Pub Date : 2003-09-30DOI: 10.1155/S0161171203205159
M. Hamadanian, A. Ashrafi
The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamine N(CH3)3 and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules.
{"title":"THE FULL NONRIGID GROUP THEORY FOR TRIMETHYLAMINE","authors":"M. Hamadanian, A. Ashrafi","doi":"10.1155/S0161171203205159","DOIUrl":"https://doi.org/10.1155/S0161171203205159","url":null,"abstract":"The nonrigid molecule group theory (NRG) in which the dynamical symmetry operations are defined as physical operations is a new field in chemistry. Smeyers in a series of papers applied this notion to determine the character table of restricted NRG of some molecules. In this note, a simple method is described by means of which it is possible to calculate character tables for the symmetry group of molecules consisting of a number of methyl groups attached to a rigid framework. We study the full NRG of trimethylamine N(CH3)3 and prove that it is a group of order 1296 with 28 conjugacy classes. The method can be generalized to apply to other nonrigid molecules. The full nonrigid (f-NRG) molecule group theory is seen to be used advantageously to study the internal dynamics of such molecules.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2701-2706"},"PeriodicalIF":1.2,"publicationDate":"2003-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203205159","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64978611","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 : 2003-07-09DOI: 10.1155/S0161171203201095
R. Fabbri, S. T. Impram, R. Johnson
We generalize a criterion of Yakubovich for the absolute stability of control processes with periodic coefficients to the case when the coefficients are bounded and uniformly continuous functions.
将周期系数控制过程绝对稳定性的Yakubovich判据推广到周期系数为有界一致连续函数的情况。
{"title":"On a criterion of Yakubovich type for the absolute stability of nonautonomous control processes","authors":"R. Fabbri, S. T. Impram, R. Johnson","doi":"10.1155/S0161171203201095","DOIUrl":"https://doi.org/10.1155/S0161171203201095","url":null,"abstract":"We generalize a criterion of Yakubovich for the absolute \u0000stability of control processes with periodic coefficients to the \u0000case when the coefficients are bounded and uniformly continuous \u0000functions.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"160 1","pages":"1027-1041"},"PeriodicalIF":1.2,"publicationDate":"2003-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203201095","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64975309","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 : 2003-07-01DOI: 10.1155/S0161171203007932
Kweimei Wu
For any two points P = ( p ( 1 ) , p ( 2 ) , … , p ( n ) ) and Q = ( q ( 1 ) , q ( 2 ) , … , q ( n ) ) of ℝ n , we define the crisp vector P Q ⟶ = ( q ( 1 ) − p ( 1 ) , q ( 2 ) − p ( 2 ) , … , q ( n ) − p ( n ) ) = Q ( − ) P . Then we obtain an n -dimensional vector space E n = { P Q ⟶ | for all P , Q ∈ ℝ n } . Further, we extend the crisp vector into the fuzzy vector on fuzzy sets of ℝ n . Let D ˜ , E ˜ be any two fuzzy sets on ℝ n and define the fuzzy vector E ˜ D ˜ ⟶ = D ˜ ⊖ E ˜ , then we have a pseudo-fuzzy vector space.
对于任何两个指向P = P (P(1)、(2 ) , ... , p (n)和Q = Q (1), Q (2 ) , ... , q (n)《柯ℝn,我们定义的向量P q⟶= q (1) P q(1)、(2)−−P (2 ) , ... , q (n)−p (n) = q(−)p。然后我们得到的是n -dimensional向量空间E n = {P Q⟶| for all P, Q∈ℝn}。,我们离extend《毛毛向量上脆皮向量变成模糊使ℝn的。让D˜,E˜成为任何两个模糊使onℝn和模糊定义的向量D E˜˜⟶= D˜⊖E˜,然后我们有一个pseudo-fuzzy向量空间。
{"title":"Extension of n-dimensional Euclidean vector space En over ℝ to pseudo-fuzzy vector space over Fp1(1)","authors":"Kweimei Wu","doi":"10.1155/S0161171203007932","DOIUrl":"https://doi.org/10.1155/S0161171203007932","url":null,"abstract":"For any two points P = ( p ( 1 ) , p ( 2 ) , … , p ( n ) ) and Q = ( q ( 1 ) , q ( 2 ) , … , q ( n ) ) of ℝ n , we define the crisp \u0000vector P Q ⟶ = ( q ( 1 ) − p ( 1 ) , q ( 2 ) − p ( 2 ) , … , q ( n ) − p ( n ) ) = Q ( − ) P . Then we obtain an n -dimensional vector space E n = { P Q ⟶ | for all P , Q ∈ ℝ n } . Further, we extend the crisp vector into the fuzzy vector on \u0000fuzzy sets of ℝ n . Let D ˜ , E ˜ be any two fuzzy sets on ℝ n and define the fuzzy vector E ˜ D ˜ ⟶ = D ˜ ⊖ E ˜ , then we have a pseudo-fuzzy vector space.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2003 1","pages":"2349-2373"},"PeriodicalIF":1.2,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203007932","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64970986","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 : 2003-04-26DOI: 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":"2003 1","pages":"1803-1806"},"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":"2003 1","pages":"3657-3678"},"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":"2003 1","pages":"879-894"},"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":"2003 1","pages":"1599-1614"},"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":"2003 1","pages":"3699-3715"},"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/S0161171203208073
L. Hacia
Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and used in the theory of nonlinear hyperbolic differential equations.
{"title":"Applications of one- and two-dimensional Volterra inequalities in differential equations of the hyperbolic type.","authors":"L. Hacia","doi":"10.1155/S0161171203208073","DOIUrl":"https://doi.org/10.1155/S0161171203208073","url":null,"abstract":"Some variants of one-dimensional and two-dimensional integral inequalities of the Volterra type are applied to study the behaviour properties of the solutions to various boundary value problems for partial differential equations of the hyperbolic type. Moreover, new types of integral inequalities for one and two variables, being a generalization of the Gronwall inequality, are presented and used in the theory of nonlinear hyperbolic differential equations.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"7 1","pages":"3373-3383"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203208073","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64981195","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/S0161171203205299
Q. Ma, L. Debnath
This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations.
{"title":"A more generalized Gronwall-like integral inequality with applications","authors":"Q. Ma, L. Debnath","doi":"10.1155/S0161171203205299","DOIUrl":"https://doi.org/10.1155/S0161171203205299","url":null,"abstract":"This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"228 1","pages":"927-934"},"PeriodicalIF":1.2,"publicationDate":"2003-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203205299","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64979068","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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