河南省城市居民消费结构比较研究

本文主要应用聚类分析方法 ,对河南省 17个地市级城市居民的消费结构进行了比较统计分析 ,从而得到了各城市居民消费结构的一些特点和规律 ,并进一步探讨了其消费结构、可支配收入与总消费支出之间的关系     

Studies on the Synthesis and Properties of K_8[TiP_2W_17O_62]·12H_2O

The present paper covers a salt of 2:18 heteropoly complex of tungstotitanophosphate prepared with the method of improved sequence preparation. The title compound was characterized by elemental analysis, 31P NMR spectra, polarography, cyclic voltammetry, IR, UV, X-ray powder diffraction , X-ray photoelectron spectra and TG-DTA analysis. The results show that the complex with the formula K8[TiP2W17O62]·12H2O has Dawson structure. Its properties such as spectra, redox behavior and thermal stability are discussed.     

Some results on controllability of a nonlinear degenerate parabolic system by bilinear control

In this paper, we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control. Based on the shrinking property of the solutions, we prove that the system is not globally approximately controllable. Furthermore, we give an approximate null controllability result. We also prove that the system is not globally exactly null controllable by a comparison principle.     

Efficient Multiparty Quantum Secret Sharing with Greenberger-Horne-Zeilinger States

An effcient multiparty quantum secret sharing scheme is proposed with Greenberger-Horne-Zeilinger （GHZ） states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations Ⅰ, σx, σx and iσy to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total effciency both approach the maximal values.     

Christoffel functions and mean convergence for Lagrange interpolation for exponential weights

For exponential weights, a necessary condition of weighted mean convergence for Lagrange interpolation is given.     

Examples of non-Kähler Hamiltonian circle manifolds with the strong Lefschetz property

In this paper we construct six-dimensional compact non-Kähler Hamiltonian circle manifolds which satisfy the strong Lefschetz property themselves but nevertheless have a non-Lefschetz symplectic quotient. This provides the first known counterexamples to the question whether the strong Lefschetz property descends to the symplectic quotient. We also give examples of Hamiltonian strong Lefschetz circle manifolds which have a non-Lefschetz fixed point submanifold. In addition, we establish a sufficient and necessary condition for a finitely presentable group to be the fundamental group of a strong Lefschetz manifold. We then use it to show the existence of Lefschetz four-manifolds with non-Lefschetz finite covering spaces.     

On uniqueness of an entire function and its derivatives

In this paper, we study the growth of solutions of a first order linear differential equation. From this we verify that a conjecture given by Brück is true under the restriction of the hyper order less than 1/2, and obtain some uniqueness theorems of a nonconstant entire function and its first derivative sharing a nonzero constant CM. The results in this paper also improve some known results. Some examples show that the results in this paper are best possible. Project supported by the NSFC (NO. A0324617) and the RFDP (NO. 20060422049). Received: 20 April 2006 Revised: 4 February 2007     

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

In this paper, the author considers the Cauchy problem for semilinear wave equations with critical exponent in n≥4 space dimensions. Under some positivity conditions on the initial data, it is proved that there can be no global solutions no matter how small the initial data are.     

Generalized KKM Type Theorems in FC-Spaces with Applications (I)

The class KKM(X,Y) (resp., s-KKM(X,Y,Z)) of set-valued mappings with KKM (resp., s-KKM) property is introduced in FC-spaces without any convexity structure. Some generalized KKM (resp., s-KKM) type theorems are proved in FC-spaces under much weak assumptions. As applications, some new section theorems and coincidence theorems are established in FC-spaces. These theorems generalize many known results in literature. The further applications of these results will be given in a follow-up paper.