Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally s...Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally supported spline, give another proof of the BM-splines in S_(100)(4d, 3d-1, △_2) and establish the BM-splines in S_2~1, and S_4,展开更多
Determining the lowest degree, dimensions and basis functions of btp (bivariate truncated power(s)) spaces with given smoothness requirements and establishing the calculation formulae of btp on a three-and four-direct...Determining the lowest degree, dimensions and basis functions of btp (bivariate truncated power(s)) spaces with given smoothness requirements and establishing the calculation formulae of btp on a three-and four-direction mesh, we give the necessary and sufficient condition for the existence of the bivariate BM-spline in S_4~2, and the bivariate BM-spline in S_2~1, in terms of linear combinations of btp. The so-called 'revolving around' teahnique is mentioned.展开更多
Let μ,ν be measures with diem L^1(μ) =dim L~∞(ν)=∞ and ⊿ be a 'subinterval' of the real line. Let E=L~∞(ν) or C_b(⊿), in this paper it turns out that the IAP for the space B(L^1(μ)→E) has a negativ...Let μ,ν be measures with diem L^1(μ) =dim L~∞(ν)=∞ and ⊿ be a 'subinterval' of the real line. Let E=L~∞(ν) or C_b(⊿), in this paper it turns out that the IAP for the space B(L^1(μ)→E) has a negative answer.展开更多
Ding Xiaxi, research professor of Wuhan Institute of Mathematical Sciences, Academia Sinica, was born in Yiyang, Hunan Province, in May 1928. After graduation in 1951 from the Department of Mathematics, Wuhan
Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
More than thirty five years ago I learned the eoncept of manifolds and the proof of de Rham theorem from a series of lectures given by Prof. Wen-tsün Wu.Prof. Wu’ s lectures are duo to the original paper of de R...More than thirty five years ago I learned the eoncept of manifolds and the proof of de Rham theorem from a series of lectures given by Prof. Wen-tsün Wu.Prof. Wu’ s lectures are duo to the original paper of de Rham. Though nowadays the proof of de Rham theorem is much shorter by using the abstract sheaf theory, but the constructive proof I learned gave mo much stronger impression. This made me展开更多
Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and o...Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.展开更多
Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?...Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n-2), (γ-1)/(2-γ)-ε), (?)ε>0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity results.Delinition 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.展开更多
We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the ...We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation展开更多
Let G be a graph and n be a positive integer. A spanning subgraph F of G is called a {1, 3, …, 2n-1} -factor if d_F(x)∈{1, 3, …, 2n-1} for all x∈ V(G). Here we give several results on {1, 3, …, 2n-1} -factors, wh...Let G be a graph and n be a positive integer. A spanning subgraph F of G is called a {1, 3, …, 2n-1} -factor if d_F(x)∈{1, 3, …, 2n-1} for all x∈ V(G). Here we give several results on {1, 3, …, 2n-1} -factors, which are the extensions of some theorems on 1-factors given by Las Vergnas, Sumner and others.展开更多
In this paper it turns out that a Banach lattice X is order isomorphic to l~1(Γ) for some nonempty set Γ iff it is a Schur space and all the infinitely dimensional, separable and closed ideals of X are order isomorp...In this paper it turns out that a Banach lattice X is order isomorphic to l~1(Γ) for some nonempty set Γ iff it is a Schur space and all the infinitely dimensional, separable and closed ideals of X are order isomorphic.展开更多
In this paper authors consider a class of the first order nonlinear neutral differential equations with several delay arguments. Sufficient conditions are obtained which ensure that all nonoscillatory solutions tend t...In this paper authors consider a class of the first order nonlinear neutral differential equations with several delay arguments. Sufficient conditions are obtained which ensure that all nonoscillatory solutions tend to zero as t→+∞. Criteria are established for all solutions to oscillate.展开更多
After giving a brief review of H(4) and SU(2) quantum algebras and their relationship, Ⅰ work out the type Ⅰ representations of H(4) quantum algebra for the case q being a root of unity, these representations are re...After giving a brief review of H(4) and SU(2) quantum algebras and their relationship, Ⅰ work out the type Ⅰ representations of H(4) quantum algebra for the case q being a root of unity, these representations are reducible but indecomposable.展开更多
Using the method of characteristic lines this paper considers the global C^1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case φ_0(x, y)=cons...Using the method of characteristic lines this paper considers the global C^1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case φ_0(x, y)=const, the global C^1 solution is obtained. For the case of isentropic exponent γ=1, a transformation about variables is introduced, which changes the system to a first order linear hyperbolic system with constant coefficients and the global C^1 solution is also obtained in this case when the initial data of the forms (φ_0(x, y), u_0(x, y), u_0(x, y))=(exp(w_(01) (c_1x+d_1y)+w_(02)(c_2x+d_2y)), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y)), where c_i and d_i(i=1, 2) are constants.展开更多
This is a study of one dimensional generalized birth-death chains in a random environment (GBDIRE). We give two sufficient conditions of recurrence for GBDIRE.
This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determinin...This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in tha loopless Eulerian case are also obtained.展开更多
In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘Examining the B-coefficient relations between two adjacent s-simplicies with given smoothness requirements, we find a compromise technique between btp-coefficients and B-coefficients to calculate a bivariate locally supported spline, give another proof of the BM-splines in S_(100)(4d, 3d-1, △_2) and establish the BM-splines in S_2~1, and S_4,
文摘Determining the lowest degree, dimensions and basis functions of btp (bivariate truncated power(s)) spaces with given smoothness requirements and establishing the calculation formulae of btp on a three-and four-direction mesh, we give the necessary and sufficient condition for the existence of the bivariate BM-spline in S_4~2, and the bivariate BM-spline in S_2~1, in terms of linear combinations of btp. The so-called 'revolving around' teahnique is mentioned.
文摘Let μ,ν be measures with diem L^1(μ) =dim L~∞(ν)=∞ and ⊿ be a 'subinterval' of the real line. Let E=L~∞(ν) or C_b(⊿), in this paper it turns out that the IAP for the space B(L^1(μ)→E) has a negative answer.
文摘Ding Xiaxi, research professor of Wuhan Institute of Mathematical Sciences, Academia Sinica, was born in Yiyang, Hunan Province, in May 1928. After graduation in 1951 from the Department of Mathematics, Wuhan
文摘Some new characterizations and immediate explicit expressions of best L(1≤p≤∞) approximation and their deviations by an n-dimensional subspace on a set of n+1 points are given.
文摘More than thirty five years ago I learned the eoncept of manifolds and the proof of de Rham theorem from a series of lectures given by Prof. Wen-tsün Wu.Prof. Wu’ s lectures are duo to the original paper of de Rham. Though nowadays the proof of de Rham theorem is much shorter by using the abstract sheaf theory, but the constructive proof I learned gave mo much stronger impression. This made me
基金Supported by Doctoral Program Foundation of Higher Education.
文摘Let φ be a normal function defined on [0, 1) and A^p(φ) Bergman space weighted with φ~p(|z|)/(1-|z|~2) for 1≤p<∞. The compactnesses of Toeplitz operaters on A^p(φ) are characterized by Carleson measures and operator algebra.
基金This work is supported in part by the Foundation of Zhongshan University, Advanced Research Center.
文摘Let us consider the following elliptic systems of second order-D_α(A_i~α(x, u, Du))=B_4(x, u, Du), i=1, …, N, x∈Q(?)R^n, n≥3 (1) and supposeⅰ) |A_i~α(x, u, Du)|≤L(1+|Du|);ⅱ) (1+|p|)^(-1)A_i~α(x, u, p)are H(?)lder-continuous functions with some exponent δ on (?)×R^N uniformly with respect to p, i.e.ⅲ) A_i~α(x, u, p) are differentiable function in p with bounded and continuous derivativesⅳ)ⅴ) for all u∈H_(loc)~1(Ω, R^N)∩L^(n(γ-1)/(2-γ))(Ω, R^N), B(x, u, Du)is ineasurable and |B(x, u, p)|≤a(|p|~γ+|u|~τ)+b(x), where 1+2/n<γ<2, τ≤max((n+2)/(n-2), (γ-1)/(2-γ)-ε), (?)ε>0, b(x)∈L2n/(n+2), n^2/(n+2)+e(Ω), (?)ε>0.Remarks. Only bounded open set Q will be considered in this paper; for all p≥1, λ≥0, which is clled a Morrey Space.Let assumptions ⅰ)-ⅳ) hold, Giaquinta and Modica have proved the regularity of both the H^1 weak solutions of (1) under controllable growth condition |B|≤α(|p|~γ+|u|^((n+2)/(n-2))+b, 0<γ≤1+2/n and the H^1∩L~∞ weak solutions of (1) under natural growth condition |B|≤α|p|~2+b with a smallness condition 2aM<λ(|u|≤M), which implys that the H^1∩L~∞ weak solutions have the same regularty in the case of 1+2/n<γ<2. In the case of γ=2, many counterexamples (see [2] showed that u must be in H^1L~∞, while in the case of 1+2/n<γ<2, we consider the H^1∩L^n(γ-1)/(2-γ) weak solutions of (1), weaken the instability conditions upon them (from L~∞ to L^n(γ-1)/(2-γ) and obtain the same regularity results. Finally we show that the exponent n(γ-1)/(2-γ) can not be docreased anymore for the sake of the regularity results.Delinition 1. We call u∈H^1∩L^n(γ-1)/(2-γ)(Q, R^N) be a weak solution of (1), providod that where We use the convention that repeated indices are summed. i, j go from 1 to N ann α, β from 1 to n.
文摘We describe the establishing process for the Boson-Fermion algebra of OSP(1, 2) starting from the fundamental Wigner operators of OSP(1, 2), and study its structure feature and representation theory. We also give the Boson-Fermion representation of OSP (1, 2), which is an infinite dimensional and grade star representation
文摘Let G be a graph and n be a positive integer. A spanning subgraph F of G is called a {1, 3, …, 2n-1} -factor if d_F(x)∈{1, 3, …, 2n-1} for all x∈ V(G). Here we give several results on {1, 3, …, 2n-1} -factors, which are the extensions of some theorems on 1-factors given by Las Vergnas, Sumner and others.
文摘In this paper it turns out that a Banach lattice X is order isomorphic to l~1(Γ) for some nonempty set Γ iff it is a Schur space and all the infinitely dimensional, separable and closed ideals of X are order isomorphic.
文摘In this paper authors consider a class of the first order nonlinear neutral differential equations with several delay arguments. Sufficient conditions are obtained which ensure that all nonoscillatory solutions tend to zero as t→+∞. Criteria are established for all solutions to oscillate.
文摘After giving a brief review of H(4) and SU(2) quantum algebras and their relationship, Ⅰ work out the type Ⅰ representations of H(4) quantum algebra for the case q being a root of unity, these representations are reducible but indecomposable.
文摘Using the method of characteristic lines this paper considers the global C^1 solution of the Cauchy problem for two-dimensional gas dynamics system. When the initial data degenerate to the special case φ_0(x, y)=const, the global C^1 solution is obtained. For the case of isentropic exponent γ=1, a transformation about variables is introduced, which changes the system to a first order linear hyperbolic system with constant coefficients and the global C^1 solution is also obtained in this case when the initial data of the forms (φ_0(x, y), u_0(x, y), u_0(x, y))=(exp(w_(01) (c_1x+d_1y)+w_(02)(c_2x+d_2y)), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y), u_(01)(c_1x+d_1y)+u_(02)(c_2x+d_2y)), where c_i and d_i(i=1, 2) are constants.
文摘This is a study of one dimensional generalized birth-death chains in a random environment (GBDIRE). We give two sufficient conditions of recurrence for GBDIRE.
基金Supported by the Italian National Research Councilthe National Natural Science Foundation of China.
文摘This paper presents the number of combinatorially distinct rooted Eulerian planar maps with the number of non-root-vertices and the number of non-root-faces as two parameters. The parametric expressions for determining the number in tha loopless Eulerian case are also obtained.
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
