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Derivations on Banach algebras Banach代数上的导数
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-04-26 DOI: 10.1155/S0161171203209108
S. Hejazian, S. Talebi
{"title":"Derivations on Banach algebras","authors":"S. Hejazian, S. Talebi","doi":"10.1155/S0161171203209108","DOIUrl":"https://doi.org/10.1155/S0161171203209108","url":null,"abstract":"Let D be a derivation on a Banach algebra; by using the operator D2, we give necessary and sufficient conditions for the separating ideal of D to be nilpotent. We also introduce an ideal M(D) and apply it to find out more equivalent conditions for the continuity of D and for nilpotency of its separating ideal.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203209108","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64983025","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}
引用次数: 33
An algebraic framework of weighted directed graphs 加权有向图的代数框架
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-03-15 DOI: 10.1155/S0161171203302170
P. Leroux
{"title":"An algebraic framework of weighted directed graphs","authors":"P. Leroux","doi":"10.1155/S0161171203302170","DOIUrl":"https://doi.org/10.1155/S0161171203302170","url":null,"abstract":"We show that an algebraic formulation of weighted directed graphs \u0000leads to introducing a k-vector space equipped with two \u0000coproducts Δ and Δ˜ verifying the so-called \u0000coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is \u0000called an L-coalgebra. Explicit examples of such \u0000spaces are constructed and links between graph theory and \u0000coassociative coalgebras are given.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203302170","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64989568","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}
引用次数: 24
On nilpotent filiform Lie algebras of dimension eight 关于八维幂零丝形李代数
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-03-01 DOI: 10.1155/S016117120311201X
P. Barbari, A. Kobotis
{"title":"On nilpotent filiform Lie algebras of dimension eight","authors":"P. Barbari, A. Kobotis","doi":"10.1155/S016117120311201X","DOIUrl":"https://doi.org/10.1155/S016117120311201X","url":null,"abstract":"The aim of this paper is to determine both the Zariski constructible set of characteristically nilpotent filiform Lie algebras g of dimension 8 and that of the set of nilpotent filiform Lie algebras whose group of automorphisms consists of unipotent automorphisms, in the variety of filiform Lie algebras of dimension 8 over C.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S016117120311201X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64974496","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}
引用次数: 0
ON HILL'S EQUATION WITH A DISCONTINUOUS COEFFICIENT 带不连续系数的希尔方程
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-02-17 DOI: 10.1155/S016117120320209X
I. Karaca
{"title":"ON HILL'S EQUATION WITH A DISCONTINUOUS COEFFICIENT","authors":"I. Karaca","doi":"10.1155/S016117120320209X","DOIUrl":"https://doi.org/10.1155/S016117120320209X","url":null,"abstract":"We research the asymptotic formula for the lengths of the \u0000instability intervals of the Hill's equation with coefficients \u0000 q ( x ) and r ( x ) , where q ( x ) is piecewise continuous and \u0000 r ( x ) has a piecewise continuous second derivative in open \u0000intervals ( 0 , b ) and ( b , a ) ( 0 b a ) .","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S016117120320209X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64976545","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}
引用次数: 1
NESTED DERIVATIVES: A SIMPLE METHOD FOR COMPUTING SERIES EXPANSIONS OF INVERSE FUNCTIONS 嵌套导数:计算反函数级数展开的简单方法
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-29 DOI: 10.1155/S0161171203303291
D. Dominici
{"title":"NESTED DERIVATIVES: A SIMPLE METHOD FOR COMPUTING SERIES EXPANSIONS OF INVERSE FUNCTIONS","authors":"D. Dominici","doi":"10.1155/S0161171203303291","DOIUrl":"https://doi.org/10.1155/S0161171203303291","url":null,"abstract":"We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first N terms of the series. We show several examples of its application in calculating the inverses of some special functions.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203303291","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990756","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}
引用次数: 28
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators Sturm-Liouville微分算子积的自伴随扩展的定义域
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI: 10.1155/S0161171203008020
S. Ibrahim
{"title":"On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators","authors":"S. Ibrahim","doi":"10.1155/S0161171203008020","DOIUrl":"https://doi.org/10.1155/S0161171203008020","url":null,"abstract":"The second-order symmetric Sturm-Liouville differential expressions τ 1 , τ 2 , … , τ n with real coefficients are considered on the interval I = ( a , b ) , − ∞ ≤ a b ≤ ∞ . It is shown that the characterization of singular selfadjoint boundary conditions involves the sesquilinear form associated with the product of Sturm-Liouville differential expressions and elements of the maximal domain of the product operators, and it is an exact parallel of the regular case. This characterization is an extension of those obtained by Everitt and Zettl (1977), Hinton, Krall, and Shaw (1987), Ibrahim (1999), Krall and Zettl (1988), Lee (1975/1976), and Naimark (1968).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203008020","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64971474","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}
引用次数: 1
Hilbert series and applications to graded rings 希尔伯特级数及其在分级环上的应用
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI: 10.1155/S0161171203107090
S. Altınok
{"title":"Hilbert series and applications to graded rings","authors":"S. Altınok","doi":"10.1155/S0161171203107090","DOIUrl":"https://doi.org/10.1155/S0161171203107090","url":null,"abstract":"This paper contains a number of practical remarks on Hilbert series that we expect to be useful in various contexts. We use the fractional Riemann-Roch formula of Fletcher and Reid to write out explicit formulas for the Hilbert series P( t)in a number of cases of interest for singular surfaces (see Lemma 2.1 )a nd 3-folds. If X is a Q-Fano 3-fold and S ∈| −KX | a K3 surface in its anticanonical system (or the general elephant of X), polarised with D = S (−KX ), we determine the relation between PX (t) and PS,D(t). We discuss the denominator � (1 − t ai ) of P( t) and, in particular, the question of how to choose a reasonably small denominator. This idea has applications to finding K3 surfaces and Fano 3-folds whose corresponding graded rings have small codimension. Most of the information about the anticanonical ring of a Fano 3-fold or K3 surface is contained in its Hilbert series. We believe that, by using information on Hilbert series, the classification of Q-Fano 3-folds is too close. Finding K3 surfaces are important because they occur as the general elephant of a Q-Fano 3-fold.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203107090","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64972842","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}
引用次数: 10
Stochastic antiderivational equations on non-Archimedean Banach spaces 非阿基米德巴拿赫空间上的随机不定方程
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI: 10.1155/S0161171203108150
S. Ludkovsky
{"title":"Stochastic antiderivational equations on non-Archimedean Banach spaces","authors":"S. Ludkovsky","doi":"10.1155/S0161171203108150","DOIUrl":"https://doi.org/10.1155/S0161171203108150","url":null,"abstract":"Stochastic antiderivational equations on Banach spaces over local non-Archimedean fields are investigated. Theorems about existence and uniqueness of the solutions are proved under definite conditions. In particular, Wiener processes are considered in relation to the non-Archimedean analog of the Gaussian measure.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203108150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973159","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}
引用次数: 5
AN IMPROVED BAYES EMPIRICAL BAYES ESTIMATOR 一种改进的贝叶斯经验贝叶斯估计器
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI: 10.1155/S0161171203110046
R. Karunamuni, N. Prasad
{"title":"AN IMPROVED BAYES EMPIRICAL BAYES ESTIMATOR","authors":"R. Karunamuni, N. Prasad","doi":"10.1155/S0161171203110046","DOIUrl":"https://doi.org/10.1155/S0161171203110046","url":null,"abstract":"Consider an experiment yielding an observable random quantity X whose distribution Fθ depends on a parameter θ with θ being distributed according to some distribution G0. We study the Bayesian estimation problem of θ under squared error loss function based on X, as well as some additional data available from other similar experiments according to an empirical Bayes structure. In a recent paper, Samaniego and Neath (1996) investigated the questions of whether, and when, this information can be exploited so as to provide a better estimate of θ in the current experiment. They constructed a Bayes empirical Bayes estimator that is superior to the original Bayes estimator, based only on the current observation X for sampling situations involving exponential families-conjugate prior pair. In this paper, we present an improved Bayes empirical Bayes estimator having a smaller Bayes risk than that of Samaniego and Neath’s estimator. We further observe that our estimator is superior to the original Bayes estimator in more general situations than those of the exponential families-conjugate prior combination.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203110046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973316","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}
引用次数: 0
FUZZY STRUCTURES OF PI( , ⊆, ⊆)BCK-IDEALS IN HYPER BCK-ALGEBRAS 超巴克代数中π(、、、)巴克理想的模糊结构
IF 1.2
INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES Pub Date : 2003-01-01 DOI: 10.1155/S0161171203110277
Y. Jun, W. H. Shim
{"title":"FUZZY STRUCTURES OF PI( , ⊆, ⊆)BCK-IDEALS IN HYPER BCK-ALGEBRAS","authors":"Y. Jun, W. H. Shim","doi":"10.1155/S0161171203110277","DOIUrl":"https://doi.org/10.1155/S0161171203110277","url":null,"abstract":"The fuzzification of PI(≪,⫅,⫅)BCK-ideals is considered. Using the notion of α-cut, characterization of fuzzy PI(≪,⫅,⫅)BCK-ideals is given. Conditions for a fuzzy set to be a fuzzy PI(≪,⫅,⫅)BCK-ideal are provided.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203110277","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64973865","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}
引用次数: 3
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