The regularity of solutions to variational inequalities involving local operators has been studied extensively. Less attention has been paid to those involving nonlocal pseudodifferential operators. We present two regularity results for such problems.
{"title":"A Note on the Regularity of the Solutions to Two Variational Inequalities Involving a Pseudodifferential Operator","authors":"R. Cooper","doi":"10.1155/2007/95738","DOIUrl":"https://doi.org/10.1155/2007/95738","url":null,"abstract":"The regularity of solutions to variational inequalities involving local operators has been studied extensively. Less attention has been paid to those involving nonlocal pseudodifferential operators. We present two regularity results for such problems.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2007 1","pages":"1-8"},"PeriodicalIF":1.2,"publicationDate":"2007-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2007/95738","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64160525","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 : 2006-07-13DOI: 10.1155/IJMMS/2006/34538
Zuodong Yang
Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations are extended to the quasilinear ones and the results of semilinear equations are developed.
{"title":"On the existence of multiple positive entire solutions for a class of quasilinear elliptic equations","authors":"Zuodong Yang","doi":"10.1155/IJMMS/2006/34538","DOIUrl":"https://doi.org/10.1155/IJMMS/2006/34538","url":null,"abstract":"Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in ℝN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations are extended to the quasilinear ones and the results of semilinear equations are developed.","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2006 1","pages":"1-19"},"PeriodicalIF":1.2,"publicationDate":"2006-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS/2006/34538","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881733","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 : 2006-06-04DOI: 10.1155/IJMMS/2006/46561
Xue Zhiqun
Let E be a real uniformly smooth Banach space, and K a nonempty closed convex subset of E. Assume that T1
设E为实一致光滑巴拿赫空间，K为E的非空闭凸子集，设T1
{"title":"Approximation of fixed points of strongly pseudocontractive mappings in uniformly smooth Banach spaces.","authors":"Xue Zhiqun","doi":"10.1155/IJMMS/2006/46561","DOIUrl":"https://doi.org/10.1155/IJMMS/2006/46561","url":null,"abstract":"Let E be a real uniformly smooth Banach space, and K a nonempty closed convex subset of E. Assume that T1","PeriodicalId":39893,"journal":{"name":"INTERNATIONAL JOURNAL OF MATHEMATICS AND MATHEMATICAL SCIENCES","volume":"2006 1","pages":"1-6"},"PeriodicalIF":1.2,"publicationDate":"2006-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/IJMMS/2006/46561","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64881798","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 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":"2007 1","pages":"1-10"},"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":"2005 1","pages":"803-813"},"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":"2005 1","pages":"3539-3550"},"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":"2005 1","pages":"975-985"},"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":"2003 1","pages":"2425-2445"},"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":"2005 1","pages":"3799-3817"},"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":"2004 1","pages":"1633-1651"},"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}
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