In this paper, we give a new approach to the computation of primary decomposition and associated prime components of a zero-dimensional polynomial ideal (f1,f2,. . . ,fn), where fi are multivariate polynomials on Z (the ring of integer). Over the past several years, a considerable number of studies have been made on the computation of primary decomposition of a zero-dimensional polynomial ideal. Many algorithms to compute primary decomposition are proposed. Most of the algorithms recently proposed are based on Groebner basis. However, the computation of Groebner basis can be very expensive to perform. Some computations are even impossible because of the physical limitation of memory in a computer. On the other hand, recent advance in numerical methods such as homotopy method made access to the zeros of a polynomial system relatively easy. Hence, instead of Groebner basis, we use the zeros of a given ideal to compute primary decomposition and associated prime components. More specifically, given a zero-dimensional ideal, we use LLL reduction algorithm by Lenstra et al. to determine the integer coefficients of irreducible polynomials in the ideal. It is shown that primary decomposition and associated prime components of the ideal can be computed, provided the zeros of the ideal are computed with enough accuracy. A numerical experiment is given to show effectiveness of our algorithm.

A hardware algorithm for modular division is proposed. It is based on the extended Euclidean algorithm (EEA). The procedure for finding the multiplicative inverse in EEA is modified so that it calculates the quotient. Modular division is carried out through iteration of simple operations, such as shifts and additions. A redundant binary representation is employed so that additions are performed without carry propagation. An n-bit modular division is carried out in O(n) clock cycles. The length of each clock cycle is constant independent of n. A modular divider based on the algorithm has a bit-slice structure and is suitable for VLSI implementation.

This paper proposes a new signaling technique which employs multilevel block codes in conjunction with phase/frequency modulation. The proposed scheme exhibits an increased minimum squared Euclidean distances (MSEDs) and outperforms other conventional schemes in terms of asymptotic coding gain and decoding complexity. The proposed scheme is also considered for non-constant amplitudes, which turned out to show even better performances at small modulation indices in some cases. Examples are given to demonstrate how to optimize the signal set for a given block code to maximize the coding gain.

In this paper, we present new algorithms to calculate the reverse distance transformation and to extract the skeleton based upon the Euclidean metric for an arbitrary binary picture. The presented algorithms are applicable to an arbitrary picture in all of n-dimensional spaces (n2) and a digitized picture sampled with the different sampling interval in each coordinate axis. The reconstruction algorithm presented in this paper is resolved to serial one-dimensional operations and efficiently executed by general purpose computer. The memory requirement is very small including only one picture array and single one-dimensional work space array for n-dimensional pictures. We introduce two different definitions of skeletons, both of them allow us to reconstruct the original binary picture exactly, and present algorithms to extract those skeltons from the result of the squared Euclidean distance transformation.

This paper deals with the uniqueness of a solution of the basic equation obtained from the analysis of resistive circuits including ideal diodes. The equation in consideration is of the type of (A-)X=b, where A is a constant matrix, b a constant vector, X an unknown vector satisfying X 0, and a diagonal matrix whose diagonal elements take the value 0 or 1 arbitrarily. The necessary and sufficient conditions for the equation to have a unique solution X 0 for an arbitrary vector b are shown. Some numerical examples are given for the illustration of the result.

The groupware for new idea generation system, GUNGEN, has been developed. GUNGEN consists of a distributed and cooperative KJ method support system and an intelligent productive work card support system. The system was implemented on a network consisting of a number of personal computers. The distributed and cooperative KJ method is carried out on computers. The ideas proposed by participants are classified into several groups on the basis of similarity and then a conclusion is derived. The intelligent productive work card support system can be used as a multimedia database to refer to the previous data of the distributed and cooperative KJ method.