In this paper the new notion of multivariate least-squares orthogonal poly-nomials from the rectangular form is introduced. Their existence and uniqueness isstudied and some methods for their recursive computation are...In this paper the new notion of multivariate least-squares orthogonal poly-nomials from the rectangular form is introduced. Their existence and uniqueness isstudied and some methods for their recursive computation are given. As an applica-is constructed.展开更多
This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eig...This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eigenvalue of M. Then there exists a constant Cm dependent only on m such that展开更多
In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields b...In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.展开更多
The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A comple...The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.展开更多
The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riema...The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space Qp^n is given. Finally, the conformal isotropic submanifolds in the conformal space展开更多
Visual secret sharing(VSS) was used in the literature to encode and decode secret images until visual multi-secret sharing(VMSS) was proposed. Distinctly, multiple secret images can be encoded or decoded at a time in ...Visual secret sharing(VSS) was used in the literature to encode and decode secret images until visual multi-secret sharing(VMSS) was proposed. Distinctly, multiple secret images can be encoded or decoded at a time in VMSS; however, only one secret image can be done in VSS. In VMSS, secrets are encoded into noise-like shares which have finally been stacked altogether so as to disclose each of the secrets by specific operations, such as rotating, flipping and sliding. Though the noise-like shares can be decoded by those operations, it is just like a fly in the ointment since they are hard to manage, to recognize and even to stack orderly. Based on some researches about user-friendly VSS for generating meaningful shares, a new friendly VMSS scheme is presented in this paper for achieving two main goals. One is trying to encode multiple secrets at a time and the other is making the decoding process easy to manage. The experimental results prove that our proposed scheme does work.展开更多
基金This work is supported by NNSF(10271022)of China.
文摘In this paper the new notion of multivariate least-squares orthogonal poly-nomials from the rectangular form is introduced. Their existence and uniqueness isstudied and some methods for their recursive computation are given. As an applica-is constructed.
基金Partially supported by the National Natural Science Foundation of China
文摘This paper aims at proving a conjecture posed by S. T. Yau: Let M be an m-dimen-sional compact Riemann manifold with the Ricci curvature≥-R, where R= const.≥0. Suppose d is the diameter of M and λ1 is the first eigenvalue of M. Then there exists a constant Cm dependent only on m such that
基金Supported by the National Natural Science Foundation of China(No.10861014)The Institute of Mathematical Sciences,Chinese University of Hongkong.
文摘In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.
基金Supported by the National Science Foundation of China under Grant Nos.11371293,11501419the Mathematical Discipline Foundation of Shaanxi Province of China under Grant No.14TSXK02+1 种基金the Natural Science Foundation of Weinan Normal University under Grant No.16ZRRC05 and 15YKS005Natural Science Foundation of Hebei Province of China under Grant No.A2018207030
文摘The functionally generalized variable separation solutions of a general KdV-type equations u_t=u_(xxx) +A(u, u_x)u_(xx) + B(u, u_x) are investigated by developing the conditional Lie-Backlund symmetry method. A complete classification of the considered equations, which admit multi-dimensional invariant subspaces governed by higher-order conditional Lie-B¨acklund symmetries, is presented. As a result, several concrete examples are provided to construct functionally generalized variable separation solutions of some resulting equations.
基金Project supported by the National Natural Science Foundation of China(No.10971055)the Natural Science Foundation of the Educational Commission of Hubei province(Key Program)(No.D1120111007)
文摘The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space Qp^n is given. Finally, the conformal isotropic submanifolds in the conformal space
基金the National Science Council(Nos.NSC102-2221-E-415-014 and 102-2221-E-415-007)
文摘Visual secret sharing(VSS) was used in the literature to encode and decode secret images until visual multi-secret sharing(VMSS) was proposed. Distinctly, multiple secret images can be encoded or decoded at a time in VMSS; however, only one secret image can be done in VSS. In VMSS, secrets are encoded into noise-like shares which have finally been stacked altogether so as to disclose each of the secrets by specific operations, such as rotating, flipping and sliding. Though the noise-like shares can be decoded by those operations, it is just like a fly in the ointment since they are hard to manage, to recognize and even to stack orderly. Based on some researches about user-friendly VSS for generating meaningful shares, a new friendly VMSS scheme is presented in this paper for achieving two main goals. One is trying to encode multiple secrets at a time and the other is making the decoding process easy to manage. The experimental results prove that our proposed scheme does work.
