Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub&...Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is展开更多
In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we estab...In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we establish some sum formulas for these matrix sequences.展开更多
As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the ...As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.展开更多
The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（...The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.展开更多
Background Extracellular matrix (ECM) orchestrates cell behaviour including growth, death, apoptosis, adhesion, migration, and invasion by activating several signalling pathways Certain components of ECM, such as ...Background Extracellular matrix (ECM) orchestrates cell behaviour including growth, death, apoptosis, adhesion, migration, and invasion by activating several signalling pathways Certain components of ECM, such as integrins, may act as receptors or co-receptors of enterovirus ECM-activated gene expressions in myocardium of viral heart disease including myocarditis and partial cardiomyopathy remain elusive This study was to investigate the expression of ECM-activated genes in myocardium of mouse with viral myocarditis Methods BALB/c mice were infected with Coxsackie virus B 3 (CVB 3) to establish an animal model of myocarditis Uninfected mice were also prepared and served as controls Specific mRNA expression pattern in myocarditic mouse heart was analysed by an in-house cDNA microarray containing 8192 genes Overexpressed ECM genes were selected and subsequently confirmed by Northern blot analysis Results Nine ECM genes were isolated, from the array of 8192 genes, as overexpressed genes in hearts of myocarditic mice in comparison with controls Subsequent Northern blot analysis confirmed that four of the nine genes were highly expressed Expression of these four genes, Fin15, ILk, Lamr1 and ADAMTS-1, has not been reported previously to be induced by Coxsackie virus Conclusion CVB 3-induced myocarditis is associated with gene expression profiles of certain ECM components展开更多
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘Assume that a convergent matrix sequence{A<sub>n</sub>}:A<sub>n</sub>→A（n→∞）, A<sub>n</sub>,A∈C<sup>3×3</sup>.We want to form a new matrix sequence {H<sub>n</sub>}, derived from {A<sub>n</sub>}, which has also A aslimit and whose convergence is faster than the of {A<sub>n</sub>}. Three rational extrapolation meth-ods for accelerating the convergence of matrix sequences {A<sub>n</sub>} are presented in this paper.The underlying methods are based on the generalized inverse for matrices which is
文摘In this study, we first give the definitions of (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas sequence. By using these formulas we define (s,t)-Jacobsthal and (s,t)-Jacobsthal Lucas matrix sequences. After that we establish some sum formulas for these matrix sequences.
基金Supported by Natural Science Foundations of China (11101108, 11171301, 10771191 and 10471124)Natural Science Foundation of Zhejiang Province of China (Y6090105)
文摘Let X and Y be Banach spaces, 0 〈 q 〈 ＋∞, i ≤ p 〈 ＋∞. In this paper, we characterize matrix transformations of lq （ X ） to lp （ Y ）.
文摘As known, the method to obtain a sequence space by using convergence field of an infinite matrix is an old method in the theory of sequence spaces. However, the study of convergence field of an infinite matrix in the space of almost convergent sequences is so new （see [15]）. The purpose of this paper is to introduce the new spaces ^ ～f and fo consisting of all sequences whose Ceshro transforms of order one are in the spaces f and ^ ～ f0, respectively. Also, in this paper, we show that ^ ～f and ^ ～f0 are linearly isomorphic to the spaces f and f0, respectively. The β- and γ-duals of the spaces ^ ～f and 2% are computed. Furthermore, the classes （^ ～f： μ） and （μ ： f） of infinite matrices are characterized for any given sequence space μ, and determined the necessary and sufficient conditions on a matrix A to satisfy Bc-core（Ax） K-core（x）, K-core（Ax） Bg-core（x）, Bc-core（Ax） Be-core（x）, Bc-core（Ax） t-core（x） for all x ∈ t∞.
文摘The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80（1948）, 167-190]. Let fo（B） and f（B） be the domain of the double sequential band matrix B（r, s） in the sequence spaces f0 and f. In this article, the β- and γ-duals of the space f（B） are determined. Additionally, we give some inclusion theorems concerning with the spaces f0（B） and f（β）. Moreover, the classes （f（B） ： μ） and （μ： f（B）） of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where μ is an arbitrary sequence space.
基金ThisworkwassupportedbytheNationalNatureScienceFoundationofChina (No 3 0 2 71665 )
文摘Background Extracellular matrix (ECM) orchestrates cell behaviour including growth, death, apoptosis, adhesion, migration, and invasion by activating several signalling pathways Certain components of ECM, such as integrins, may act as receptors or co-receptors of enterovirus ECM-activated gene expressions in myocardium of viral heart disease including myocarditis and partial cardiomyopathy remain elusive This study was to investigate the expression of ECM-activated genes in myocardium of mouse with viral myocarditis Methods BALB/c mice were infected with Coxsackie virus B 3 (CVB 3) to establish an animal model of myocarditis Uninfected mice were also prepared and served as controls Specific mRNA expression pattern in myocarditic mouse heart was analysed by an in-house cDNA microarray containing 8192 genes Overexpressed ECM genes were selected and subsequently confirmed by Northern blot analysis Results Nine ECM genes were isolated, from the array of 8192 genes, as overexpressed genes in hearts of myocarditic mice in comparison with controls Subsequent Northern blot analysis confirmed that four of the nine genes were highly expressed Expression of these four genes, Fin15, ILk, Lamr1 and ADAMTS-1, has not been reported previously to be induced by Coxsackie virus Conclusion CVB 3-induced myocarditis is associated with gene expression profiles of certain ECM components
