• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.2
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• pp.103-109
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• 2021

About the orthogonal Hadamard matrix announced by Hadamard in France in 1893, Professor Moon Ho Lee newly defined it as Center Weight Hadamard in 1989 and announced it, and discovered the Jacket matrix in 1998. The Jacket matrix is a generalization of the Hadamard matrix. In this paper, we propose a method of obtaining the Symmetric Jacket matrix, analyzing important properties and patterns, and obtaining the Jacket matrix's determinant and Eigenvalue, and proved it using Eigen decomposition. These calculations are useful for signal processing and orthogonal code design. To analyze the matrix system, compare it with DFT, DCT, Hadamard, and Jacket matrix. In the symmetric matrix of Galois Field, the element-wise inverse relationship of the Jacket matrix was mathematically proved and the orthogonal property AB=I relationship was derived.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.6
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• pp.319-327
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• 2016

In this paper we investigate that most of plants and animals have the symmetric property, such as a tree or a sheep's horn. In addition, the human body is also symmetric and contains the DNA. We can see the logarithm helices in Fibonacci series and animals, and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein's spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants and animals are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.10 no.2
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• pp.93-103
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• 1985

The digital signal processing technique by bandwidth compression has been grown up ragidly owing to integrated circuit developments. In this project, we have proposed the Lee Weighted Hadamard (LWH) transform which retains the main properties of Hadamard matirx. The LWH matrix was weighted in the center of the spatial domain. The human visual of the mid spatial are emphasized more than the low and high spatial frequencies. The fast algorithms of the LWH transform has been studied for hardware realization. The result of this project are availabel to airplane photograph, X-Ray, CATV and the artificial satellite of the digital image processing.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.2A
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• pp.116-123
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• 2002

The jacket matrix is based on the Walsh-Hadamard matrix and an extension of it. While elements of the Walsh-Hadamard matrix are +1, or -1, those of the Jacket matrix are ${\pm}$1 and ${\pm}$$\omega$, which is $\omega$, which is ${\pm}$j and ${\pm}$2$\sub$n/. This matrix has weights in the center part of the matrix and its size is 1/4 of Hadamard matrix, and it has also two parts, sigh and weight. In this paper, instead of the conventional Jacket matrix where the weight is imposed by force, a simple Jacket sequence generation method is proposed. The Jacket sequence is generated by AND and Exclusive-OR operations between the binary indices bits of row and those of column. The weight is imposed on the element by when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by jacket sequence using row and column binary index bits. Using Distributed Arithmetic (DA), we present a VLSI architecture of the Fast Jacket transform is presented. The Jacket matrix is able to be applied to cryptography, the information theory and complex spreading jacket QPSK modulation for WCDMA.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.3
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• pp.197-203
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• 1986

The images which are scanned by CCTV are converted to digital signal and 6502 Microcomputer processes data by Transform coding. Thus data is reduced to $64{ imes}64$pixels and input by outer memory using same address with inner one for the fast process. Hadmard Transform, Weighted Hadamard Transform which is weighted in the center of matrix and Haar Transform are programmed by assembly language and every Transform is dome within one second.

• Advances in nano research
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• v.16 no.3
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• pp.231-249
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• 2024

When the amplitude of the vibrations is equivalent to that clearance, the vibrations for small amplitudes will really be significantly nonlinear. Nonlinearities will not be significant for amplitudes that are rather modest. Finally, nonlinearities will become crucial once again for big amplitudes. Therefore, the concrete panel system may experience a big amplitude in this work as a result of the high temperature. Based on the 3D modeling of the shell theory, the current work shows the influences of the von Kármán strain-displacement kinematic nonlinearity on the constitutive laws of the structure. The system's governing Equations in the nonlinear form are solved using Kronecker and Hadamard products, the discretization of Equations on the space domain, and Duffing-type Equations. Thermo-elasticity Equations. are used to represent the system's temperature. The harmonic solution technique for the displacement domain and the multiple-scale approach for the time domain are both covered in the section on solution procedures for solving nonlinear Equations. An effective data-driven solution is often utilized to predict how different systems would behave. The number of hidden layers and the learning rate are two hyperparameters for the network that are often chosen manually when required. Additionally, the data-driven method is offered for addressing the nonlinear vibration issue in order to reduce the computing cost of the current study. The conclusions of the present study may be validated by contrasting them with those of data-driven solutions and other published articles. The findings show that certain physical and geometrical characteristics have a significant effect on the existing concrete panel structure's susceptibility to temperature change and GPL weight fraction. For building construction industries, several useful recommendations for improving the thermo-mechanics' behavior of structural concrete panels are presented.