Bulletin of Mathematical Sciences and Applications最新文献

{"title":"Solving Fundamental Solution of Non-Homogeneous Heat Equation with Dirichlet Boundary Conditions","authors":"Kahsay Godifey Wubneh","doi":"10.18052/www.scipress.com/bmsa.22.1","DOIUrl":"https://doi.org/10.18052/www.scipress.com/bmsa.22.1","url":null,"abstract":"In this study, we developed a solution of nonhomogeneous heat equation with Dirichlet boundary conditions. moreover, the non-homogeneous heat equation with constant coefficient. since heat equation has a simple form, we would like to start from the heat equation to find the exact solution of the partial differential equation with constant coefficient. to emphasize our main results, we also consider some important way of solving of partial differential equation specially solving heat equation with Dirichlet boundary conditions. the main results of our paper are quite general in nature and yield some interesting solution of non-homogeneous heat equation with Dirichlet boundary conditions and it is used for problems of mathematical modeling and mathematical physics.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114726243","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":"Invariants in Optimal Control: An Exact Solution of the Optimal Stabilization Problem","authors":"G. Kondratiev","doi":"10.18052/www.scipress.com/bmsa.21.9","DOIUrl":"https://doi.org/10.18052/www.scipress.com/bmsa.21.9","url":null,"abstract":"The stabilizing optimal feedback is a function onthe separatrix of stable points of the associated Hamiltoniansystem. Three geometric objects - the symplectic form, Hamiltonianvector field, and Lyapunov function, generating the separatrix - are %intrinsic to the optimal control system. They areinvariantly attached to the optimal control system under canonicaltransformations of the phase space. The separatrix equations can be writtenin terms of these invariants through invariant operations.There is a computable representative of the equivalence class,containing the original system. It is its linear approximation system at the stable point.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130471218","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 Descriptive Time Series Analysis Applied to the Fit of Carbon-Dioxide (CO2)","authors":"C. Nweke, G. Mbaeyi, K. Ojide, O. Elemuche, O. Nwebe","doi":"10.18052/www.scipress.com/bmsa.21.1","DOIUrl":"https://doi.org/10.18052/www.scipress.com/bmsa.21.1","url":null,"abstract":"The study examined the use of population spectrum in determining the nature (deterministic and stochastic) of trend and seasonal component of given time series. It also adopts the use of coefficient of variation approach in the choice of appropriate model in descriptive time series technique. Illustrations were carried out using average monthly atmospheric Carbon dioxide (C02) from 2000-2017 with 2018 used for forecast. Spectrum analysis showed that the descriptive technique of time series is more appropriate for analysis of the study data. The coefficient of variation revealed that the multiplicative model was appropriate for the CO2 data while the forecast and the actual values showed no significant mean difference at 5% level of significance.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127595063","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":"On F-Polynomial, Multiple and Hyper F-Index of some Molecular Graphs","authors":"S. Ghobadi, M. Ghorbaninejad","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.20.36","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.20.36","url":null,"abstract":"A graph can be recognized by a numeric number, a polynomial, a sequence of numbers or a matrix which represent the whole graph, and these representations are aimed to be uniquely defined for that graph. Topological index is a numeric quantity with a graph which characterizes the topology of the graph and is invariant under graph automorphism. In this paper, we compute F-polynomial, Multiple F-index and Hyper F-index for some special graphs.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117283908","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":"Soliton Solutions of Space-Time Fractional-Order Modified Extended Zakharov-Kuznetsov Equation in Plasma Physics","authors":"Muhammad Ali, S. Husnine, Sana Noor, Turgut Ak","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.20.1","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.20.1","url":null,"abstract":"The aim of this article is to calculate the soliton solutions of space-time fractional-order modified extended Zakharov-Kuznetsov equation which is modeled to investigate the waves in magnetized plasma physics. Fractional derivatives in the form of modified Riemann-Liouville derivatives are used. Complex fractional transformation is applied to convert the original nonlinear partial differential equation into another nonlinear ordinary differential equation. Then, soliton solutions are obtained by using (1/G')-expansion method. Bright and dark soliton solutions are also obtain with ansatz method. These solutions may be of significant importance in plasma physics where this equation is modeled for some special physical phenomenon.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129898990","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":"Ablowitz-Kaup-Newel-Segur Formalism and N-Soliton Solutions of Generalized Shallow Water Wave Equation","authors":"Supratim Das","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.20.25","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.20.25","url":null,"abstract":"We apply Ablowitz-Kaup-Newel-Segur hierarchy to derive the generalized shallow waterwave equation and we also investigate N-soliton solutions of the derived equation using InverseScattering Transform method and Hirota’s bilinear method.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"1990 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130885681","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":"Comparative Study of Matlab ODE Solvers for the Korakianitis and Shi Model","authors":"E. Emagbetere, O. Oluwole, T. Salau","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.19.31","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.19.31","url":null,"abstract":"Changing parameters of the Korakianitis and Shi heart valve model over a cardiac cycle has led to the investigation of appropriate numerical technique(s) for good speed and accuracy. Two sets of parameters were selected for the numerical test. For the seven MATLAB ODE solvers, the computed results, computational cost and execution time were observed for varied error tolerance and initial time steps. The results were evaluated with descriptive statistics; the Pearson correlation and ANOVA at α0.05. The dependence of the computed result, accuracy of the method, computational cost and execution time of all the solvers, on relative tolerance and initial time steps were ascertained. Our findings provide important information that can be useful for selecting a MATLAB ODE solver suitable for differential equation with time varying parameters and changing stiffness properties.","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126013845","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":"Computing F-Index of Different Corona Products of Graphs","authors":"Nilanjan De","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.19.24","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.19.24","url":null,"abstract":"F-index of a graph is equal to the sum of cubes of degree of all the vertices of a given graph. Among different products of graphs, as corona product of two graphs is one of most important, in this study, the explicit expressions for F-index of different types of corona product of are obtained. Introduction A topological index is defined as a real valued function, which maps each molecular graph to a real number and is necessarily invariant under automorphism of graphs. There are various topological indices having strong correlation with the physicochemical characteristics and have been found to be useful in isomer discrimination, quantitative structure-activity relationship (QSAR) and structure-property relationship (QSPR). In this article, as a molecular graph, we consider only finite, connected and undirected graphs without any self-loops or multiple edges. Let G be such a graph with vertex set V (G) and edge set E(G) so that the order and size of G is equal to n and m respectively. Let the edge connecting the vertices u and v is denoted by uv. Let, the degree of the vertex v in G is denoted by dG(v), which is the number of edges incident to v, that is, the number of first neighbors of v. Among various degree-based topological indices, the first (M1(G)) and the second (M2(G)) Zagreb index of a G are one of the oldest and most studied topological indices introduced in [13] by Gutman and Trinajstić and defined as","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"127 43","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131746608","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":"Extrapolation Problem for Continuous Time Periodically Correlated Isotropic Random Fields","authors":"I. Golichenko, O. Masyutka, M. Moklyachuk","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.19.1","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.19.1","url":null,"abstract":"","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126283696","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":"Quadratic B-Spline Galerkin Method for Numerical Solutions of Fractional Telegraph Equations","authors":"O. Tasbozan, A. Esen","doi":"10.18052/WWW.SCIPRESS.COM/BMSA.18.23","DOIUrl":"https://doi.org/10.18052/WWW.SCIPRESS.COM/BMSA.18.23","url":null,"abstract":"Letters which were written by two famous mathematicians G.W. Leibnitz and L’Hospital to each other in 1695 can be considered as the beginning of the fractional calculus’ taking part in literature. After that time, a huge contribution has been made for the development of arbitrary order differentiation and integration by a lot of famous mathematicians such as Euler, Laplace, Fourier, Lacroix, Abel, Riemann, Liouville, Caputo [7]. Fractional order differentiation concept helps to state the many physical problems and lead to huge amount of applications [8]. Recently scientists have shown the effectiveness of the fractional order differential equations on expressing the complex events and modelling many physical, engineering phenomenons in their studies [4]. The huge amount of applications on these type equations can bee seen frequently in various fields such as viscoelastic, biology, signal process, electromagnetic, chaos and fractals, traffic system, chemistry, control system, economics, finance and etc. [9]. Riemann-Liouville fractional concept which proposed by two famous mathematicians Riemann and Liouville is composed of fractional integral and fractional derivative. In this concept, in the fractional initial value problems, the initial conditions are comprised of limit values of Rieman-Liouville derivative in the initial point. This situation causes a big problem in solving fractional initial value problems. There isn’t any physical meaning of these initial points. Caputo’s fractional derivative which is presented byM. Caputo in 1967 involves the limit values in the initial points of integer order derivatives with initial values that are given with fractional order equation. Due to this user friendliness of Caputo’s definition, many scientists prefer Caputo’s derivative as fractional derivative operator in many in their studies [4]. In last decades, the importance of fractional order differential equations increased rapidly. Due to this increasement investigating the analytical and numerical solutions of fractional order differential equations(FDEs) becomes an attractive topic for scientists. So a lot of methods are used to obtain analytical and numerical solutions of FDEs such as Laplace transform method [4], power series method [4], finite element method [10, 11], Adomian decomposition method [12], variational iteration method [13], differential transform method [14], homotopy perturbation method [15], homotopy analysis method [16, 17], finite difference methods [18], and etc. Finite elements method which is used commonly in various fields of physics and engineering, first arise in 1960. Argyris, Clough and Zienkiewicz made contribution to this method [19]. After the development of computer technology in recent 50 years, this method has been occupied in an important place in solving many problems which arise in physics and engineering [20]. Bulletin of Mathematical Sciences and Applications Submitted: 2016-09-21 ISSN: 2278-9634, Vol. 18, pp ","PeriodicalId":252632,"journal":{"name":"Bulletin of Mathematical Sciences and Applications","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121151944","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}