• Bulletin of the Korean Mathematical Society
• /
• v.44 no.2
• /
• pp.225-231
• /
• 2007

Given an injective envelope E of a left R-module M, there is an associative Galois group Gal$({\phi})$. Let R be a left noetherian ring and E be an injective envelope of M, then there is an injective envelope $E[x^{-1}]$ of an inverse polynomial module $M[x^{-1}]$ as a left R[x]-module and we can define an associative Galois group Gal$({\phi}[x^{-1}])$. In this paper we describe the relations between Gal$({\phi})$ and Gal$({\phi}[x^{-1}])$. Then we extend the Galois group of inverse polynomial module and can get Gal$({\phi}[x^{-s}])$, where S is a submonoid of $\mathbb{N}$ (the set of all natural numbers).

• Journal of applied mathematics & informatics
• /
• v.17 no.1_2_3
• /
• pp.585-590
• /
• 2005

An efficient procedure for finding the inverse of a nonsingular matrix is developed by solving directly for the UL decomposition of the inverse based on the entries of the original nonsingular matrix.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.35-59
• /
• 2006

In this paper, we generalized the results of [23, 26], and get the results of the condition number of the W-weighted Drazin-inverse solution of linear system W AW\chi=b, where A is an $m{\times}n$ rank-deficient matrix and the index of A W is $k_1$, the index of W A is $k_2$, b is a real vector of size n in the range of $(WA)^{k_2}$, $\chi$ is a real vector of size m in the range of $(AW)^{k_1}$. Let $\alpha$ and $\beta$ be two positive real numbers, when we consider the weighted Frobenius norm $\|[{\alpha}W\;AW,\;{\beta}b]\|$(equation omitted) on the data we get the formula of condition number of the W-weighted Drazin-inverse solution of linear system. For the normwise condition number, the sensitivity of the relative condition number itself is studied, and the componentwise perturbation is also investigated.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.1C
• /
• pp.8-13
• /
• 2006

A new RS(Reed Solomon) Decoder design method, using Galois Subfield GF($2^4$) Multiplier, is described. The Decoder is designed using Normalized error position stored ROM. Here New Inverse Calculator in GF($2^8$) is designed, which is simpler and faster than the classical GF($2^8$) direct inverse calculator, using the Galois Subfield GF($2^4$) Arithmatic operator.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.87-102
• /
• 2011

The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of fixed points of a weak relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping by a new hybrid method in a Banach space. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space $l^2$. Our results improve and extend the corresponding results announced by Ying Liu[Ying Liu, Strong convergence theorem for relatively nonexpansive mapping and inverse-strongly-monotone mapping in a Banach space, Appl. Math. Mech. -Engl. Ed. 30(7)(2009), 925-932] and some others.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.2
• /
• pp.137-145
• /
• 2004

We give characterization of ${\Omega}$-stable diffeomorphisms via the notions of weak inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of diffeomorphisms with the weak inverse shadowing property with respect to the class $\mathcal{T}_h$ coincides with the set of ${\Omega}$-stable diffeomorphisms.

• Journal of applied mathematics & informatics
• /
• v.23 no.1_2
• /
• pp.461-470
• /
• 2007

Parameter identification is studied in viscoelastic rods by solving an inverse problem numerically. The material properties of the rod, which appear in the constitutive relations, are recovered by optimizing an objective function constructed from reference strain data. The resulting inverse algorithm consists of an optimization algorithm coupled with a corresponding direct algorithm that computes the strain fields given a set of material properties. Numerical results are presented for two model inverse problems; (i)the effect of noise in the reference strain fields (ii) the effect of minimal reference data in space and/or time data.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.2 no.2
• /
• pp.67-80
• /
• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• Journal of computational fluids engineering
• /
• v.2 no.2
• /
• pp.35-43
• /
• 1997

An efficient inverse method for 1.he supersonic/hypersonic axisymmetric body design is developed for the parabolized Navier-Stokes equations. The developed method is examined numerically for three extreme testcases in the supersonic(M/sub ∞/=3.0) and hypersonic(M/sub ∞/=6.28) speeds. The first one is a negative pressure distribution near a vacuum pressure and the second one is a positive pressure distribution over the whole region of the body. The last one is the case of abrupt change of pressure distribution to zero in the forward region of the body. These testcases show the robustness of the method. By introducing a regular-falsi method and by using a not-fully converged inverse solution, the convergence behavior was greatly improved.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.33 no.1C
• /
• pp.12-18
• /
• 2008

This paper This paper proposes a new inverse-quantization(IQ) table interpolation algorithm, specialized Digital Signal Processor(DSP) instructions and hardware architecture for digital audio codecs. Non-linear inverse quantization algorithm is representatively used in both MPEG-1 Layer-3 and MPEG-2/4 Advanced Audio Coding(AAC). The proposed instructions are optimized for the non-linear inverse quantization. The proposed algorithm can minimize operational complexity which reduces total computational load. Performance comparisons show a significant improvement of average error. The proposed instructions and hardware architecture can reduce 20% of the instruction counts and minimize computational loads of IQ algorithms effectively compared with existing IQ table interpolation algorithms. Proposed algorithm can implement commercial DSPs.