The Convergence and Stability of Splitting Finite-Difference Schemes for Nonlinear Evolutionary Equations

We consider a splitting finite-difference scheme for an initial-boundary value problem for a two-dimensional nonlinear evolutionary equation. The problem is split into nonlinear and linear parts. The linear part is also split into locally one-dimensional equations. We prove the convergence and stability of the scheme in L ₂ and C norms. Printed in Lietuvos Matematikos Rinkinys, Vol. 45, No. 3, pp. 413–434, July–September, 2005.     

Basic Properties of the (t, n)-Threshold Visual Secret Sharing Scheme with Perfect Reconstruction of Black Pixels

In this paper we consider the (t, n)-threshold visual secret sharing scheme (VSSS) in which black pixels in a secret black-white images is reproduced perfectly as black pixels when we stack arbitrary t shares. This paper provides a new characterization of the (t, n)-threshold visual secret sharing scheme with such a property (hereafter, we call such a VSSS the (t, n)-PBVSSS for short). We use an algebraic method to characterize basis matrices of the (t, n)-PBVSSS in a certain class of matrices. We show that the set of all homogeneous polynomials each element of which yields basis matrices of the (t, n)-PBVSSS becomes a set of lattice points in an (n−t+1)-dimensional linear space. In addition, we prove that the optimal basis matrices in the sense of maximizing the relative difference among all the basis matrices in the class coincides with the basis matrices given by Blundo, Bonis and De Santis [3] for all n≥ t ≥ 2.     

基于移动Agent技术的医学图像检索方法

针对现有医学图像检索方法中，检索算法速度较慢、准确性较低以及远程检索时占用大量带宽等问题，设计并实现了一种基于移动Agent技术的医学图像检索方法，重点讨论了该方法实现的关键技术，包括提升框架下的M带整数小波变换和提取多通道纹理特征的检索算法．模拟实验结果表明，该方法实时性较强，占用网络带宽较少，采用的算法运算速度提高近10倍、运算复杂度降低约50％，提取的纹理特征能充分表达图像内容，较好地满足了医学图像的检索要求，实现了对医学图像库快速较准确的检索．     

Bicircular projections and characterization of Hilbert spaces

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

     

Tensor Products of Quantum Structures and Their Applications in Quantum Measurements

Tensor products of quantum logics and effect algebras with some known problems are reviewed. It is noticed that although tensor products of effect algebras having at least one state exist, in the category of complex Hilbert space effect algebras similar problems as with tensor products of projection lattices occur. Nevertheless, if one of the two coupled physical systems is classical, tensor product exists and can be considered as a Boolean power. Some applications of tensor products (in the form of Boolean powers) to quantum measurements are reviewed.     

Diffraction by a wedge at skew incidence: integral representations of Cauchy-Carleman for the electromagnetic fields

An electromagnetic diffraction problem in a wedge shaped region is reduced to a system of coupled functional difference equations by means of Sommerfeld integrals and Malyuzhinets theorem. By introducing an integral operator it is shown that the solutions of this system of functional equations can be defined in terms of integral representations whose kernels are solutions of a singular integral equation of Cauchy-Carleman type for which an explicit solution is given.     

On polynomial symbols for subdivision schemes

Given a dilation matrix A :ℤ^d→ℤ^d, and G a complete set of coset representatives of 2π(A ^−Tℤ^d/ℤ^d), we consider polynomial solutions M to the equation ∑ _g∈G M(ξ+g)=1 with the constraints that M≥0 and M(0)=1. We prove that the full class of such functions can be generated using polynomial convolution kernels. Trigonometric polynomials of this type play an important role as symbols for interpolatory subdivision schemes. For isotropic dilation matrices, we use the method introduced to construct symbols for interpolatory subdivision schemes satisfying Strang–Fix conditions of arbitrary order. Research partially supported by the Danish Technical Science Foundation, Grant No. 9701481, and by the Danish SNF-PDE network.     

Division and <Emphasis Type="Italic">k</Emphasis>-th root theorems for <Emphasis Type="Italic">Q</Emphasis>-manifolds

We prove that a locally compact ANR-space X is a Q-manifold if and only if it has the Disjoint Disk Property (DDP), all points of X are homological Z _∞-points and X has the countable-dimensional approximation property (cd-AP), which means that each map f: K → X of a compact polyhedron can be approximated by a map with the countable-dimensional image. As an application we prove that a space X with DDP and cd-AP is a Q-manifold if some finite power of X is a Q-manifold. If some finite power of a space X with cd-AP is a Q-manifold, then X ² and X × [0, 1] are Q-manifolds as well. We construct a countable family χ of spaces with DDP and cd-AP such that no space X ∈ χ is homeomorphic to the Hilbert cube Q whereas the product X × Y of any different spaces X, Y ∈ χ is homeomorphic to Q. We also show that no uncountable family χ with such properties exists. This work was supported by the Slovenian-Ukrainian (Grant No. SLO-UKR 04-06/07)     

Quantitative vibration amplitude measurement with time-averaged digital speckle pattern interferometry

A new method of using time-averaged digital speckle pattern interferometry for the quantitative measurement of vibration amplitude was developed. Signal processing techniques especially the Hilbert transformation for quantitative evaluation of the Bessel fringes obtained in time-averaged digital speckle pattern interferometry were explored. The quadrature signal after Hilbert transformation is equivalent to a 90° phase-shifted interferogram for a monotonically increasing or decreasing phase function. An algorithm was developed for Bessel fringe contrast enhancement and phase extraction. The techniques were tested numerically and experimentally. Sub-fringe quantification of the time-averaged vibration fringes is realised with the proposed method. Compared with the commonly used phase shift method which requires a minimum of two images for image processing, this method requires only one fringe pattern for data extraction.     

On the departure process of a leaky bucket system with long-range dependent input traffic

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic may have for the design and performance of these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite variance, and a regularly varying tail, i.e., P(τ >К) ~ К^-Lα L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks. This revised version was published online in June 2006 with corrections to the Cover Date.