Pub Date : 2019-08-22DOI: 10.18311/JIMS/2019/23448
A. R. J. Srikanth, R. Kumar, G. Deekshitulu
In this paper a special sub class of rough set algebra (RSA) is identied and coined as core rough set algebra(CRSA). Further we studied the relationship between CRSA and core regular double Stone algebra (CRDSA) introduced in [10]. In fact, a representation theorem for CRDSA in terms of rough sets is established.
{"title":"Core Rough Algebras and its Connection with Core Regular Double Stone Algebra","authors":"A. R. J. Srikanth, R. Kumar, G. Deekshitulu","doi":"10.18311/JIMS/2019/23448","DOIUrl":"https://doi.org/10.18311/JIMS/2019/23448","url":null,"abstract":"In this paper a special sub class of rough set algebra (RSA) is identied and coined as core rough set algebra(CRSA). Further we studied the relationship between CRSA and core regular double Stone algebra (CRDSA) introduced in [10]. In fact, a representation theorem for CRDSA in terms of rough sets is established.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42151099","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 : 2019-01-01DOI: 10.18311/JIMS/2019/22578
V. K. Srivastava, H. Chandra
In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on l p (1 ≤ p < ∞). We prove that no composition operator is hypercyclic on l p . Further, we also prove that C Φ : l p → l p is supercyclic if and only if Φ is injective and Φ n has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.
讨论了l p(1≤p <∞)上复合算子的超环性、超环性和环性。证明了l p上没有复合算子是超循环的。进一步证明了对于任意n∈n，当且仅当Φ是内射且Φ n在n中没有不动点时，C Φ: l p→l p是超循环的，并给出了复合算子循环的充分条件和必要条件。
{"title":"Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on L p Spaces","authors":"V. K. Srivastava, H. Chandra","doi":"10.18311/JIMS/2019/22578","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22578","url":null,"abstract":"In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on l p (1 ≤ p < ∞). We prove that no composition operator is hypercyclic on l p . Further, we also prove that C Φ : l p → l p is supercyclic if and only if Φ is injective and Φ n has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67507676","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 : 2018-12-12DOI: 10.18311/jims/2019/22576
B. Prasad
The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S 1 , S 2 and one commensal species S 3 . Further, S 1 and S 2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. Trajectories of the perturbations over the equilibrium states are illustrated. Further the global stability of the system is established with the aid of suitably constructed Liapunov's function.
{"title":"Stability Analysis of a Three Species Non-linear Eco-system with Restricted Resources","authors":"B. Prasad","doi":"10.18311/jims/2019/22576","DOIUrl":"https://doi.org/10.18311/jims/2019/22576","url":null,"abstract":"The aim of this paper is to introduce the model and the study of a three species non linear ecosystem with restricted resources. In this paper, the system comprises of two species hosts S 1 , S 2 and one commensal species S 3 . Further, S 1 and S 2 are neutral and all the three species posses restricted resources. Commensalism is a symbiotic interaction between two or more populations which live together, and in which only one of the populations (commensalism) is beneted while the other (host) is not effected. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight equilibrium states are established. The system would be stable if all the characteristic roots are negative, in case they are real, and have negative real parts, in case they are complex. Trajectories of the perturbations over the equilibrium states are illustrated. Further the global stability of the system is established with the aid of suitably constructed Liapunov's function.","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":"42329557","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 : 2018-12-12DOI: 10.18311/JIMS/2019/20803
A. Mala, Abhishek Singh, D. Saxena
Theory of Weierstrass transform is ventured to derive properties of the Mexican hat wavelet transform by Pathak et al . [3]. In this paper, distributional Mexican hat wavelet transform is studied and an asymptotic behaviour for the same is established. Further, tauberian result of Mexican hat wavelet transform is derived.
{"title":"Asymptotic Behaviour of Distributional Mexican Hat Wavelet Transform","authors":"A. Mala, Abhishek Singh, D. Saxena","doi":"10.18311/JIMS/2019/20803","DOIUrl":"https://doi.org/10.18311/JIMS/2019/20803","url":null,"abstract":"Theory of Weierstrass transform is ventured to derive properties of the Mexican hat wavelet transform by Pathak et al . [3]. In this paper, distributional Mexican hat wavelet transform is studied and an asymptotic behaviour for the same is established. Further, tauberian result of Mexican hat wavelet transform is derived.","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":"43185752","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 : 2018-12-12DOI: 10.18311/JIMS/2019/22487
S. Singh, V. Yadav
In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.
{"title":"Elliptic WP-Bailey Transform and its Applications","authors":"S. Singh, V. Yadav","doi":"10.18311/JIMS/2019/22487","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22487","url":null,"abstract":"In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.","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":"43386861","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 : 2018-12-12DOI: 10.18311/JIMS/2019/22526
A. Banerjee, M. B. Ahamed
In this paper, with the help of weighted sharing method, we have extended the question of Yang [8] from value sharing to set sharing which in turn have improved the results of Li-Gu [6] and Yi [10, 11] to a large extent.
{"title":"Generalization on the Question of C. C. Yang in the Light of Weighted Shared Sets","authors":"A. Banerjee, M. B. Ahamed","doi":"10.18311/JIMS/2019/22526","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22526","url":null,"abstract":"In this paper, with the help of weighted sharing method, we have extended the question of Yang [8] from value sharing to set sharing which in turn have improved the results of Li-Gu [6] and Yi [10, 11] to a large extent.","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":"46338619","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 : 2018-12-12DOI: 10.18311/JIMS/2019/22577
Reshma Sanjhira, B. V. Nathwani, B. I. Dave
The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.
{"title":"Generalized Mittag-Leffler Matrix Function and Associated Matrix Polynomials","authors":"Reshma Sanjhira, B. V. Nathwani, B. I. Dave","doi":"10.18311/JIMS/2019/22577","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22577","url":null,"abstract":"The Mittag-Leffler function has been found useful in solving certain problems in Science and Engineering. On the other hand, noticing the occurrence of certain matrix functions in Special functions’ theory in general and in Statistics and Lie group theory in particular, we introduce here a matrix analogue of a recently generalized form of Mittag-Leffler function. This function yields the matrix analogues of the Saxena-Nishimoto’s function, Bessel-Maitland function, Dotsenko function and the Elliptic Function. We obtain matrix differential equation and eigen matrix function property for the proposed matrix function. Also, a generalized Konhauser matrix polynomial is deduced and its inverse series relations and generating function are derived.","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":"47417870","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 : 2018-12-12DOI: 10.18311/jims/2019/16122
R. Nirmalkumar, R. Murugesu
In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.
{"title":"Approximate Controllability Results for Neutral Stochastic Differential Equations of Sobolev Type with Unbounded Delay in Hilbert Spaces","authors":"R. Nirmalkumar, R. Murugesu","doi":"10.18311/jims/2019/16122","DOIUrl":"https://doi.org/10.18311/jims/2019/16122","url":null,"abstract":"In this paper, we discuss the approximate controllability of the neutral stochastic differential equations of Sobolev type with unbounded delay in Hilbert Spaces. A set of sufficient conditions are established for the existence and approximate controllability of the mild solutions using Krasnoselskii-Schaefer-type fixed point theorems and stochastic analysis theory. An application involving partial differential equation with unbounded delay is addressed.","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":"46035135","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 : 2018-12-12DOI: 10.18311/jims/2019/22485
K. J. Ingale, J. N. Chaudhari
Since the product of even number of elements of ternary semiring S may not be element of S , the concept of 2-absorbing ideal in S can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal T -ideals in the ternary semiring of non-positive integers.
{"title":"3-Absorbing Principal T -Ideals in the Ternary Semiring of Non-positive Integers","authors":"K. J. Ingale, J. N. Chaudhari","doi":"10.18311/jims/2019/22485","DOIUrl":"https://doi.org/10.18311/jims/2019/22485","url":null,"abstract":"Since the product of even number of elements of ternary semiring S may not be element of S , the concept of 2-absorbing ideal in S can not be defined. In this paper, we introduce the concept of 3-absorbing ideals in a commutative ternary semiring with identity element and obtain characterizations of 3-absorbing principal ideals and 3-absorbing principal T -ideals in the ternary semiring of non-positive integers.","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":"48007882","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 : 2018-12-12DOI: 10.18311/JIMS/2019/22561
K. N. Darji, R. Vyas
For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑ m γ m | ˆ f(m)| β , where 0 < β < 2 and {γ m } is a weighted sequence, is obtained and is extended for two dimensional analogue.
{"title":"Weighted β−absolute Convergence of Single and Double Walsh−Fourier Series of Functions of Φ − ∧ −BV","authors":"K. N. Darji, R. Vyas","doi":"10.18311/JIMS/2019/22561","DOIUrl":"https://doi.org/10.18311/JIMS/2019/22561","url":null,"abstract":"For one variable function of Φ − ∧−bounded variation on [0,1] the sufficient condition for the weighted β−absolute convergence of its Walsh−Fourier series ∑ m γ m | ˆ f(m)| β , where 0 < β < 2 and {γ m } is a weighted sequence, is obtained and is extended for two dimensional analogue.","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":"48545701","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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