• Journal of the Korea Computer Industry Society
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• v.4 no.4
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• pp.523-532
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• 2003

In this paper, we designed a 128-bit block cipher, Lambda, which has 16-round extended Feistel structure and analyzed its secureness by the differential cryptanalysis and linear cryptanalysis. We could have full diffusion effect from the two rounds of the Lambda. Because of the strong diffusion effect of the algorithm, we could get a 8-round differential characteristic with probability $2^{-192}$ and a linear characteristic with probability $2^{-128}$. For the Lambda with 128-bit key, there is no shortcut attack, which is more efficient than the exhaustive key search, for more than 8 rounds of the algorithm.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.4
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• pp.221-237
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• 2013

In this paper an asymptotic numerical method named as Initial Value Method (IVM) is suggested to solve the singularly perturbed weakly coupled system of reaction-diffusion type second order ordinary differential equations with negative shift (delay) terms. In this method, the original problem of solving the second order system of equations is reduced to solving eight first order singularly perturbed differential equations without delay and one system of difference equations. These singularly perturbed problems are solved by the second order hybrid finite difference scheme. An error estimate for this method is derived by using supremum norm and it is of almost second order. Numerical results are provided to illustrate the theoretical results.

• International Journal of Contents
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• v.11 no.4
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• pp.56-69
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• 2015

This paper proposes an efficient image encryption scheme based on quintuple encryption using two chaotic maps. The encryption process is realized with quintuple encryption by calling the encrypt(E) and decrypt(D) functions five times with five different keys in the form EDEEE. The decryption process is accomplished in the reverse direction by invoking the encrypt and decrypt functions in the form DDDED. The keys for the quintuple encryption/decryption processes are generated by using a Tent map. The chaotic values for the encrypt/decrypt operations are generated by using a Gumowski-Mira map. The encrypt function E is composed of three stages: permutation, pixel value rotation and diffusion. The permutation stage scrambles all the rows and columns to chaotically generated positions. This stage reduces the correlation radically among the neighboring pixels. The pixel value rotation stage circularly rotates all the pixels either left or right, and the amount of rotation is based on chaotic values. The last stage performs the diffusion four times by scanning the image in four different directions: Horizontally, Vertically, Principal diagonally and Secondary diagonally. Each of the four diffusion steps performs the diffusion in two directions (forward and backward) with two previously diffused pixels and two chaotic values. This stage ensures the resistance against the differential attacks. The security and performance of the proposed method is investigated thoroughly by using key space, statistical, differential, entropy and performance analysis. The experimental results confirm that the proposed scheme is computationally fast with security intact.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1057-1069
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• 2008

We consider singularly perturbed Boundary Value Problems (BVPs) for third and fourth order Ordinary Differential Equations(ODEs) of convection-diffusion type with discontinuous source term and a small positive parameter multiplying the highest derivative. Because of the type of Boundary Conditions(BCs) imposed on these equations these problems can be transformed into weakly coupled systems. In this system, the first equation does not have the small parameter but the second contains it. In this paper a computational method named as 'An asymptotic finite element method' for solving these systems is presented. In this method we first find an zero order asymptotic approximation to the solution and then the system is decoupled by replacing the first component of the solution by this approximation in the second equation. Then the second equation is independently solved by a fitted mesh Finite Element Method (FEM). Numerical experiments support our theoritical results.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.04a
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• pp.41-45
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• 2002

Transient magnetic diffusion process in a melt-cast BSCCO-2212 tube is analyzed by an analytical method. The transient diffusion equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical current model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.04a
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• pp.309-314
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• 1998

The moisture diffusion and self-desiccation cause the differential drying shrinkage and autogenous shrinkage at early ages, respecitvely. Thus total shrinkage strain includes the differential drying shrinkage and self-desiccation shrinkage. Thus in this study the shrinkage strain was measured at various positions in the exposed concrete and in the sealed concrete the self-desiccation shrinkage was measured. In low-strength concrete, the differential drying shrinkage increases very rapidly, but self-desiccation shrinkage is very small. But high-strength concrete shows the reverse result. And the analytical results for differential drying shrinkage were in good agreement with the test results.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.757-762
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• 2009

In allelic model $X\;=\;(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;{\int}^t_0\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. We can also obtain a new diffusion operator $L^*$ for diffusion coefficient and we prove that unique solution for $L^*$-martingale problem exists. In this note, we define new symmetric preserving transformation. Uniqueness for martingale problem and symmetric property will be proved.

• Journal of the Korea Computer Industry Society
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• v.5 no.3
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• pp.405-414
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• 2004

In this paper, we designed a 128-bits block cipher, Circle-g, which has 18-rounds modified Feistel structure and analyzed its secureness by the differential cryptanalysis and linear cryptanalysis. We could have full diffusion effect from the two rounds of the Circle-g. Because of the strong diffusion effect of the F-function of the algorithm, we could get a 9-rounds DC characteristic with probability 2^{-144} and a 12-rounds LC characteristic with probability 2^{-144}. For the Circle-g with 128-bit key, there is no shortcut attack, which is more efficient than the exhaustive key search, for more than 12 rounds of the algorithm.

• Magazine of the Korea Concrete Institute
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• v.6 no.4
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• pp.102-112
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• 1994

The drying shrinkage of concrete has a close relation to the water movement. Since the diffusion process of water in concrete is strongly dependent on the temperature and the pore humidity, the process is highly nonlinear phenomena. This study consists of two parts. The first is the development of a finite element program which is capable of simulating the rnoisture distri- ,bution in concrete, and the other is the estimation of the differential drying shrinkage and stress considering creep by using the modified elastic modulus due to inner temperature change and maturity. It is shown that the analytical results of this study are in good agreement with experlimental data in the literatures, and results calculated by BP-KX model. The internal stress caused by moisture distribution which was resulted from the diffusion process, was calculated :quantitatively. The tensile stress which occured in the drying outer zone mostly exceeded the tensile strength of concrete, and necessarily would result in crack formation.