients of the constructed methods. The results received here are the development of Dahlquist’s results. Using Dahlquist’s theory in solving initial-value problem for the Volterra integro-differential equation engaged the known scientists as P.Linz, J.R.Sobka, A.Feldstein, A.A.Makroglou, V.R.Ibrahimov, M.N.Imanova, O.S.Budnikova, M.V.Bulatova, I.G.Buova and ets. The scientists taking into account the direct connection between the initial value problem for both ODEs and the Volterra integrodifferential equations, the scientists tried to modify methods, that are used in solving ODEs and applied them to solve Integro-differential equations. Here, proved that some modifications of the methods, which are usually applied to solve initial-value problems for ODEs, can be adapted for solving the Volterra integro-differential equations. Here, for this aim, it is suggested to use a multistep method with the new properties. In this case, a question arises, how one can determine the validity of calculated values. For this purpose, it is proposed here to use bilateral methods. As is known for the calculation of the validity values of the solution of investigated problems, usually have used the predictor-corrector method or to use some bounders for the step-size. And to define the value of the boundaries, one can use the stability region using numerical methods. As was noted above, for this aim proposed to use bilateral methods. For the illustration advantage of bilateral methods is the use of very simple methods, which are called Euler’s explicit and implicit methods. In the construction of the bilateral methods it often becomes necessary to define the sign for some coefficients. By taking this into account, here have defined the sign for some coefficients.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135616812","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}

{"title":"Partial-Sum Matrix and its Rank","authors":"Thitarie Rungratgasame, Punna Charrasangsakul","doi":"10.37394/23206.2023.22.84","DOIUrl":"https://doi.org/10.37394/23206.2023.22.84","url":null,"abstract":"A partial-sum matrix is a matrix whose entries are partial sums of a seires associate with a sequence. The rank of a partial-sum matrix associate with any recurrence sequence can be related to the rank of an associate recurrence matrix, a matrix whose entries are from the same recurrence sequence. In particular, we find ranks of partial-sum matrices associated with arithmetic series and geometric series.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570023","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}

{"title":"Two Different Solution Techniques for an Optimal Control Problem with a Stochastic Switching Time","authors":"Alessandra Buratto, Luca Grosset, Maddalena Muttoni","doi":"10.37394/23206.2023.22.80","DOIUrl":"https://doi.org/10.37394/23206.2023.22.80","url":null,"abstract":"In optimal control theory, strategic decision making requires the consideration of unforeseen disruptions that may arise within a predetermined time horizon. In this context, we introduce the concept of ”stochastic switching time” as a random moment in time at which a sudden, irreversible alteration takes place in the system’s dynamics or in the payoff function. To address optimal decision-making under such uncertain conditions, the literature presents two prominent methodologies: the ”backward” approach and the ”heterogeneous” approach. In this study, we offer an exposition and a comparative analysis of these two approaches. Finally, we present an illustrative example to show, in a detailed context, the advantages and disadvantages associated with these two solution strategies.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"15 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135569434","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}

{"title":"DELTD: An R Package for Kernel Density Estimation using Lifetime Distributions","authors":"Javaria Ahmad Khan, Atif Akbar, B. M. Golam Kibria","doi":"10.37394/23206.2023.22.82","DOIUrl":"https://doi.org/10.37394/23206.2023.22.82","url":null,"abstract":"The R package DELTD is for estimating densities by asymmetrical kernels and calculating MSE. This package is to estimate densities that are free of boundary bias. The major concern of the package is to enhance its usefulness in performing inference regarding stated kernels. For this purpose, some lifetime distributions, i.e. Beta, Birnbaum-Saunders, Erlang, Gamma, and Lognormal are considered here due to their usefulness in life data analysis, where their estimated values for density estimation can also be observed. Tuna data is also presented in this package. By using these kernels, densities will be free of boundary problems. This package is a collection of asymmetrical kernels which belong to the lifetime distribution.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"99 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135617946","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}

{"title":"Notes on subsemigroups of Nm0(+)","authors":"Barbora Batíková, Antonín Jančařík, Petr Němec, Tomáš Kepka","doi":"10.37394/23206.2023.22.85","DOIUrl":"https://doi.org/10.37394/23206.2023.22.85","url":null,"abstract":"The paper summarizes and extends the knowledge of various subsemigroups of N m 0 (+) (= N0(+)m). It creates a theoretical basis for further study in this area and applications in other areas, such as the investigation of context-free languages. The last chapter introduces the notion of pure subsemigroups and presents one construction of a pure subsemigroup to a chosen semisubgroup of N m 0 (+).","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135618042","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}

{"title":"Reduction of Search Space for the Mean Partition Problem","authors":"Jyrko Correa-Morris","doi":"10.37394/23206.2023.22.81","DOIUrl":"https://doi.org/10.37394/23206.2023.22.81","url":null,"abstract":"The contributions of this paper are threefold. First, it conducts a formal comparison of the primary approaches to consensus clustering, using the concepts of agreement and consent. Secondly, it presents theoretical evidence justifying the preference for mean-based methods, which rely on consent, over other agreement-based procedural methods like the q-rule, which are now mostly used as quality evaluators in practice. Thirdly, the paper computes the exact reduction achieved by criteria available in existing literature to assess the quality of mean-based consensus solutions and reduce the search space’s size. Finally, it compiles the regions where consensus functions associated with well-known dissimilarity measures, such as the Mirkin metric and Variation of Information, accumulate their consensus solutions.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135616807","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}

{"title":"Solving the Cauchy Problem Related to the Helmholtz Equation through a Genetic Algorithm","authors":"Jamal Daoudi, Chakir Tajani","doi":"10.37394/23206.2023.22.79","DOIUrl":"https://doi.org/10.37394/23206.2023.22.79","url":null,"abstract":"The Cauchy problem associated with the Helmholtz equation is an ill-posed inverse problem that is challenging to solve due to its instability and sensitivity to noise. In this paper, we propose a metaheuristic approach to solve this problem using Genetic Algorithms in conjunction with Tikhonov regularization. Our approach is able to produce stable, convergent, and accurate solutions for the Cauchy problem, even in the presence of noise. Numerical results on both regular and irregular domains show the effectiveness and accuracy of our approach.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135094927","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}

{"title":"A Study of Generalized Fuzzy Dishkant Implications","authors":"Dimitrios S. Grammatikopoulos, Basil Papadopoulos","doi":"10.37394/23206.2023.22.78","DOIUrl":"https://doi.org/10.37394/23206.2023.22.78","url":null,"abstract":"In this paper, we revisit the generalized Dishkant implications and provide analytical proof that they are a new fuzzy implications’ class that contains the known class of Dishkant implications. Both classes are not always fuzzy implications. For this reason we use the term operations instead of implications in general. Nonetheless, it will be demonstrated that a necessary but not sufficient condition for a generalized Dishkant operation to be a fuzzy implication exists. Furthermore, the intersection of the sets of generalized Dishkant operations and Dishkant operations (respectively, implications) is provided. At the end, we prove a theorem for F- conjugation in GDoperations.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095297","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}

{"title":"Positive Definite Kernels for Partitions","authors":"Jyrko Correa-Morris","doi":"10.37394/23206.2023.22.77","DOIUrl":"https://doi.org/10.37394/23206.2023.22.77","url":null,"abstract":"This paper presents a comprehensive exploration of various families of positive definite kernels for comparing partitions. It not only reviews existing examples from the literature but also introduces novel classes of positive definite kernels. These new classes include kernels based on agreement and ones designed using the concept of hidden variables. The study also focuses on assessing the compatibility of these kernels with structural properties that capture the intrinsic notion of proximity between partitions. Notably, agreement-based kernels are demonstrated to align well with this notion. Moreover, the paper provides two generic procedures for designing hidden-feature-based kernels that also adhere to the specified structural properties.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135095334","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}

{"title":"Conformal Self Mappings of the Fundamental Domains of Analytic Functions and Computer Experimentation","authors":"Andrei-Florin Albişoru, Dorin Ghişa","doi":"10.37394/23206.2023.22.72","DOIUrl":"https://doi.org/10.37394/23206.2023.22.72","url":null,"abstract":"Conformal self mappings of a given domain of the complex plane can be obtained by using the Riemann Mapping Theorem in the following way. Two different conformal mappings φ and ψ of that domain onto one of the standard domains: the unit disc, the complex plane or the Riemann sphere are taken and then ψ −1 ◦ φ is what we are looking for. Yet, this is just a theoretical construction, since the Riemann Mapping Theorem does not offer any concrete expression of those functions. The Möbius transformations are concrete, but they can be used only for particular circular domains. We are proving in this paper that conformal self mappings of any fundamental domain of an arbitrary analytic function can be obtained via Möbius transformations as long as we allow that domain to have slits. Moreover, those mappings enjoy group properties. This is a totally new topic. Although fundamental domains of some elementary functions are well known, the existence of such domains for arbitrary analytic functions has been proved only in our previous publications mentioned in the References section. No other publication exists on this topic and the reference list is complete. We deal here with conformal self mappings of fundamental domains in its whole generality and present sustaining illustrations. Those related to the case of Dirichlet functions represent a real achievement. Computer experimentation with these mappings are made for the most familiar analytic functions.","PeriodicalId":55878,"journal":{"name":"WSEAS Transactions on Mathematics","volume":"540 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":"134957950","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}