Pub Date : 2018-12-12DOI: 10.18311/JIMS/2019/22525
R. Yadav
In this article we introduce two categories of Riemannian manifolds. We also study some properties of such categories and compare them with the previously known categories.
本文介绍了黎曼流形的两类。我们还研究了这些范畴的一些性质，并将它们与以前已知的范畴进行了比较。
{"title":"On Some Categories of Riemannian Manifolds","authors":"R. Yadav","doi":"10.18311/JIMS/2019/22525","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22525","url":null,"abstract":"In this article we introduce two categories of Riemannian manifolds. We also study some properties of such categories and compare them with the previously known categories.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48193915","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20142
Leetika Kathuria, M. Raka
In this paper, we give a proof of the generalization of a result of Birch and Swinnerton-Dyer [1956], which has been used by Hans-Gill, Sehmi and authors while obtaining estimates on the classical conjecture of Minkowski on the product of n non-homogeneous linear forms.
{"title":"A Generalization of a Result of Birch and Swinnerton-Dyer","authors":"Leetika Kathuria, M. Raka","doi":"10.18311/JIMS/2018/20142","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20142","url":null,"abstract":"In this paper, we give a proof of the generalization of a result of Birch and Swinnerton-Dyer [1956], which has been used by Hans-Gill, Sehmi and authors while obtaining estimates on the classical conjecture of Minkowski on the product of n non-homogeneous linear forms.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46768289","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20144
Ranjit R. Dhunde, G. L. Waghmare
In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.
{"title":"Solutions of Some Linear Fractional Partial Differential Equations in Mathematical Physics","authors":"Ranjit R. Dhunde, G. L. Waghmare","doi":"10.18311/JIMS/2018/20144","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20144","url":null,"abstract":"In this article, we use double Laplace transform method to find solution of general linear fractional partial differential equation in terms of Mittag-Leffler function subject to the initial and boundary conditions. The efficiency of the method is illustrated by considering fractional wave and diffusion equations, Klein-Gordon equation, Burger’s equation, Fokker-Planck equation, KdV equation, and KdV-Burger’s equation of mathematical physics.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48961487","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20986
R. Sharma, A. B. Singh
Let R be a ring, (M, ≤) a strictly ordered monoid and ω : M → End(R) a monoid homomorphism. The skew generalized power series ring R[[M; ω]] is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev Neumann rings and generalized power series rings. In this paper, we introduce concept of strongly (M, ω)-reversible ring (strongly reversible ring related to skew generalized power series ring R[[M, ω]]) which is a uni ed generalization of strongly reversible ring and study basic properties of strongly (M; ω)-reversible. The Nagata extension of strongly reversible is proved to be strongly reversible if R is Armendariz. Finally, it is proved that strongly reversible ring strictly lies between reduced and reversible ring in the expanded diagram given by Diesl et. al. [7].
{"title":"Unified Extensions of Strongly Reversible Rings and Links with Other Classic Ring Theoretic Properties","authors":"R. Sharma, A. B. Singh","doi":"10.18311/JIMS/2018/20986","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20986","url":null,"abstract":"Let R be a ring, (M, ≤) a strictly ordered monoid and ω : M → End(R) a monoid homomorphism. The skew generalized power series ring R[[M; ω]] is a compact generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomials rings, (skew) Laurent power series rings, (skew) group rings, (skew) monoid rings, Mal'cev Neumann rings and generalized power series rings. In this paper, we introduce concept of strongly (M, ω)-reversible ring (strongly reversible ring related to skew generalized power series ring R[[M, ω]]) which is a uni ed generalization of strongly reversible ring and study basic properties of strongly (M; ω)-reversible. The Nagata extension of strongly reversible is proved to be strongly reversible if R is Armendariz. Finally, it is proved that strongly reversible ring strictly lies between reduced and reversible ring in the expanded diagram given by Diesl et. al. [7].","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45989085","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 : 2018-06-01DOI: 10.18311/JIMS/2018/16383
G. Prasad, R. Dimri
In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].
在新的广义度量空间中，利用二元关系的局部g传递性，建立了压缩映射的重合点定理。在本文的结果中，我们使用了一些标准度量概念的关系理论类比，如连续性、完备性和正则性。这样，我们的结果扩展、修正和推广了最近的一些不动点定理，如Karapinar et al . [J]。不动点理论应用，18(2016)645-671]，Alam和Imdad[不动点理论，已出版]。
{"title":"Coincidence Theorems in New Generalized Metric Spaces Under Locally g-transitive Binary Relation","authors":"G. Prasad, R. Dimri","doi":"10.18311/JIMS/2018/16383","DOIUrl":"https://doi.org/10.18311/JIMS/2018/16383","url":null,"abstract":"In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42055545","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 : 2018-06-01DOI: 10.18311/JIMS/2018/21407
S. K. Upadhyay, M. Chauhan
The characterizations of pseudo-differential operators L(x,D) and H(x,D) associated with the homogeneous symbol l(x; ξ), involving Hankel transformation are investigated by using the theory of n-dimensional Hankel transform.
{"title":"Pseudo-Differential Operators of Homogeneous Symbol Associated with n-Dimensional Hankel Transformation","authors":"S. K. Upadhyay, M. Chauhan","doi":"10.18311/JIMS/2018/21407","DOIUrl":"https://doi.org/10.18311/JIMS/2018/21407","url":null,"abstract":"The characterizations of pseudo-differential operators L(x,D) and H(x,D) associated with the homogeneous symbol l(x; ξ), involving Hankel transformation are investigated by using the theory of n-dimensional Hankel transform.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42552357","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20984
Anuj Kumar, S. Upadhyay
An n-dimensional continuous fractional wavelet transform involving n-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type WM(Rn), WΩ (Cn) and WΩM (Cn). It is shown that continuous fractional wavelet transform, WαψΦ : WM(Rn) → WM(Rn × R+), WαψΦ : WΩ (Cn) → WΩ (Cn × R+) and WαψΦ : WΩM (Cn) → WΩM (Cn × R+) are linear and continuous maps, where Rn and Cn are the usual Euclidean spaces.
{"title":"The Continuous Fractional Wavelet Transform on W-Type Spaces","authors":"Anuj Kumar, S. Upadhyay","doi":"10.18311/JIMS/2018/20984","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20984","url":null,"abstract":"An n-dimensional continuous fractional wavelet transform involving <em>n</em>-dimensional fractional Fourier transform is studied and its properties are obtained on Gel'fand and Shilov spaces of type <em>W<sub>M</sub></em>(R<sup>n</sup>), <em>W</em><sup>Ω</sup> (C<sup>n</sup>) and W<sup>Ω</sup><sub>M</sub> (C<sup>n</sup>). It is shown that continuous fractional wavelet transform, W<sup>α</sup><sub>ψ</sub>Φ : W<sub>M</sub>(R<sup>n</sup>) → W<sub>M</sub>(R<sup>n</sup> × R<sub>+</sub>), W<sup>α</sup><sub>ψ</sub>Φ : W<sup>Ω</sup> (C<sup>n</sup>) → W<sup>Ω</sup> (C<sup>n</sup> × R<sub>+</sub>) and W<sup>α</sup><sub>ψ</sub>Φ : W<sup>Ω</sup><sub>M</sub> (C<sup>n</sup>) → W<sup>Ω</sup><sub>M</sub> (C<sup>n</sup> × R<sub>+</sub>) are linear and continuous maps, where R<sup>n</sup> and C<sup>n</sup> are the usual Euclidean spaces.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47208352","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20145
Prasenjit Bal, S. Bhowmik, D. Gauld
In this paper a new covering notion, called M-star-Lindelof, is introduced and studied. This notion of covering arises from the selection hypothesis SS*D,fin(D, D). The stronger form SS*D,1(D, D) of the selection hypothesis SS*D,fin(D, D) will also be discussed. We then consider weaker versions of these properties involving iterations of the star operator.
{"title":"On Selectively Star-Lindelof Properties","authors":"Prasenjit Bal, S. Bhowmik, D. Gauld","doi":"10.18311/JIMS/2018/20145","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20145","url":null,"abstract":"In this paper a new covering notion, called <em>M-</em>star-Lindelof, is introduced and studied. This notion of covering arises from the selection hypothesis SS*<sub>D,fin</sub>(D, D). The stronger form SS*<sub>D,1</sub>(D, D) of the selection hypothesis SS*<sub>D,fin</sub>(D, D) will also be discussed. We then consider weaker versions of these properties involving iterations of the star operator.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42188835","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20981
Abdul Hassen, Christopher R. Ernst
In this article, we shall consider a generalization of Euler's numbers and polynomials based on modifying the corresponding generating function. We shall prove some recurrence relations, an explicit formula, and multiplicative properties of the generalized numbers.
{"title":"A Simple Generalization of Euler Numbers and Polynomials","authors":"Abdul Hassen, Christopher R. Ernst","doi":"10.18311/JIMS/2018/20981","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20981","url":null,"abstract":"In this article, we shall consider a generalization of Euler's numbers and polynomials based on modifying the corresponding generating function. We shall prove some recurrence relations, an explicit formula, and multiplicative properties of the generalized numbers.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42054474","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 : 2018-06-01DOI: 10.18311/JIMS/2018/20979
Aparna Chaturvedi, Prakriti Rai
There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.
{"title":"Some Properties of Extended Hypergeometric Function and Its Transformations","authors":"Aparna Chaturvedi, Prakriti Rai","doi":"10.18311/JIMS/2018/20979","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20979","url":null,"abstract":"There emerges different extended versions of Beta function and hypergeometric functions containing extra parameters. We obtain some properties of certain functions like extended Generalized Gauss hypergeometric functions, extended Confluent hypergeometric functions including transformation formulas, Mellin transformation for the generalized extended Gauss hypergeometric function in one, two and more variables.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46901598","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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