Operators on the orthogonal complement of the Dirichlet space(Ⅱ)

In this paper we first prove that a dual Hankel operator R φ on the orthogonal complement of the Dirichlet space is compact for φ∈ W 1,∞(D),and then that a semicommutator of two Toeplitz operators on the Dirichlet space or two dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space is compact.We also prove that a dual Hankel operator R φ with φ∈ W 1,∞(D) is of finite rank if and only if B φ is orthogonal to the Dirichlet space for some finite Blaschke product B,and give ...     

Highly selective coextraction of rhodamine B and dibenzyl phthalate based on high‐density dual‐template imprinted shells on silica microparticles

A simple one‐pot approach based on molecularly imprinted polymer shells dispersed on the surface of silica for simultaneous determination of rhodamine B and dibenzyl phthalate (DBzP) has been developed. Highly dense molecularly imprinted polymer shells were formed in the mixture of acetonitrile and toluene by the copolymerization of methacrylic acid and ethylene glycol dimethacrylate, as well as two templates, rhodamine B and dibenzyl phthalate, directed by the vinyl end groups functional monolayer at surface silica microspheres after 3‐methacryloxypropyl trimethoxysilane modification. The obtained imprinted polymer shells showed large average pore diameter (102.5 nm) and about 100 nm shell thickness. The imprinted particles also showed high imprinting factor (α_RhB = 3.52 and α_DBzP = 3.94), rapid binding kinetics, and excellent selective affinity capacity for rhodamine B and dibenzyl phthalate containing another three competitors in mixed solution. Moreover, the imprinted particles coupled with ultra high performance liquid chromatography was successfully applied to simultaneous analysis of rhodamine B and dibenzyl phthalate in two spiked beverage samples with average recoveries in the range of 88.0−93.0% for rhodamine B and 84.0–92.0% for dibenzyl phthalate with the relative standard deviation lower than 5.1%.     

诱惑态在“双探测器”准单光子光源量子密钥分发系统中的应用

现在诱惑态已被证明是一种可以大大提高量子密钥分发安全性能的现实可行的方法.由于考虑到现实应用中激光器在调制过程中的消光比不能做到100%，以及激光器固有的自发辐射因而使得制备真空态并不是一件容易的事情. 因此本文将对理想情况下准单光子光源量子密钥分发系统应用中的诱惑态结论作了补充和扩展，提出了两个弱光强态的诱惑态方案和一个弱光强诱惑态方案.最后，将“双探测器”的理论应用在准单光子源(HSPS)光源系统中，使系统的安全传输距离可达到2215km，比使用普通探测器的系统增加了约50km.     

A combination of potential reduction steps and steepest descent steps for solving convex programming problems

This paper studies the possibility of combining interior point strategy with a steepest descent method when solving convex programming problems, in such a way that the convergence property of the interior point method remains valid but many iterations do not request the solution of a system of equations. Motivated by this general idea, we propose a hybrid algorithm which combines a primal–dual potential reduction algorithm with the use of the steepest descent direction of the potential function. The complexity of the potential reduction algorithm remains valid but the overall computational cost can be reduced. Our numerical experiments are also reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Two-colour HgCdTe infrared detectors operating above 200 K

The performance of dual waveband HgCdTe photodiodes fabricated using metaloorganic chemical vapour deposition operated at high temperatures is presented. The effect of additional separating layer on the quantum efficiency and cross-talk of the photodiodes is analyzed. The photodiodes with cutoff wavelengths up to 6 μm, good R₀A product, and high quantum efficiency at 200 K have been demonstrated. The temperature dependence of the differential resistance is discussed. It is shown that the multilayer heterojunction P-n-N-n-P structure operating in a simultaneous mode has better performance than a structure operating in a sequential mode.     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

On the Infinitesimal Rigidity of Homogeneous Varieties

Let XP be a variety (respectively an open subset of an analytic submanifold) and let xX be a point where all integer valued differential invariants are locally constant. We show that if the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Segre P× P, n,m2, a Grassmaniann G(2,n+2), n4, or the Cayley plane OP², then X is the corresponding homogeneous variety (resp. an open subset of the corresponding homogeneous variety). The case of the Segre P²×P² had been conjectured by Griffiths and Harris in [GH]. If the projective second fundamental form of X at x is isomorphic to the second fundamental form of a point of a Veronese v₂(P) and the Fubini cubic form of X at x is zero, then X=v₂ (P) (resp. an open subset of v₂(P)). All these results are valid in the real or complex analytic categories and locally in the C category if one assumes the hypotheses hold in a neighborhood of any point x. As a byproduct, we show that the systems of quadrics I₂(P P) S²C, I₂(P¹× P) S²C and I₂(S₅) S²C¹⁶ are stable in the sense that if A S^* is an analytic family such that for t0,AA, then A₀A. We also make some observations related to the Fulton–:Hansen connectedness theorem.     

Affine-Invariant Distances, Envelopes and Symmetry Sets

Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.     

Operations that preserve total dual integrality

There are many useful operations, such as adding slack variables, taking scalar multiples of inequalities, and applying Fourier-Motzkin elimination, that can be performed on a linear system such that if the system defines an integer polyhedron then so does the derived system. The topic dealt with here is whether or not these operations also preserve total dual integrality of linear systems.     

Lattice Approach to Wigner-Type Theorems

The Wigner's Theorem states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex Hilbert space which preserves orthogonality is induced by either a unitary or an anti-unitary operator. There exist many Wigner-type theorems, in particular in indefinite metric spaces, von Neumanns algebras and Banach spaces and we try to find a common origin of all these results by using properties of the lattice subspaces of certain topological vector spaces. We prove a Wigner-type theorem for a pair of dual spaces which allows us to obtain, as particular cases, the usual Wigner's Theorem and some of its generalizations. PACS: 02.40.Dr, 03.65.Fd,03.65.Ta AMS Subject Classification (1991): 06C15, 46A20, 81P10.