Pub Date : 2017-07-01DOI: 10.18311/JIMS/2017/15836
G. Andrews
The Bhargava-Adiga summation rivals the 1 ψ 1 -summation of Ramanujan in elegance. This paper is devoted to two applications in the theory of integer partitions leading to partition questions related to Gauss's celebrated three triangle theorem.
{"title":"The Bhargava-Adiga Summation and Partitions","authors":"G. Andrews","doi":"10.18311/JIMS/2017/15836","DOIUrl":"https://doi.org/10.18311/JIMS/2017/15836","url":null,"abstract":"The Bhargava-Adiga summation rivals the 1 ψ 1 -summation of Ramanujan in elegance. This paper is devoted to two applications in the theory of integer partitions leading to partition questions related to Gauss's celebrated three triangle theorem.","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":"48817227","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 correct the contractive condition of Manro and Kang [16] and prove some common fixed point theorems for four faintly compatible mappings using subsequential continuous mappings in Intuitionistic Fuzzy metric spaces. We also provide an example in support of our main result. Our results improve and generalize the results of Manro and Kang [16].
{"title":"Fixed Point Theorems for Faintly Compatible Mappings in Intuitionistic Fuzzy Metric Space","authors":"K. Wadhwa, V. P. Bhardwaj","doi":"10.18311/JIMS/2017/6106","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6106","url":null,"abstract":"In this paper, we correct the contractive condition of Manro and Kang [16] and prove some common fixed point theorems for four faintly compatible mappings using subsequential continuous mappings in Intuitionistic Fuzzy metric spaces. We also provide an example in support of our main result. Our results improve and generalize the results of Manro and Kang [16].","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47141890","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}
Outer and inner measures of a measure μ are defined and used to prove results involving them on a lattice l and its complement l '. Most of the results concern slightly regular measures, and vague measures. Then outer and inner measures associated to two measures μ, ν are then used to prove results involving them on two lattices l 1 , and l 2 where l 1 ⊂ l 2 .
{"title":"Slightly Regular and Vague Measures","authors":"James Camacho","doi":"10.18311/JIMS/2017/7661","DOIUrl":"https://doi.org/10.18311/JIMS/2017/7661","url":null,"abstract":"Outer and inner measures of a measure μ are defined and used to prove results involving them on a lattice l and its complement l '. Most of the results concern slightly regular measures, and vague measures. Then outer and inner measures associated to two measures μ, ν are then used to prove results involving them on two lattices l 1 , and l 2 where l 1 ⊂ l 2 .","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45054216","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}
The purpose of this paper is to establish some fixed point and common fixed point theorems under contractive type conditions involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize some previous works from the existing literature.
{"title":"Some Fixed Point Theorems Under Contractive Type Conditions in Complex Valued Metric Spaces","authors":"G. Saluja","doi":"10.18311/JIMS/2017/6122","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6122","url":null,"abstract":"The purpose of this paper is to establish some fixed point and common fixed point theorems under contractive type conditions involving rational expression in the setting of complex valued metric spaces. The results presented in this paper extend and generalize some previous works from the existing literature.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43705621","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}
Let 1 < s 1 < . . . < s k be integers, and assume that κ ≥ 2 (so s k ≤ 3). Then there exists a local UFD (Unique Factorization Domain) (R,M) such that: (1) Height(M) = s k . (2) R = R' = ∩{VI (V,N) € V j }, where V j (j = 1, . . . , κ) is the set of all of the Rees valuation rings (V,N) of the M-primary ideals such that trd((V I N) I (R I M)) = s j - 1. (3) With V 1 , . . . , V κ as in (2), V 1 ∪ . . . V κ is a disjoint union of all of the Rees valuation rings of allof the M-primary ideals, and each M-primary ideal has at least one Rees valuation ring in each V j .
设1 < s 1 <…< s k为整数，且假设k≥2(因此s k≤3)，则存在一个局部UFD (Unique Factorization Domain) (R,M)使得:(1)Height(M) = s k。(2) R = R ' =∩{VI V (V, N)€j}, V j (j = 1,。， κ)是M个基本理想的所有Rees估值环(V,N)的集合，使得trd((vi N) I (ri M)) = s j - 1。(3)有了v1，…， V κ as in (2)， v1∪…V κ是所有m -初级理想的所有Rees估值环的不相交并，并且每个m -初级理想在每个V j中至少有一个Rees估值环。
{"title":"Integral Closure of Noetherian Domains and Intersections of Rees Valuation Rings, (II)","authors":"Paula Kemp, L. Ratliff, Kishor Shah","doi":"10.18311/jims/2017/6108","DOIUrl":"https://doi.org/10.18311/jims/2017/6108","url":null,"abstract":"Let 1 < s 1 < . . . < s k be integers, and assume that κ ≥ 2 (so s k ≤ 3). Then there exists a local UFD (Unique Factorization Domain) (R,M) such that: (1) Height(M) = s k . (2) R = R' = ∩{VI (V,N) € V j }, where V j (j = 1, . . . , κ) is the set of all of the Rees valuation rings (V,N) of the M-primary ideals such that trd((V I N) I (R I M)) = s j - 1. (3) With V 1 , . . . , V κ as in (2), V 1 ∪ . . . V κ is a disjoint union of all of the Rees valuation rings of allof the M-primary ideals, and each M-primary ideal has at least one Rees valuation ring in each V j .","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43103074","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 propose a fuzzy Simpson's 3/8 th rule with positive coeffcient for solving fuzzy integral based on four equally spaced points. In this way a new direction for the numerical solution of fuzzy integral is suggested. This method is illustrated by solving some examples and comparison made with exact solution and are presented.
{"title":"Fuzzy Simpson's 3/8 th Rule for Integration of Fuzzy Functions","authors":"T. Ramachandran, R. Parimala","doi":"10.18311/JIMS/2017/6617","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6617","url":null,"abstract":"In this paper,we propose a fuzzy Simpson's 3/8 th rule with positive coeffcient for solving fuzzy integral based on four equally spaced points. In this way a new direction for the numerical solution of fuzzy integral is suggested. This method is illustrated by solving some examples and comparison made with exact solution and are presented.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42905271","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}
Let {T n } n ≥ 0 and {T n [1] } n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {T n } n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of T n [1] } n ≥ 1 and the log-balancedness of some sequences involving T n [1] . In addition, we discuss the monotonicity of some sequences related to T n [1] .
{"title":"The Log-Behavior of the Partial Sum for the Tribonacci Numbers","authors":"Feng-Zhen Zhao","doi":"10.18311/JIMS/2017/6115","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6115","url":null,"abstract":"Let {T n } n ≥ 0 and {T n [1] } n ≥ 0 denote the tribonacci sequence and the sequence for the partial sum of {T n } n ≥ 0, respectively. In this paper, we mainly investigate the log-concavity of T n [1] } n ≥ 1 and the log-balancedness of some sequences involving T n [1] . In addition, we discuss the monotonicity of some sequences related to T n [1] .","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48866571","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}
Generally selection principles deal with two collections of families of subsets. In this paper we have introduce some new star-selection principles termed as SS* C,1 ( A, B ) and SS* C,fin ( A, B ) which deal with three collections of subsets or families of subsets of a set. As a initiation of a systemic study, some properties of the new selection principles are investigated which show them to be distinct from existing selection principles.
{"title":"Star-Selection Principle: Another New Direction","authors":"Prasenjit Bal, S. Bhowmik","doi":"10.18311/JIMS/2017/6124","DOIUrl":"https://doi.org/10.18311/JIMS/2017/6124","url":null,"abstract":"Generally selection principles deal with two collections of families of subsets. In this paper we have introduce some new star-selection principles termed as SS* C,1 ( A, B ) and SS* C,fin ( A, B ) which deal with three collections of subsets or families of subsets of a set. As a initiation of a systemic study, some properties of the new selection principles are investigated which show them to be distinct from existing selection principles.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49294519","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}
The manuscript implements Connes-Kreimer Hopf algebraic renormalization of Feynman diagrams and Dubois-Violette type noncommutative differential geometry to discover a new class of differential calculi with respect to infinite formal expansions of Feynman diagrams which are generated by Dyson-Schwinger equations.
{"title":"Application of Deformed Lie Algebras to Non-Perturbative Quantum Field Theory","authors":"Ali Shojaei-Fard","doi":"10.18311/JIMS/2017/5839","DOIUrl":"https://doi.org/10.18311/JIMS/2017/5839","url":null,"abstract":"The manuscript implements Connes-Kreimer Hopf algebraic renormalization of Feynman diagrams and Dubois-Violette type noncommutative differential geometry to discover a new class of differential calculi with respect to infinite formal expansions of Feynman diagrams which are generated by Dyson-Schwinger equations.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46499497","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}
We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form {Δu = α 1 (f (v)) - 1/ u n ) + β 1 (h (u) - 1/ u n ), x € Ω), -Δv = α 2 (g (u)) - 1/ v θ ) + β 2 (k (v) - 1/ u θ ), x € Ω), u = v =0, x € δΩ), where Ω is a bounded smooth domain of R N , η, θ e (0, 1), and α 1 , α 2 , β 1 and β 2 are nonnegative parameters. Here f, g, h, k e C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α 1 + β 1 and α 2 + β 2 large.
{"title":"On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters","authors":"S. H. Rasouli","doi":"10.18311/jims/2017/6110","DOIUrl":"https://doi.org/10.18311/jims/2017/6110","url":null,"abstract":"We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form {Δu = α 1 (f (v)) - 1/ u n ) + β 1 (h (u) - 1/ u n ), x € Ω), -Δv = α 2 (g (u)) - 1/ v θ ) + β 2 (k (v) - 1/ u θ ), x € Ω), u = v =0, x € δΩ), where Ω is a bounded smooth domain of R N , η, θ e (0, 1), and α 1 , α 2 , β 1 and β 2 are nonnegative parameters. Here f, g, h, k e C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α 1 + β 1 and α 2 + β 2 large.","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42889641","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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