The main objective of this study is to find novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation, which occurs in unidirectional water wave propagation. The generalized Rosenau-Kawaha...The main objective of this study is to find novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation, which occurs in unidirectional water wave propagation. The generalized Rosenau-Kawahara-RLW equation comprises three equations Rosenau equation, Kawahara equation, RLW equation and also p-th order nonlinear term. All these equations describe the wave phenomena especially the wave-wave and wave-wall interactions in shallow and narrow channel waters. The auxiliary equation method is employed to get the analytical results.展开更多
This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouvill...This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.展开更多
In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes c...In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in Ⅱ. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88： 43-57]. We prove that these classes of regular graphs have constant metric dimension.展开更多
In today’s educational environment,educators face challenges in manually crafting various documents,leading to inefficiencies and time constraints.To address this,our study introduces a novel software solution design...In today’s educational environment,educators face challenges in manually crafting various documents,leading to inefficiencies and time constraints.To address this,our study introduces a novel software solution designed to automate document creation and standardize processing in academic institutions.Leveraging Python and LaTeX technologies,particularly the PyLaTeX library,the application streamlines document workflows by generating templated PDFs.Through user input,the application automates document structure and formatting,reducing preparation time and effort.Backed by Python,LaTeX,and PyLaTeX,alongside ElectronJS,JavaScript,and Bootstrap for the frontend,our research encompasses a comprehensive methodology,including literature review,software design,experimentation,and efficiency evaluation.Mathematical analysis underscores the application’s effectiveness,demonstrating significant time savings and productivity enhancements.By improving document workflows,our research contributes to advancing educational practices and lays the groundwork for future investigations in this domain.展开更多
Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,...Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.展开更多
文摘The main objective of this study is to find novel wave solutions for the time-fractional generalized Rosenau-Kawahara-RLW equation, which occurs in unidirectional water wave propagation. The generalized Rosenau-Kawahara-RLW equation comprises three equations Rosenau equation, Kawahara equation, RLW equation and also p-th order nonlinear term. All these equations describe the wave phenomena especially the wave-wave and wave-wall interactions in shallow and narrow channel waters. The auxiliary equation method is employed to get the analytical results.
基金partially supportedby Ministerio de Ciencia e Innovacion-SPAINFEDER,project MTM2010-15314supported by the Ministry of Science and Education of the Republic of Kazakhstan through the Project No.0713 GF
文摘This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.
基金supported by National University of Sceinces and Technology (NUST),Islamabadgrant of Higher Education Commission of Pakistan Ref.No:PMIPFP/HRD/HEC/2011/3386support of Slovak VEGA Grant 1/0130/12
文摘In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in Ⅱ. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88： 43-57]. We prove that these classes of regular graphs have constant metric dimension.
文摘In today’s educational environment,educators face challenges in manually crafting various documents,leading to inefficiencies and time constraints.To address this,our study introduces a novel software solution designed to automate document creation and standardize processing in academic institutions.Leveraging Python and LaTeX technologies,particularly the PyLaTeX library,the application streamlines document workflows by generating templated PDFs.Through user input,the application automates document structure and formatting,reducing preparation time and effort.Backed by Python,LaTeX,and PyLaTeX,alongside ElectronJS,JavaScript,and Bootstrap for the frontend,our research encompasses a comprehensive methodology,including literature review,software design,experimentation,and efficiency evaluation.Mathematical analysis underscores the application’s effectiveness,demonstrating significant time savings and productivity enhancements.By improving document workflows,our research contributes to advancing educational practices and lays the groundwork for future investigations in this domain.
基金Supported by Slovak VEGA Grant 1/0130/12Higher Education Commission Pakistan (Grant No.HEC(FD)/2007/555)the Ministry of Education of the Czech Republic (Grant No. MSM6198910027)
文摘Let G = （V, E） be a finite, simple and undirected graph with p vertices and q edges. An （a, d）-vertex-antimagic total labeling of G is a bijection f from V（G） t2 E（G） onto the set of consecutive integers 1, 2,... ,p ＋ q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f（x） assigned to the vertex x together with all values f（xy） assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1,..., r ＋ 1.
