Pub Date : 2017-07-01DOI: 10.18311/jims/2017/15570
Abdelkader Hamtat, D. Behloul
The object of this paper is to find all solutions of the dio-phantine equation x 2 + 13 k = y n , in positive integers x, y with n ≥ 3.
本文的目的是在n≥3的正整数x，y中求丢番图方程x2+13k=yN的所有解。
{"title":"On the Diophantine Equation X 2 + 13 K = Y N","authors":"Abdelkader Hamtat, D. Behloul","doi":"10.18311/jims/2017/15570","DOIUrl":"https://doi.org/10.18311/jims/2017/15570","url":null,"abstract":"The object of this paper is to find all solutions of the dio-phantine equation x 2 + 13 k = y n , in positive integers x, y with n ≥ 3.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44419109","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 : 2017-07-01DOI: 10.18311/JIMS/2017/15569
Purnima Pandit
In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.
{"title":"Exact Solution of Semi-linear Fuzzy System","authors":"Purnima Pandit","doi":"10.18311/JIMS/2017/15569","DOIUrl":"https://doi.org/10.18311/JIMS/2017/15569","url":null,"abstract":"In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43755199","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 : 2017-07-01DOI: 10.18311/JIMS/2017/14928
R. Rangarajan, S. Kumar
In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations.
{"title":"Homotopy-laplace Decomposition Method to Solve Nonlinear Differential-difference Equations","authors":"R. Rangarajan, S. Kumar","doi":"10.18311/JIMS/2017/14928","DOIUrl":"https://doi.org/10.18311/JIMS/2017/14928","url":null,"abstract":"In the recent literature, nonlinear differential equations, integro- differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the recent literature, nonlinear dierential equations, integro-differential equations, differential-difference equations and integro-differential-difference equations are studied. Laplace decomposition method and Homotopy analysis method are two powerful decomposition methods employed in the literature to solve above nonlinear problems. In the present paper a new method is proposed motivated by the above two methods to solve both nonlinear differential-difference equations and integro-differential-difference equations.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43946345","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 : 2017-07-01DOI: 10.18311/JIMS/2017/14852
B de Malafosse
Given any sequence a = (a n ) n≥1 of positive real numbers and any set E of complex sequences, we write E a for the set of all sequences y = (y n ) n≥1 such that y/a = (y n /a n ) n≥1 ∈ E; in particular, c a denotes the set of all sequences y such that y/a converges. Let Φ = {c 0 , c, l ∞ , l p , w 0 , w ∞ },(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E a +F' x where F∈{c 0, l p , w 0 , w ∞ } and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r n ) n and we deal with the case when F = F'. Finally we solve the equation E r + (l p ) x = l p with E = c 0 , c, s 1 , or l p (p≥1). These results extend those stated in [10].
{"title":"On New Classes of Sequence Spaces Inclusion Equations Involving the Sets C 0 , C, l P , (1 ≤ P ≤ ∞), W 0 and W ∞","authors":"B de Malafosse","doi":"10.18311/JIMS/2017/14852","DOIUrl":"https://doi.org/10.18311/JIMS/2017/14852","url":null,"abstract":"Given any sequence a = (a n ) n≥1 of positive real numbers and any set E of complex sequences, we write E a for the set of all sequences y = (y n ) n≥1 such that y/a = (y n /a n ) n≥1 ∈ E; in particular, c a denotes the set of all sequences y such that y/a converges. Let Φ = {c 0 , c, l ∞ , l p , w 0 , w ∞ },(p≥1).. In this paper we apply a result stated in [9] and we deal with the class of (SSIE) of the form F ⊂ E a +F' x where F∈{c 0, l p , w 0 , w ∞ } and E, F' ∈ Φ. We then obtain the solvability of the corresponding (SSIE) in the particular case when a = (r n ) n and we deal with the case when F = F'. Finally we solve the equation E r + (l p ) x = l p with E = c 0 , c, s 1 , or l p (p≥1). These results extend those stated in [10].","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48491815","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 : 2017-07-01DOI: 10.18311/JIMS/2017/14851
R. Jana, S. J. Rapeli, A. K. Shukla
Polynomial sets of type zero and its properties together with various applications were studied in the past. In the Rota theory, the polynomials of Sheer A-type zero are called Sheer sequences. In particular, members of the q-analogue of the Sheer class A-type zero can be called q-Sheer sequences. In the present paper, an attempt is made to discuss q-analogues of generalized Sheer polynomials in two variables and their properties.
{"title":"Generalized Sheffer's Classification and Their q-Analague","authors":"R. Jana, S. J. Rapeli, A. K. Shukla","doi":"10.18311/JIMS/2017/14851","DOIUrl":"https://doi.org/10.18311/JIMS/2017/14851","url":null,"abstract":"Polynomial sets of type zero and its properties together with various applications were studied in the past. In the Rota theory, the polynomials of Sheer A-type zero are called Sheer sequences. In particular, members of the q-analogue of the Sheer class A-type zero can be called q-Sheer sequences. In the present paper, an attempt is made to discuss q-analogues of generalized Sheer polynomials in two variables and their properties.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44056218","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 : 2017-07-01DOI: 10.18311/JIMS/2017/14969
Meera H. Chudasama, B. I. Dave
We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.
{"title":"A New Class of Functions Suggested by the Generalized Basic Hypergeometric Function","authors":"Meera H. Chudasama, B. I. Dave","doi":"10.18311/JIMS/2017/14969","DOIUrl":"https://doi.org/10.18311/JIMS/2017/14969","url":null,"abstract":"We introduce an extended generalized basic hypergeometric function rΦs+p in which p tends to infinity together with the summation index. We define the difference operators and obtain infinite order difference equation, for which these new special functions are eigen functions. We derive some properties, as the order zero of this function, differential equation involving a particular hyper-Bessel type operators of infinite order, and contiguous function relations. A transformation formula and an l-analogue of the q-Maclaurin's series are also obtained.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42617690","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 : 2017-07-01DOI: 10.18311/JIMS/2017/15455
Okoh Ufuoma
This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of infinitesimals and limits.
{"title":"Bhaskara's Arithmetic Operation of Division by Zero with Application in the Foundation of the Differential Calculus","authors":"Okoh Ufuoma","doi":"10.18311/JIMS/2017/15455","DOIUrl":"https://doi.org/10.18311/JIMS/2017/15455","url":null,"abstract":"This article is concerned mainly with Bhaskara's arithmetic operation of division by zero. This is the simplest of all for teaching analysis and is the most consistent and philosophical. Some mathematicians have attempted to impugn it, but when I examined their reasonings, I observed that they have done so because they have failed to comprehend the true behavior of zero. In this article I have aimed to clarify and justify Bhaskara's law of impending operations involving zero and furnish hints at the foundations upon which the arithmetic operation of division by zero rests its claims to be preferred to its fashionable rivals, the methods of infinitesimals and limits.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46949649","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}
It is shown that a soft set can be represented as a crisp set of soft elements and a soft group as a ordinary group of soft elements. From this view point it is immediate that soft group share the properties of ordinary group. Also using soft elements the definitions of soft co-sets, soft homomorphism and cyclic soft groups are presented and their properties are studied.
{"title":"Soft Set and Soft Group from Classical View Point","authors":"S. Ray, S. Goldar","doi":"10.18311/JIMS/2017/6123","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6123","url":null,"abstract":"It is shown that a soft set can be represented as a crisp set of soft elements and a soft group as a ordinary group of soft elements. From this view point it is immediate that soft group share the properties of ordinary group. Also using soft elements the definitions of soft co-sets, soft homomorphism and cyclic soft groups are presented and their properties are studied.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47833560","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 : 2017-07-01DOI: 10.18311/JIMS/2017/14850
S. Episkoposian, T. Saghatelyan
In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.
{"title":"Convergence and Integrability of Series with Monotone Decreasing Coefficients by Chrestenson - Levy Systems","authors":"S. Episkoposian, T. Saghatelyan","doi":"10.18311/JIMS/2017/14850","DOIUrl":"https://doi.org/10.18311/JIMS/2017/14850","url":null,"abstract":"In this paper we consider problems of convergence and integrability of series with monotone decreasing coefficients by Chrestenson - Levy systems. In particular we generalize some results, known for classical Walsh systems. Interest in questions arises due to a rapidly developed greedy algorithm in recent years, where in particular the important role played a representation of functions by series with monotone coefficients.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46761217","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}
In this paper we extend the theorem of Walsh and some results proved by R. Bakic to a half plane and complement of an open disk.
本文将沃尔什定理和R. Bakic证明的一些结果推广到开盘的半平面和补上。
{"title":"Generalization of the Grace Theorem","authors":"N. A. Rather, M. Ibrahim","doi":"10.18311/JIMS/2017/6117","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6117","url":null,"abstract":"In this paper we extend the theorem of Walsh and some results proved by R. Bakic to a half plane and complement of an open disk.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47354692","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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