• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1223-1228
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• 2006

This paper presents an experimental investigation of a recently developed Kronecker Product (KP) method to determine the type, location, and intensity of structural damage from an identified state-space model of the system. Although this inverse problem appears to be highly nonlinear, the system mass, stiffness, and damping matrices are identified through a series of transformations, and with the aid of the Kronecker product, only linear operations are involved in the process. Since a state-space model can be identified directly from input-output data, an initial finite element model and/or model updating are not required. The test structure is a two-degree-of-freedom torsional system in which mass and stiffness are arbitrarily adjustable to simulate various conditions of structural damage. This simple apparatus demonstrates the capability of the damage detection method by not only identifying the location and the extent of the damage, but also differentiating the nature of the damage. The potential applicability of the KP method for structural damage identification is confirmed by laboratory test.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.9 no.8
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• pp.1774-1779
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• 2005

This paper propose the design method of the constructing the digital logic systems over galois fields using by the galois field decision diagram(GFDD) that is based on the graph theory. The proposed design method is as following. First of all, we discuss the mathematical properties of the galois fields and the basic properties of the graph theory. After we discuss the operational domain and the functional domain, we obtain the transformation matrixes, $\psi$GF(P)(1) and $\xi$GF(P)(1), in the case of one variable, that easily manipulate the relationship between two domains. And we extend above transformation matrixes to n-variable case, we obtain $\psi$GF(P)(1) and $\xi$GF(P)(1). We discuss the Reed-Muller expansion in order to obtain the digital switching functions of the P-valued single variable. And for the purpose of the extend above Reed-Muller expansion to more two variables, we describe the Kronecker product arithmetic operation.

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.503-508
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• 2004

This paper proposes an efficient computation method for fixed and mixed polarity Reed -Muller function vector over Galois field GF(p). Function vectors of fixed polarity Heed Muller function with single variable can be generated by proposed method. The n-variable function vectors can be calculated by means of the Kronecker product of a single variable function vector corresponding to each variable. Thus, all fixed and mixed polarity Reed-Muller function vectors are calculated directly without using a polarity function vector table or polarity coefficient matrix.

• Journal of the Korean Professional Engineers Association
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• v.20 no.1
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• pp.14-20
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• 1987

The development of the FHT (fast Hadamard transform) was presented and based on the derivation by Cooley-Tukey algorithm. Alternately, it can be derived by matrix partitioning or matrix factorization techniques. This paper proposes a simple sparse matrix technique by Kronecker product of successive lower Hadamard matrix. The following shows how the Kronecker product can be mathematically defined and efficiently implemented using a matrix factorization methods.

• IEIE Transactions on Smart Processing and Computing
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• v.3 no.1
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• pp.19-27
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• 2014

Compressive sensing is an emerging sampling technique which enables sampling a signal at a much lower rate than the Nyquist rate. In this paper, we propose a novel framework based on Kronecker compressive sensing that provides multi-resolution image reconstruction capability. By exploiting the relationship of the sensing matrices between low and high resolution images, the proposed method can reconstruct both high and low resolution images from a single measurement vector. Furthermore, post-processing using BM3D improves its recovery performance. The experimental results showed that the proposed scheme provides significant gains over the conventional framework with respect to the objective and subjective qualities.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.6
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• pp.598-606
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• 1990

Common problems encountered when orthogonal functions are used in system analysis and state estimation are the time consuming process of high order matrix inversion required in finding the Kronecker products and the truncation errors. In this paper, therefore, a method for the analysis of bilinear systems using Walsh, Block pulse, and Haar functions is devised, Then, state estimation of bilinear system is also studied based on single term expansion of orthogonal functions. From the method presented here, when compared to the other conventional methods, we can obtain the results with simpler computation as the number of interval increases, and the results approach the original function faster even at randomly chosen points regardless of the definition of intervals. In addition, this method requires neither the inversion of large matrices on obtaining the expansion coefficients nor the cumbersome procedures in finding Kronecker products. Thus, both the computing time and required memory size can be significantly reduced.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.11
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• pp.2705-2712
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• 2000

In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

• Korean Journal of Mathematics
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• v.20 no.4
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• pp.371-379
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• 2012

Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.289-297
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• 1994

A block design will be said to have Property C if the concordance matrix can be expressed as a linear combination of Kronecker product of permutation matrices. No matrix inversions are necessary for the intrablock analysis of the block designs which possesses the Property C(Paik, 1985). In this paper, in order to show the Li type PBIB designs possesses the Property C, we suggest the structure of the concordance matrices of Li type PBIB designs are multi-nested block circulant pattern.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.6
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• pp.135-140
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• 2016

In this paper, we analyze the [UC;AG] code which is genetic information standard DNA code, with 64 trigram. DNA which contains human genetic information, is a shape of adding three billion pairs of four bases which are A(adenine), C(cytosine), G(guanine) and T(thymine) to phosphoric acid and glucose. We present standard DNA code to 64 trigram which is $64{\times}4$ matrix with Kronecker product. This $64{\times}4$ matrix has double helix duplex property, and we can get the $4{\times}4$ matrix RNA code by removing the duplex of it. We present the DNA double helix to matrices and analysis the trigram array code of genetic information and the examples of it are presented in example 5, 6.