Pub Date : 2018-06-01DOI: 10.18311/JIMS/2018/20971
M. Sahai, R. Sharma, P. Kumari
In this article Jordan regular units have been introduced. In particular, it is proved that for n ≥ 2, the general linear group GL(2; F2n) can be generated by Jordan regular units. Further, presentations of GL(2, F4); GL(2, F8); GL(2, F16) and GL(2, F32) have been obtained having Jordan regular units as generators.
{"title":"Jordan Regular Generators of General Linear Groups","authors":"M. Sahai, R. Sharma, P. Kumari","doi":"10.18311/JIMS/2018/20971","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20971","url":null,"abstract":"In this article Jordan regular units have been introduced. In particular, it is proved that for n ≥ 2, the general linear group GL(2; F<sub>2<sup>n</sup></sub>) can be generated by Jordan regular units. Further, presentations of GL(2, F<sub>4</sub>); GL(2, F<sub>8</sub>); GL(2, F<sub>16</sub>) and GL(2, F<sub>32</sub>) have been obtained having Jordan regular units as generators.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42078691","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/2018/20123
Paula Kemp, L. Ratliff, Kishor Shah
It is shown that, for all local rings (R,M), there is a canonical bijection between the set DO(R) of depth one minimal prime ideals ω in the completion ^R of R and the set HO(R/Z) of height one maximal ideals ̅M' in the integral closure (R/Z)' of R/Z, where Z := Rad(R). Moreover, for the finite sets D := {V*/V* := (^R/ω)', ω ∈ DO(R)} and H := {V/V := (R/Z)'̅M', ̅M' ∈ HO(R/Z)}:
(a) The elements in D and H are discrete Noetherian valuation rings.
{"title":"On Nagata's Result about Height One Maximal Ideals and Depth One Minimal Prime Ideals (I)","authors":"Paula Kemp, L. Ratliff, Kishor Shah","doi":"10.18311/JIMS/2018/20123","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20123","url":null,"abstract":"<p>It is shown that, for all local rings (R,M), there is a canonical bijection between the set <em>DO(R)</em> of depth one minimal prime ideals ω in the completion <em><sup>^</sup>R</em> of <em>R</em> and the set <em>HO(R/Z)</em> of height one maximal ideals <em>̅M'</em> in the integral closure <em>(R/Z)'</em> of <em>R/Z</em>, where <em>Z </em>:<em>= Rad(R)</em>. Moreover, for the finite sets <strong>D</strong> := {<em>V*/V* </em>:<em>= (<sup>^</sup>R/ω)'</em>, ω ∈ DO(R)} and H := {<em>V/V := (R/Z)'<sub><em>̅M'</em></sub>, <em>̅M'</em> ∈ HO(R/Z)</em>}:</p><p>(a) The elements in <strong>D</strong> and <strong>H</strong> are discrete Noetherian valuation rings.</p><p>(b) <strong>D</strong> = {<em><sup>^</sup>V</em> ∈ <strong>H</strong>}.</p>","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47686351","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/2018/20970
Bhanu Gupta, Amit Sharma, S. Srivastava
It is a need of time to use hybrid approach (biological and chemical) to control agriculture pests effectively, economically and safely. Most of the pests and natural enemies in their life history goes through two stages namely immature larva and mature adult. From this biological point of view, we purpose a pest control model with stage structuring in pests and natural enemies in the presence of impulsively released natural enemy and chemical pesticides. Using Floquet theory and small ampli- tude perturbation technique, the local stability of periodic solutions are discussed. The suffcient conditions for the global attractively of pest- extinction periodic solution and permanence of the system are obtained by using comparison technique of differential equations with impulsive effect. At last an extensive simulation is done to verify the theoretical ndings and to see the rich dynamical behavior of the system.
{"title":"Mathematical Study of Hybrid Impulsive Pest Control Model with Stage Structuring","authors":"Bhanu Gupta, Amit Sharma, S. Srivastava","doi":"10.18311/JIMS/2018/20970","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20970","url":null,"abstract":"It is a need of time to use hybrid approach (biological and chemical) to control agriculture pests effectively, economically and safely. Most of the pests and natural enemies in their life history goes through two stages namely immature larva and mature adult. From this biological point of view, we purpose a pest control model with stage structuring in pests and natural enemies in the presence of impulsively released natural enemy and chemical pesticides. Using Floquet theory and small ampli- tude perturbation technique, the local stability of periodic solutions are discussed. The suffcient conditions for the global attractively of pest- extinction periodic solution and permanence of the system are obtained by using comparison technique of differential equations with impulsive effect. At last an extensive simulation is done to verify the theoretical ndings and to see the rich dynamical behavior of the system.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46913094","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/2018/20039
J. Singh, C. Lalmalsawma
The object of the present paper is to study generalized pseudo-projectively recurrent manifolds. Some geometric properties of generalized pseudo-projectively recurrent manifolds have been studied under certain curvature conditions. Finally the existence of generalized pseudo-projectively recurrent manifold is shown by examples.
{"title":"On Generalized Pseudo-Projectively Recurrent Manifolds","authors":"J. Singh, C. Lalmalsawma","doi":"10.18311/JIMS/2018/20039","DOIUrl":"https://doi.org/10.18311/JIMS/2018/20039","url":null,"abstract":"The object of the present paper is to study generalized pseudo-projectively recurrent manifolds. Some geometric properties of generalized pseudo-projectively recurrent manifolds have been studied under certain curvature conditions. Finally the existence of generalized pseudo-projectively recurrent manifold is shown by examples.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41365090","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/2018/21408
S. Saha, Santanu Roy
In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.
{"title":"New Classes of Statistically Pre-Cauchy Triple Sequences of Fuzzy Numbers Defined by Orlicz Function","authors":"S. Saha, Santanu Roy","doi":"10.18311/JIMS/2018/21408","DOIUrl":"https://doi.org/10.18311/JIMS/2018/21408","url":null,"abstract":"In this article, the concept of statistically pre-Cauchy sequence of fuzzy real numbers having multiplicity greater than two defined by Orlicz function is introduced. A characterization of the class of bounded statistically pre-Cauchy triple sequences of fuzzy numbers with the help of Orlicz function is presented. Then a necessary and suffcient condition for a bounded triple sequence of fuzzy real numbers to be statistically pre-Cauchy is proved. Also a necessary and sufficient condition for a bounded triple sequence of fuzzy real numbers to be statistically convergent is derived. Further, a characterization of the class of bounded statistically convergent triple sequences of fuzzy numbers is presented and linked with Cesaro summability.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47350915","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/2018/16260
Ahmed A. Hamoud, K. Ghadle
In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.
{"title":"Modified Adomian Decomposition Method for Solving Fuzzy Volterra-Fredholm Integral Equation","authors":"Ahmed A. Hamoud, K. Ghadle","doi":"10.18311/JIMS/2018/16260","DOIUrl":"https://doi.org/10.18311/JIMS/2018/16260","url":null,"abstract":"In this paper, a modied Adomian decomposition method has been applied to approximate the solution of the fuzzy Volterra-Fredholm integral equations of the first and second Kind. That, a fuzzy Volterra-Fredholm integral equation has been converted to a system of Volterra-Fredholm integral equations in crisp case. We use MADM to find the approximate solution of this system and hence obtain an approximation for the fuzzy solution of the Fuzzy Volterra-Fredholm integral equation. A nonlinear evolution model is investigated. Moreover, we will prove the existence, uniqueness of the solution and convergence of the proposed method. Also, some numerical examples are included to demonstrate the validity and applicability of the proposed technique.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"85 1","pages":"53-69"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47027592","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/2018/16611
Deshna Loonker
The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform. Further, solution obtained is considered in distributional sense by employing integral equations to distribution spaces and as well as using the distributional Dunkl transform for its solution.
{"title":"Solution of Integral Equations by Dunkl and Distributional Dunkl Transform","authors":"Deshna Loonker","doi":"10.18311/JIMS/2018/16611","DOIUrl":"https://doi.org/10.18311/JIMS/2018/16611","url":null,"abstract":"The paper investigates the Dunkl transform and distributional Dunkl transform and the basic properties as convolution. The integral equations such as Volterra integral equation of first and second kind and Abel integral equation are solved by using dunkl transform. Further, solution obtained is considered in distributional sense by employing integral equations to distribution spaces and as well as using the distributional Dunkl transform for its solution.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"85 1","pages":"132-138"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44134610","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/2018/18897
K. Mahesh, Aditya Kolachana, K. Ramasubramanian
While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.
{"title":"An Appraisal of the Greek and Indian Approaches in Determining the Surface Area of a Sphere","authors":"K. Mahesh, Aditya Kolachana, K. Ramasubramanian","doi":"10.18311/JIMS/2018/18897","DOIUrl":"https://doi.org/10.18311/JIMS/2018/18897","url":null,"abstract":"While both the Greek and Indian civilisations have made immense contributions to the development of mathematics, their approaches to various problems widely differ, both in terms of the techniques employed by them and in their scope. We demonstrate this in the context of determining the surface area of a sphere. While the solution to this problem is attributed to Archimedes (3rd cent. BCE) in the Greek tradition, the first surviving proof in the Indian tradition can be found in Bhāskara’s Siddhāntaśiromaṇi (12th cent. CE). In this paper, we discuss the approaches taken by Archimedes and Bhāskara and compare their techniques from a mathematical as well as a pedagogical standpoint.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"85 1","pages":"139-169"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45477975","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/2018/18898
S. Majumder, S. Saha
The purpose of this paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. In this paper, we not only point out some gaps in the proof of the main results in [14], but also rectify the errors and present our main results in a more compact way. Also we exhibit two examples to show that one of the conditions of our result is the best possible.
{"title":"On the Uniqueness of Certain Type of Difference Polynomial Sharing a Small Function","authors":"S. Majumder, S. Saha","doi":"10.18311/JIMS/2018/18898","DOIUrl":"https://doi.org/10.18311/JIMS/2018/18898","url":null,"abstract":"The purpose of this paper is to study the uniqueness problems of certain type of difference polynomial sharing a small function. In this paper, we not only point out some gaps in the proof of the main results in [14], but also rectify the errors and present our main results in a more compact way. Also we exhibit two examples to show that one of the conditions of our result is the best possible.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"85 1","pages":"170-191"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49222313","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/2018/18896
K. Chand, Nidhi Thakur
The present study analyses the effects of Hall current and heat absorption on a viscous, incompressible, optically thick and electrically conducting viscoelastic fluid flow past an infinite vertical porous plate through porous medium in rotating system with variable suction, thermal radiation and chemical reaction in the presence of uniform magnetic field. The perturbation technique is employed to solve the governing nonlinear partial differential equations to obtain the expressions for velocity, temperature and concentration profile. With the help of graphs and tables, the effects of pertinent flow parameters on the velocity, temperature and concentration fields, shear stress, Nusselt number and Sherwood number within the boundary layer are discussed. The results reveal that the observed parameters in rotating system have a noteworthy influence on the ow, heat and mass transfer.
{"title":"Effects of Rotation, Radiation and Hall Current on MHD Flow of A Viscoelastic Fluid Past an Infinite Vertical Porous Plate through Porous Medium with Heat Absorption, Chemical Reaction and Variable Suction","authors":"K. Chand, Nidhi Thakur","doi":"10.18311/JIMS/2018/18896","DOIUrl":"https://doi.org/10.18311/JIMS/2018/18896","url":null,"abstract":"The present study analyses the effects of Hall current and heat absorption on a viscous, incompressible, optically thick and electrically conducting viscoelastic fluid flow past an infinite vertical porous plate through porous medium in rotating system with variable suction, thermal radiation and chemical reaction in the presence of uniform magnetic field. The perturbation technique is employed to solve the governing nonlinear partial differential equations to obtain the expressions for velocity, temperature and concentration profile. With the help of graphs and tables, the effects of pertinent flow parameters on the velocity, temperature and concentration fields, shear stress, Nusselt number and Sherwood number within the boundary layer are discussed. The results reveal that the observed parameters in rotating system have a noteworthy influence on the ow, heat and mass transfer.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"85 1","pages":"16-31"},"PeriodicalIF":0.0,"publicationDate":"2018-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46912469","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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