Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/15896
S. Velmurugan, N. Subramanian
In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ− Cauchy triple sequences.
{"title":"Bernstein Operator of Rough λ-statistically and ρ Cauchy Sequences Convergence on Triple Sequence Spaces","authors":"S. Velmurugan, N. Subramanian","doi":"10.18311/JIMS/2018/15896","DOIUrl":"https://doi.org/10.18311/JIMS/2018/15896","url":null,"abstract":"In this article, using the concept of natural density, we introduce the notion of Bernstein polynomials of rough λ−statistically and ρ−Cauchy triple sequence spaces. We define the set of Bernstein polynomials of rough statistical limit points of a triple sequence spaces and obtain to λ−statistical convergence criteria associated with this set. We examine the relation between the set of Bernstein polynomials of rough λ−statistically and ρ− Cauchy triple sequences.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42452557","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/14940
Hongmei Han
In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H , construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.
{"title":"Sturm-Liouville Problems with Discontinuities at Two Interior Points","authors":"Hongmei Han","doi":"10.18311/JIMS/2018/14940","DOIUrl":"https://doi.org/10.18311/JIMS/2018/14940","url":null,"abstract":"In this paper, we study the Sturm-Liouville operator with eigenparameter-dependent boundary conditions and transmission conditions at two interior points. We establish a new operator A associated with the problem, prove the operator A is self-adjoint in an appropriate space H , construct the basic solutions and investigate some properties of the eigenvalues and corresponding eigenfunctions, then obtain asymptotic formulas for the eigenvalues and eigenfunctions, its Green function and the resolvent operator are also involved.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44035540","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/11049
K. G. Mirajkar, Bhagyashri R. Doddamani
In this paper, we determine the first four types of atom bond connectivity indices of Jahangir graphs.
本文确定了Jahangir图的前四类原子键连接性指数。
{"title":"Atom Bond Connectivity Indices of Jahangir Graphs (J n,m )","authors":"K. G. Mirajkar, Bhagyashri R. Doddamani","doi":"10.18311/JIMS/2018/11049","DOIUrl":"https://doi.org/10.18311/JIMS/2018/11049","url":null,"abstract":"In this paper, we determine the first four types of atom bond connectivity indices of Jahangir graphs.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46106888","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/17945
Rajesh V. Savalia, B. I. Dave
The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γ p and Pochhammer p-symbol (x) n,p due to Rafael Diaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain p -deformed combinatorial identities are illustrated in the last section.
{"title":"p-Deformation of a General Class of Polynomials and its Properties","authors":"Rajesh V. Savalia, B. I. Dave","doi":"10.18311/JIMS/2018/17945","DOIUrl":"https://doi.org/10.18311/JIMS/2018/17945","url":null,"abstract":"The work incorporates the extension of the Srivastava-Pathan’s generalized polynomial by means of p-generalized gamma function: Γ p and Pochhammer p-symbol (x) n,p due to Rafael Diaz and Eddy Pariguan [Divulgaciones Mathematicas Vol.15, No. 2(2007), pp. 179-192]. We establish the inverse series relation of this extended polynomial with the aid of general inversion theorem. We also obtain the generating function relations and the differential equation. Certain p -deformed combinatorial identities are illustrated in the last section.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44654201","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/14929
Varsha Karanjgaokar
In this paper we estimate the rate of convergence of wavelet expansion of functions f ∈ L p , 1 ≤ p ≤ ∞ at a point x. The pointwise and L p results were obtained by Kelly, S. [4]. Our result generalizes her result.
{"title":"On the Rate of Convergence of Wavelet Expansions","authors":"Varsha Karanjgaokar","doi":"10.18311/JIMS/2018/14929","DOIUrl":"https://doi.org/10.18311/JIMS/2018/14929","url":null,"abstract":"In this paper we estimate the rate of convergence of wavelet expansion of functions f ∈ L p , 1 ≤ p ≤ ∞ at a point x. The pointwise and L p results were obtained by Kelly, S. [4]. Our result generalizes her result.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67507542","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/17869
S. Debnath, D. Rakshit
In this paper we have established some basic properties of rough convergence for fuzzy number sequences. Also introduce the set of rough limit points of a sequence of fuzzy number using α-level set and prove some results associated with this set.
{"title":"On Rough Convergence of Fuzzy Numbers Based on α-Level Sets","authors":"S. Debnath, D. Rakshit","doi":"10.18311/JIMS/2018/17869","DOIUrl":"https://doi.org/10.18311/JIMS/2018/17869","url":null,"abstract":"In this paper we have established some basic properties of rough convergence for fuzzy number sequences. Also introduce the set of rough limit points of a sequence of fuzzy number using α-level set and prove some results associated with this set.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43118032","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/14953
B. M. Najmabadi, T. L. Shateri
In this paper we introduce the new concept of 2-inner product map that takes values on locally C* -algebras. Then we prove some results on Schwarz inequality, the polarization identity and related important properties.
{"title":"2-Inner Product which Takes Values in a Locally C* - Algebras","authors":"B. M. Najmabadi, T. L. Shateri","doi":"10.18311/JIMS/2018/14953","DOIUrl":"https://doi.org/10.18311/JIMS/2018/14953","url":null,"abstract":"In this paper we introduce the new concept of 2-inner product map that takes values on locally C* -algebras. Then we prove some results on Schwarz inequality, the polarization identity and related important properties.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43350891","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}
Pub Date : 2018-01-04DOI: 10.18311/JIMS/2018/15930
Mohammad Qasim Mann’a
Here we introduce some new results which are relative to the concept of topological monoid-groupoid and prove that the category of topological monoid coverings of X is equivalent to the category covering groupoids of the monoid-groupoid π 1 (X). Also, it is shown that the monoid structure of monoid-groupoid lifts to a universal covering groupoid.
{"title":"Monoid and Topological Groupoid","authors":"Mohammad Qasim Mann’a","doi":"10.18311/JIMS/2018/15930","DOIUrl":"https://doi.org/10.18311/JIMS/2018/15930","url":null,"abstract":"Here we introduce some new results which are relative to the concept of topological monoid-groupoid and prove that the category of topological monoid coverings of X is equivalent to the category covering groupoids of the monoid-groupoid π 1 (X). Also, it is shown that the monoid structure of monoid-groupoid lifts to a universal covering groupoid.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43962758","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}
Pub Date : 2018-01-04DOI: 10.18311/jims/2018/18900
F. Kudayeva, Arslan A. Kaigermazov, Elizaveta K. Edgulova, M. M. Tkhabisimova, A. R. Bechelova
Free boundary problems are considered to be the most difcult and the least researched in the eld of mathematical physics. The present article is concerned with the research of the following issue: treatment of one-dimensional free boundary problems. The treated problem contains a nonlinear evolutionary equation, which occurs within the context of mathematical modeling of cryosurgery problems. In the course of the research, an integral expression has been obtained. The obtained integral expression presents a general solution to the non-homogeneous evolutionary equation which contains the functions that represent simple-layer and double-layer heat potential density. In order to determine the free boundary and the density of potential a system of nonlinear, the second kind of Fredholm integral equations was obtained within the framework of the given work. The treated problem has been reduced to the system of integral equations. In order to reduce the problem to the integral equation system, a method of heat potentials has been used. In the obtained system of integral equations instead of K(ξ; x; τ - t) in case of Dirichlet or Neumann conditions the corresponding Greens functions G(ξ; x; τ - t) or N(ξ; x; τ - t) have been applied. Herewith the integral expression contains fewer densities, but the selection of arbitrary functions is reserved. The article contains a number of results in terms of building a mathematical model of cooling and freezing processes of biological tissue, as well as their effective solution development.
{"title":"Heat Potentials Method in the Treatment of One-Dimensional Free Boundry Problems Applied in Cryomedicine","authors":"F. Kudayeva, Arslan A. Kaigermazov, Elizaveta K. Edgulova, M. M. Tkhabisimova, A. R. Bechelova","doi":"10.18311/jims/2018/18900","DOIUrl":"https://doi.org/10.18311/jims/2018/18900","url":null,"abstract":"Free boundary problems are considered to be the most difcult and the least researched in the eld of mathematical physics. The present article is concerned with the research of the following issue: treatment of one-dimensional free boundary problems. The treated problem contains a nonlinear evolutionary equation, which occurs within the context of mathematical modeling of cryosurgery problems. In the course of the research, an integral expression has been obtained. The obtained integral expression presents a general solution to the non-homogeneous evolutionary equation which contains the functions that represent simple-layer and double-layer heat potential density. In order to determine the free boundary and the density of potential a system of nonlinear, the second kind of Fredholm integral equations was obtained within the framework of the given work. The treated problem has been reduced to the system of integral equations. In order to reduce the problem to the integral equation system, a method of heat potentials has been used. In the obtained system of integral equations instead of K(ξ; x; τ - t) in case of Dirichlet or Neumann conditions the corresponding Greens functions G(ξ; x; τ - t) or N(ξ; x; τ - t) have been applied. Herewith the integral expression contains fewer densities, but the selection of arbitrary functions is reserved. The article contains a number of results in terms of building a mathematical model of cooling and freezing processes of biological tissue, as well as their effective solution development.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46322116","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}
Pub Date : 2018-01-01DOI: 10.18311/JIMS/2018/16577
K. Izuchi, Y. Izuchi
The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.
利用强算子拓扑在有界调和函数空间上的加权复合算子空间中确定了路径连通分量。
{"title":"Path Connected Components in the Spaces of Weighted Composition Operators with the Strong Operator Topology II","authors":"K. Izuchi, Y. Izuchi","doi":"10.18311/JIMS/2018/16577","DOIUrl":"https://doi.org/10.18311/JIMS/2018/16577","url":null,"abstract":"The path connected components are determined in the space of weighted composition operators on the space of bounded harmonic functions with the strong operator topology.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67507603","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}
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