Morphological ordered gray-scale erosion for optical image processing

An ordered gray-scale erosion is suggested according to the definition of hit-miss transform. Instead of using three operations, two images, and two structuring elements, the developed operation requires only one operation and one structuring element, but with three gray-scale levels. Therefore, a union of the ordered gray-scale erosions with different structuring elements can constitute a simple image algebra to program any combined image processing function. An optical parallel ordered gray-scale erosion processor is developed based on the incoherent correlation in a single channel. Experimental results are also given for an edge detection and a pattern recognition. (C) 1998 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(98)00306-7].

Design and properties analysis of multi-layer dielectric used in pulse compressor gratings

Used in chirped-pulse amplification system and based on multi-layer thin film stack, pulse compressor gratings (PCG) are etched by ion-beam and holographic techniques. Diffraction efficiency and laser-induced damage threshold rely on the structural parameters of gratings. On the other hand, they depend greatly on the design of multi-layer. A theoretic design is given for dielectric multi-layer, which is exposed at 413.1 nm and used at 1053 nm. The influences of coating design on optical characters are described in detail. The analysis shows that a coating stack of H3L (H2L) (boolean AND) 9H0.5L2.01H meets the specifications of PCG well. And there is good agreement of transmission between experimental and the theoretic design. (c) 2005 Elsevier GmbH. All rights reserved.

On diagonal-Schur complements of block diagonally dominant matrices

It is known that the diagonal-Schur complements of strictly diagonally dominant matrices are strictly diagonally dominant matrices [J.Z. Liu, Y.Q. Huang, Some properties on Schur complements of H-matrices and diagonally dominant matrices, Linear Algebra Appl. 389 (2004) 365-380], and the same is true for nonsingular H-matrices [J.Z. Liu, J.C. Li, Z.T. Huang, X. Kong, Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices, Linear Algebra Appl. 428 (2008) 1009-1030]. In this paper, we research the properties on diagonal-Schur complements of block diagonally dominant matrices and prove that the diagonal-Schur complements of block strictly diagonally dominant matrices are block strictly diagonally dominant matrices, and the same holds for generalized block strictly diagonally dominant matrices. (C) 2010 Elsevier Inc. All rights reserved.

Compact Reconfigurable Binary-Decision-Diagram Logic Circuit on a GaAs Nanowire Network

We describe a reconfigurable binary-decision-diagram logic circuit based on Shannon's expansion of Boolean logic function and its graphical representation on a semiconductor nanowire network. The circuit is reconfigured by using programmable switches that electrically connect and disconnect a small number of branches. This circuit has a compact structure with a small number of devices compared with the conventional look-up table architecture. A variable Boolean logic circuit was fabricated on an etched GaAs nanowire network having hexagonal topology with Schottky wrap gates and SiN-based programmable switches, and its correct logic operation together with dynamic reconfiguration was demonstrated.

Compact universal logic gates realized using quantization of current in nanodevices

This paper proposes novel universal logic gates using the current quantization characteristics of nanodevices. In nanodevices like the electron waveguide (EW) and single-electron (SE) turnstile, the channel current is a staircase quantized function of its control voltage. We use this unique characteristic to compactly realize Boolean functions. First we present the concept of the periodic-threshold threshold logic gate (PTTG), and we build a compact PTTG using EW and SE turnstiles. We show that an arbitrary three-input Boolean function can be realized with a single PTTG, and an arbitrary four-input Boolean function can be realized by using two PTTGs. We then use one PTTG to build a universal programmable two-input logic gate which can be used to realize all two-input Boolean functions. We also build a programmable three-input logic gate by using one PTTG. Compared with linear threshold logic gates, with the PTTG one can build digital circuits more compactly. The proposed PTTGs are promising for future smart nanoscale digital system use.

Diassociativity in Conjugacy Closed Loops

Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators have order 2. If Q is power-associative and |Q| is finite and relatively prime to 6, then Q is a group. If Q is a finite non-associative extra loop, then 16 ∣ |Q|.

On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

On a Certain Algebraic Property of Block Ciphers

This is a study on a certain group theoretic property of the set of encryption functions of a block cipher. We have shown how to construct a subset which has this property in a given symmetric group by a computer algebra software GAP4.2 (Groups, Algorithms, and Programming, Version 4.2). These observations on group structures of block ciphers suggest us that we may be able to set a trapdoor based on meet-in-the-middle attack on block ciphers.

on quadratic bent functions in polynomial forms

In this correspondence, we construct some new quadratic bent functions in polynomial forms by using the theory of quadratic forms over finite fields. The results improve some previous work. Moreover, we solve a problem left by Yu and Gong in 2006.

on lin-bose problem

This paper study generalized Serre problem proposed by Lin and Bose in multidimensional system theory context [Multidimens. Systems and Signal Process. 10 (1999) 379; Linear Algebra Appl. 338 (2001) 125]. This problem is stated as follows. Let F ∈ Al×m be a full row rank matrix, and d be the greatest common divisor of all the l × l minors of F. Assume that the reduced minors of F generate the unit ideal, where A = K[x 1,...,xn] is the polynomial ring in n variables x 1,...,xn over any coefficient field K. Then there exist matrices G ∈ Al×l and F1 ∈ A l×m such that F = GF1 with det G = d and F 1 is a ZLP matrix. We provide an elementary proof to this problem, and treat non-full rank case.

求解布尔与非线性数值约束相混合的约束问题

布尔与数值变量相混合的约束问题有着广泛的应用,但是当约束中的数值变量间存在非线性关系时该问题求解起来十分困难.目前的许多求解方法都是不完备的,即这些方法不能完全肯定某些包含非线性数值表达式的约束是否能够成立.针对这种问题,提出了将非线性数值约束转化为特殊形式的优化问题,采用全局优化算法对其进行求解的方法.已经实现了一个基于此方法的原型工具.实验结果表明,该方法能够有效地求解非线性混合约束问题,并且总能够得到该约束条件是否可满足的结果.

a constraint solver and its application to path feasibility analysis

Many testing methods are based on program paths. A well-known problem with them is that some paths are infeasible. To decide the feasibility of paths, we may solve a set of constraints. In this paper, we describe constraint-based tools that can be used for this purpose. They accept constraints expressed in a natural form, which may involve variables of different types such as integers, Booleans, reals and fixed-size arrays. The constraint solver is an extension of a Boolean satisfiability checker and it makes use of a linear programming package. The solving algorithm is described, and examples are given to illustrate the use of the tools. For many paths in the testing literature, their feasibility can be decided in a reasonable amount of time.