We have expressed the tensor commutation matrix n⊗n as linear combination of the tensor products of the generalized Gell-Mann matrices. The tensor commutation matrices 3⊗2 and 2⊗3 have been expressed in terms of the classical Gell-Mann matrices and the Pauli matrices.
{"title":"Expression of a Tensor Commutation Matrix in Terms of the Generalized Gell-Mann Matrices","authors":"Rakotonirina Christian","doi":"10.1155/2007/20672","DOIUrl":"https://doi.org/10.1155/2007/20672","url":null,"abstract":"We have expressed the tensor commutation matrix n⊗n as linear combination of the tensor products of the generalized Gell-Mann matrices. The tensor commutation matrices 3⊗2 and 2⊗3 have been expressed in terms of the classical Gell-Mann matrices and the Pauli matrices.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2005-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2007/20672","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64140576","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 concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey (1993). They conjectured that every graph G can be incidence colored with Δ(G)
{"title":"The incidence chromatic number of some graph","authors":"Liu Xikui, Li Yan","doi":"10.1155/IJMMS.2005.803","DOIUrl":"https://doi.org/10.1155/IJMMS.2005.803","url":null,"abstract":"The concept of the incidence chromatic number of a graph was introduced by Brualdi and Massey (1993). They conjectured that every graph G can be incidence colored with Δ(G)","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.803","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881287","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}
By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.
{"title":"Viscosity solutions of fully nonlinear functional parabolic PDE","authors":"Liu Wei-an, Lu Gang","doi":"10.1155/IJMMS.2005.3539","DOIUrl":"https://doi.org/10.1155/IJMMS.2005.3539","url":null,"abstract":"By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown. Then the existence and uniqueness are established by the fixed point theory.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.3539","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881540","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 study the almost sure (strong) stability of weighted sums of NA random variables and obtain some new results which extend earlier results of Matula (1992), Chow and Teicher (1971), Jamison et al. (1965), and Petrov (1975).
我们研究了NA随机变量加权和的几乎确定(强)稳定性，并得到了一些新的结果，这些结果扩展了Matula(1992)、Chow和Teicher(1971)、Jamison et al.(1965)和Petrov(1975)的早期结果。
{"title":"Strong stability of weighted sums of NA random variables","authors":"Gan Shixin","doi":"10.1155/IJMMS.2005.975","DOIUrl":"https://doi.org/10.1155/IJMMS.2005.975","url":null,"abstract":"We study the almost sure (strong) stability of weighted sums of NA random variables and obtain some new results which extend earlier results of Matula (1992), Chow and Teicher (1971), Jamison et al. (1965), and Petrov (1975).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2005-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.975","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881479","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 : 2004-05-21DOI: 10.1155/S0161171203209169
Heath Emerson
For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra, we construct a canonical K-homology class. This class induces a Poincare duality map K∗(C(∂Γ)⋊Γ)→K∗
{"title":"The Baum-Connes conjecture, noncommutative Poincaré duality,and the boundary of the free group","authors":"Heath Emerson","doi":"10.1155/S0161171203209169","DOIUrl":"https://doi.org/10.1155/S0161171203209169","url":null,"abstract":"For every hyperbolic group Γ with Gromov boundary ∂Γ, one can form the cross product C∗-algebra C(∂Γ)⋊Γ. For each such algebra, we construct a canonical K-homology class. This class induces a Poincare duality map K∗(C(∂Γ)⋊Γ)→K∗","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171203209169","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64983068","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}
Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. In addition, a pseudodifferentiability of such measures is investigated.
{"title":"Non-archimedean valued quasi-invariant descending at infinity measures","authors":"S. Ludkovsky","doi":"10.1155/IJMMS.2005.3799","DOIUrl":"https://doi.org/10.1155/IJMMS.2005.3799","url":null,"abstract":"Measures with values in non-Archimedean fields, which are quasi-invariant and descending at infinity on topological vector spaces over non-Archimedean fields, are studied in this paper. Moreover, their characteristic functionals are considered. In particular, measures having convolution properties like classical Gaussian measures are investigated in the paper. Applications of such measures to pseudodifferential operators and stochastic processes are considered. Nevertheless, it is proved that there does not exist the complete non-Archimedean analog of Gaussian measures. Theorems about either equivalence or orthogonality of measures from the considered class are proved. In addition, a pseudodifferentiability of such measures is investigated.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS.2005.3799","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881643","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 : 2004-01-01DOI: 10.1155/S016117120421225X
S. V. Lüdkovsky
{"title":"Stochastic processes and antiderivational equations on non-Archimedean manifolds","authors":"S. V. Lüdkovsky","doi":"10.1155/S016117120421225X","DOIUrl":"https://doi.org/10.1155/S016117120421225X","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S016117120421225X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64991105","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 : 2004-01-01DOI: 10.1155/S0161171204203088
Gülen Başcanbaz-Tunca
We investigate the spectrum of the differential operator L λ defined by the Klein-Gordon s -wave equation y ″ + ( λ − q ( x ) ) 2 y = 0 , x ∈ ℝ + = [ 0 , ∞ ) , subject to the spectral parameter-dependent boundary condition y ′ ( 0 ) − ( a λ + b ) y ( 0 ) = 0 in the space L 2 ( ℝ + ) , where a ≠ ± i , b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that L λ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim x → ∞ q ( x ) = 0 , sup x ∈ R + { exp ( ϵ x ) | q ′ ( x ) | } ∞ , 0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> ϵ > 0 , hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.
我们研究微分算子的谱Lλ定义的克莱因-戈登s波方程y”+(λ−q (x)) 2 y = 0, x∈ℝ+ =[0,∞),光谱parameter-dependent边界条件y '(0)−(λ+ b) y (0) = 0 L 2(ℝ+),一个≠±我,b是复杂的常数,q是复值函数。讨论谱，我们证明了L λ具有有限个数的特征值和谱奇点，如果条件lim x→∞q (x) = 0, sup x∈R + {exp (λ λ) | q ' (x) |}∞，0$" xmlns:mml="http://www.w3.org/1998/Math/MathML"> λ > 0，成立。最后给出了谱奇异点对应的主函数的性质。
{"title":"Spectral properties of the Klein-Gordon s-wave equation with spectral parameter-dependent boundary condition","authors":"Gülen Başcanbaz-Tunca","doi":"10.1155/S0161171204203088","DOIUrl":"https://doi.org/10.1155/S0161171204203088","url":null,"abstract":"We investigate the spectrum of the differential operator L λ defined by the Klein-Gordon s -wave equation y ″ + ( λ − q ( x ) ) 2 y = 0 , x ∈ ℝ + = [ 0 , ∞ ) , subject to the spectral parameter-dependent boundary condition y ′ ( 0 ) − ( a λ + b ) y ( 0 ) = 0 in the space L 2 ( ℝ + ) , where a ≠ ± i , b are complex constants, q is a complex-valued function. Discussing the spectrum, we prove that L λ has a finite number of eigenvalues and spectral singularities with finite multiplicities if the conditions lim x → ∞ q ( x ) = 0 , sup x ∈ R + { exp ( ϵ x ) | q ′ ( x ) | } ∞ , 0$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> ϵ > 0 , hold. Finally we show the properties of the principal functions corresponding to the spectral singularities.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204203088","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64990924","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 : 2004-01-01DOI: 10.1155/S0161171204404566
S. Choudhuri, M. Chattopadhyay
{"title":"Magnetoelastic plane waves in rotating media in thermoelasticity of type II (G-N model)","authors":"S. Choudhuri, M. Chattopadhyay","doi":"10.1155/S0161171204404566","DOIUrl":"https://doi.org/10.1155/S0161171204404566","url":null,"abstract":"","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204404566","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64991278","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 : 2004-01-01DOI: 10.1155/S0161171204403548
Li Songxiao, Zhuang Xiangling
Let φ(z)=(φ1(z),…,φn(z)) be a holomorphic self-map of 𝔻n and ψ(z) a holomorphic function on 𝔻n, where 𝔻n is the unit polydiscs of ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(𝔻n) and β-Bloch space ℬβ(𝔻n).
{"title":"Essential norm of weighted composition operator between α-Bloch space and β-Bloch space in polydiscs","authors":"Li Songxiao, Zhuang Xiangling","doi":"10.1155/S0161171204403548","DOIUrl":"https://doi.org/10.1155/S0161171204403548","url":null,"abstract":"Let φ(z)=(φ1(z),…,φn(z)) be a holomorphic self-map of 𝔻n and ψ(z) a holomorphic function on 𝔻n, where 𝔻n is the unit polydiscs of ℂn. Let 0<α, β<1, we compute the essential norm of a weighted composition operator ψCφ between α-Bloch space ℬα(𝔻n) and β-Bloch space ℬβ(𝔻n).","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2004-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/S0161171204403548","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64991148","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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