Pub Date : 2003-04-26DOI: 10.1155/S0161171203209108
S. Hejazian, S. Talebi
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.
{"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}
Pub Date : 2003-03-15DOI: 10.1155/S0161171203302170
P. Leroux
We show that an algebraic formulation of weighted directed graphs leads to introducing a k-vector space equipped with two coproducts Δ and Δ˜ verifying the so-called coassociativity breaking equation (Δ˜⊗id)Δ=(id⊗Δ)Δ˜. Such a space is called an L-coalgebra. Explicit examples of such spaces are constructed and links between graph theory and coassociative coalgebras are given.
{"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}
Pub Date : 2003-03-01DOI: 10.1155/S016117120311201X
P. Barbari, A. Kobotis
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.
{"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}
Pub Date : 2003-02-17DOI: 10.1155/S016117120320209X
I. Karaca
We research the asymptotic formula for the lengths of the instability intervals of the Hill's equation with coefficients q ( x ) and r ( x ) , where q ( x ) is piecewise continuous and r ( x ) has a piecewise continuous second derivative in open intervals ( 0 , b ) and ( b , a ) ( 0 b a ) .
研究了系数为q (x)和r (x)的Hill’s方程不稳定区间长度的渐近公式，其中q (x)是分段连续的，r (x)在开区间(0,b)和(b, a) (0, b, a)上有分段连续的二阶导数。
{"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}
Pub Date : 2003-01-29DOI: 10.1155/S0161171203303291
D. Dominici
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.
{"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}
Pub Date : 2003-01-01DOI: 10.1155/S0161171203008020
S. Ibrahim
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).
{"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}
Pub Date : 2003-01-01DOI: 10.1155/S0161171203107090
S. Altınok
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.
本文包含了一些关于希尔伯特级数的实用评论，我们希望这些评论在各种情况下都是有用的。我们使用Fletcher和Reid的分数Riemann-Roch公式来写出Hilbert级数P(t)在奇异曲面(见引理2.1)和3-fold的一些情况下的显式公式。如果X是Q-Fano 3-fold，并且S∈|−KX |是其反正则系统(或X的一般象)中的K3曲面，且D = S (- KX)极化，则我们确定PX (t)与PS,D(t)之间的关系。我们讨论P(t)的分母，特别是如何选择一个合理的小分母的问题。该方法可用于寻找具有小余维的梯度环的K3曲面和Fano 3-fold。法诺3折曲面或K3曲面的反正则环的大部分信息都包含在其希尔伯特级数中。我们认为，利用Hilbert级数的信息，Q-Fano 3-fold的分类过于接近。找到K3曲面是很重要的，因为它们是Q-Fano三折的一般特征。
{"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}
Pub Date : 2003-01-01DOI: 10.1155/S0161171203108150
S. Ludkovsky
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.
{"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}
Pub Date : 2003-01-01DOI: 10.1155/S0161171203110046
R. Karunamuni, N. Prasad
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.
{"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}
Pub Date : 2003-01-01DOI: 10.1155/S0161171203110277
Y. Jun, W. H. Shim
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.
{"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}
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