How do the positive embeddings of Banach lattices depend on the αth derivatives of K?

Let K and S be locally compact Hausdorff spaces and X be an abstract th-0005" class="section_image" src="/cms/asset/dc58f095-e00a-4670-9249-c31ec2428145/mana201600244-math-0005.png"> space. Suppose that T is a positive Banach lattice isomorphism from th-0006" class="section_image" src="/cms/asset/0857d118-e3c6-4053-bdc6-0c03d89d0055/mana201600244-math-0006.png"> into th-0007" class="section_image" src="/cms/asset/5031ca4d-88b2-47b0-bcb3-71354ab7947f/mana201600244-math-0007.png">. Then for each ordinal α the cardinalities of the αth derivatives th-0008" class="section_image" src="/cms/asset/05ec3089-d511-4c56-97a9-46514a0ec616/mana201600244-math-0008.png"> and th-0009" class="section_image" src="/cms/asset/e9b60cc7-3504-4907-a06c-ec8577daf47d/mana201600244-math-0009.png"> satisfy the following inequality th-0010.png" alt="urn:x-wiley:0025584X:media:mana201600244:mana201600244-math-0010" title="urn:x-wiley:0025584X:media:mana201600244:mana201600244-math-0010"> Moreover, if th-0011.png" alt="urn:x-wiley:0025584X:media:mana201600244:mana201600244-math-0011" title="urn:x-wiley:0025584X:media:mana201600244:mana201600244-math-0011"> then th-0012" class="section_image" src="/cms/asset/21e69e9c-373e-49cc-8aa2-39c082e59361/mana201600244-math-0012.png"> is a continuous image of a subset of th-0013" class="section_image" src="/cms/asset/d9a6bebf-f3f1-40ed-b312-6ebc5dc58bc8/mana201600244-math-0013.png"> which can be taken closed when K is compact. The first statement of this result for th-0014" class="section_image" src="/cms/asset/904422f0-a4c9-40a5-8da2-deedea8cbd94/mana201600244-math-0014.png"> is a vector‐valued extension of a Cengiz's theorem and the second one is vector‐valued version of a Holsztyński's theorem. A simple example shows that the number th-0015" class="section_image" src="/cms/asset/28a25383-34c2-497d-85c4-4a3f4b8098b9/mana201600244-math-0015.png"> is sharp in these vector‐valued theorems.     

Boundedness of the fbi transform on sobolev spaces and propagation of singularities

It is shown that the FBI transform of Baouendi, Chang and Treves is bounded on Sobolev spaces.Applications to the propagation of singularities are given     

Theory of third-harmonic generation using double half-Gaussian hollow beams and self-phase-matching

We first (to best of out knowledge) use the slowly varying envelope approximation (SVEA) to obtain the equation of third harmonic (TH) generated by focusing the double half-Gaussian hollow beams into an atomic medium. The two-dimension intensity distribution is achieved by simulating, and it is similar to that generated by the 0th order Bessel beams. In addition to the similarities between the experimental setups, we demonstrate the accuracy of the equation. Compared with that generated by the Bessel beams, the pattern of the TH intensity generated by the double half-Gaussian hollow beams has salient features.     

kth Order convergence for a semilinear elliptic boundary value problem in the divergence form

The convergence problem of approximate solutions for a semilinear elliptic boundary value problem in the divergence form is studied. By employing the method of quasilinearization, a sequence of approximate solutions converging with the kth (k ? 2) order convergence to a weak solution for a semilinear elliptic problem is obtained via the variational approach.     

Composition operators from F(p, q, s) spaces to the nth weighted-type spaces on the unit disc

In this note we characterize the boundedness and compactness of the composition operator from the general function space F(p, q, s) to the nth weighted-type space on the unit disk, where the nth weighted-type space has been recently introduced by Stevo Stevi?.     

基于熵值法的浙江省“十一五”基础研究热点分析与思考

熵值法是一种科学、简单、实用的综合评价方法．由于熵值法是一种客观赋权法，因此可以避免人为因素带来的偏差．以浙江省“十一五”期间6个基础研究学科领域获得浙江省自然科学基金资助项目的情况作为数据源，采用熵值法对这些数据进行分析总结，揭示了浙江省在基础学科领域的研究热点，并据此对浙江省“十二五”期间基础学科领域的研究发展趋势进行了预测和思考．     

模型外载与自重并存变动外载的光弹性分析法

提出一个变动模型外载，分析大模型在外载与自重共同作用时的尤弹性法。它与用离心力模拟自重试验的传统方法完全不同，只要在大模型上变动外载，就可以获得上述两种载荷共同作用下的应力分析结果。此法避免了用离心模型自重受模型尺寸限制等诸多因素影响的缺点，为自重不可的大型复杂空间工程结构模型试验应力分析提出了一条新的途径。文中给出了本方法的基本原理及其简要的实验验证和工程应用结果。     

Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations

The paper discusses both pth moment and almost sure exponential stability of solutions to neutral stochastic functional differential equations and neutral stochastic differential delay equations, by using the Razumikhin-type technique. The main goal is to find sufficient stability conditions that could be verified more easily then by using the usual method with Lyapunov functionals. The analysis is based on paper [X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (2) (1997) 389-401], referring to mean square and almost sure exponential stability.     

Towards Strong Duality in Integer Programming

We consider in this paper the Lagrangian dual method for solving general integer programming. New properties of Lagrangian duality are derived by a means of perturbation analysis. In particular, a necessary and sufficient condition for a primal optimal solution to be generated by the Lagrangian relaxation is obtained. The solution properties of Lagrangian relaxation problem are studied systematically. To overcome the difficulties caused by duality gap between the primal problem and the dual problem, we introduce an equivalent reformulation for the primal problem via applying a pth power to the constraints. We prove that this reformulation possesses an asymptotic strong duality property. Primal feasibility and primal optimality of the Lagrangian relaxation problems can be achieved in this reformulation when the parameter p is larger than a threshold value, thus ensuring the existence of an optimal primal-dual pair. We further show that duality gap for this partial pth power reformulation is a strictly decreasing function of p in the case of a single constraint. Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. Research supported by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E, and the National Natural Science Foundation of China under Grants 79970107 and 10571116.     

Enhancement of magnetoresistances at room temperature in YSZ doping La0.67Sr0.33MnO3 system

The temperature dependence of the resistance of composite samples (1−x)La_0.67Sr_0.33MnO₃+xYSZ with different YSZ doping level x was investigated at magnetic fields 0-3 T, where YSZ represents yttria-stabilized zirconia. Results show that the YSZ dopant does not only adjust the metal-insulator transition temperature, but also increases the magnetoresistance effect. With increase of YSZ doping level for the range of x<2%, the metal-insulator transition temperature values T_P of the composites decrease, but T_P increases with increase of x further for the range of x>2%. Meanwhile, in the YSZ-doped composites, a broad metal-insulator transition temperature region was found at zero and low magnetic field, which results in an obvious enhanced magnetoresistance in the temperature range 10-350 K. Specially, a larger magnetoresistance value was observed at room temperature at 3 T, which is encouraging with regard to the potential application of magnetoresistance materials.