• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1069-1096
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• 2015

In this article we introduce a numerical method, named Gegenbauer wavelets method, which is derived from conventional Gegenbauer polynomials, for solving fractional initial and boundary value problems. The operational matrices are derived and utilized to reduce the linear fractional differential equation to a system of algebraic equations. We perform the convergence analysis for the Gegenbauer wavelets method. We also combine Gegenbauer wavelets operational matrix method with quasilinearization technique for solving fractional nonlinear differential equation. Quasilinearization technique is used to discretize the nonlinear fractional ordinary differential equation and then the Gegenbauer wavelet method is applied to discretized fractional ordinary differential equations. In each iteration of quasilinearization technique, solution is updated by the Gegenbauer wavelet method. Numerical examples are provided to illustrate the efficiency and accuracy of the methods.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2339-2348
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• 1994

The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.3 s.246
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• pp.279-286
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• 2006

The main purpose of this paper is to apply differential transformation method(DTM) and generalized differential quadrature method(GDQM) to vibration analysis of Euler-Bernoulli beam with open cracks on elastic foundation. In this paper the concepts of DTM and GDQM were briefly introduced. The governing equation of motion of the beam with open cracks on elastic foundation is derived. The cracks are modeled by massless substitute spring. The effects of the crack location, size and the foundation constants, on the natural frequencies of the beam, are investigated. Numerical calculations are carried out and compared with previous published results.

• KIEE International Transactions on Power Engineering
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• v.4A no.3
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• pp.146-151
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• 2004

The most widely used primary protection for the internal fault detection of the power transformer is current ratio differential relaying (CRDR) with harmonic restraint. However, the second harmonic component could be decreased by magnetizing inrush when there have been changes to the material of the iron core or its design methodology. The higher the capacitance of the high voltage status and underground distribution, the more the differential current includes the second harmonic during the occurrence of an internal fault. Therefore, the conventional second harmonic restraint CRDR must be modified. This paper proposes a numerical algorithm for enhanced power transformer protection. This algorithm enables a clear distinction regarding internal faults as well as magnetizing inrush and steady state. It does this by analyzing the RMS fluctuation of terminal voltage, instantaneous value of the differential current, RMS changes, harmonic component analysis of differential current, and analysis of flux-differential slope characteristics. Based on the results of testing with WatATP99 simulation data, the proposed algorithm demonstrated more rapid and reliable performance.

• Proceedings of the KIEE Conference
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• 1995.07b
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• pp.901-903
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• 1995

The ordinary differential equation (ODE) method has been widely used for the convergence analysis of stochastic recursive algorithms. The principal objective of this method is to associate to a given algorithm a differential equation with continuous righthand side. Usually some assumptions should be imposed to get such a differential equation. If any of assumptions fails, then the ODE method cannot be used. Recently a new method using differential inclusions (DIs) was introduced in [3], which is useful to deal with those cases. The DI method shares the same idea with the ODE method, but it is different in that a differential inclusion is identified instead of a differential equation with continuous righthand side. In this paper, we briefly review the DI method and then analyze a Robbins and Monro (RM)-type algorithm. Our focus is placed on the projected algorithm.

• Structural Engineering and Mechanics
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• v.35 no.5
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• pp.645-658
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• 2010

In this study, the Differential Transform Method (DTM) is employed in order to solve the governing differential equation of a moving Bernoulli-Euler beam with axial force effect and investigate its free flexural vibration characteristics. The free vibration analysis of a moving Bernoulli-Euler beam using DTM has not been investigated by any of the studies in open literature so far. At first, the terms are found directly from the analytical solution of the differential equation that describes the deformations of the cross-section according to Bernoulli-Euler beam theory. After the analytical solution, an efficient and easy mathematical technique called DTM is used to solve the differential equation of the motion. The calculated natural frequencies of the moving beams with various combinations of boundary conditions using DTM are tabulated in several tables and are compared with the results of the analytical solution where a very good agreement is observed.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.437-448
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• 2016

Gene set analysis utilizing biologic information is expected to produce more interpretable results because the occurrence of tumors (or diseases) is believed to be associated with the regulation of related genes. Many methods have been developed to identify statistically significant gene sets across different phenotypes; however, most focus exclusively on either the differential gene expression or the differential correlation structure in the gene set. This research provides a new method that simultaneously considers the differential expression of genes and differential coexpression with multiple genes in the gene set. Application of this NEW method is illustrated with real microarray data example, p53; subsequently, a simulation study compares its type I error rate and power with GSEA, SAMGS, GSCA and GSNCA.

• Journal of Communications and Networks
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• v.12 no.6
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• pp.582-591
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• 2010

Probabilistic modeling and analysis of correlation metrics have been receiving considerable interest for a long period of time because they can be used to evaluate the performance of communication receivers, including satellite broadcasting receivers. Although differential correlators have a simple structure and practical importance over channels with severe frequency offsets, closedform expressions for the output distribution of differential correlators do not exist. In this paper, we present detection error probability expressions for frame synchronization using differential correlation, and demonstrate their accuracy over channel parameters of practical interest. The derived formulas are presented in terms of the Marcum Q-function, and do not involve numerical integration, unlike the formulas derived in some previous studies. We first determine the distributions and error probabilities for single-span differential correlation metric, and then extend the result to multispan differential correlation metric with certain approximations. The results can be used for the performance analysis of various detection strategies that utilize the differential correlation structure.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.12C
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• pp.995-1003
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• 2010

The content-based hashing for authentication and copy protection of image, video and 3D model has to satisfy the robustness and the security. For the security analysis of the hash value, the modelling method based on differential entropy had been presented. But this modelling can be only applied to the image hashing. This paper presents the modelling for the security analysis of the hash feature value in 3D model hashing based on differential entropy. The proposed security analysis modeling design the feature extracting methods of two types and then analyze the security of two feature values by using differential entropy modelling. In our experiment, we evaluated the security of feature extracting methods of two types and discussed about the trade-off relation of the security and the robustness of hash value.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.24 no.6
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• pp.1117-1127
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• 2014

Differential Fault Analysis(DFA) is widely known for one of the most powerful method for analyzing block cipher. it is applicable to block cipher such as DES, AES, ARIA, SEED, and lightweight block cipher such as PRESENT, HIGHT. In this paper, we introduce a differential fault analysis on the lightweight block cipher LEA for the first time. we use 300 chosen fault injection ciphertexts to recover 128-bit master key. As a result of our attack, we found a full master key within an average of 40 minutes on a standard PC environment.