• The Transactions of the Korean Institute of Electrical Engineers B
• /
• v.53 no.4
• /
• pp.214-214
• /
• 2004

This paper describes a busbar current differential relay in conjunction with a current transformer(CT) compensating algorithm irrespective of the level of the remanent flux. The compensating algorithm detects the start of first saturation if the third-difference function of the current exceeds the threshold; it estimates the core flux at the first saturation start by inserting the negative value of the third-difference function of the current into the magnetization curve; thereafter, it calculates the core flux during the fault and compensates the distorted current using the magnetization curve. The algorithm estimates the correct secondary current irrespective of the level of the remanent flux and needs no saturation point of the magnetization curve. The proposed relay can improve not only security of the relay on an external fault with CT saturation but sensitivity of the relay on an internal fault; the relay can improve the operating speed on n internal fault with CT saturation. This paper concludes by implementing the relay into a digital signal processor based prototype relay.

• International Journal of Aeronautical and Space Sciences
• /
• v.18 no.4
• /
• pp.816-826
• /
• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• The Pure and Applied Mathematics
• /
• v.26 no.3
• /
• pp.157-175
• /
• 2019

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.

• Kyungpook Mathematical Journal
• /
• v.28 no.2
• /
• pp.185-196
• /
• 1988

We study existence of polynomial integrating factors and solutions F(x, y)=c of first order nonlinear differential equations. We characterize the homogeneous case, and give algorithms for finding existence of and a basis for polynomial solutions of linear difference and differential equations and rational solutions or linear differential equations with polynomial coefficients. We relate singularities to nature of the solution. Solution of differential equations in closed form to some degree might be called more an art than a science: The investigator can try a number of methods and for a number of classes of equations these methods always work. In particular integrating factors are tricky to find. An analogous but simpler situation exists for integrating inclosed form, where for instance there exists a criterion for when an exponential integral can be found in closed form. In this paper we make a beginning in several directions on these problems, for 2 variable ordinary differential equations. The case of exact differentials reduces immediately to quadrature. The next step is perhaps that of a polynomial integrating factor, our main study. Here we are able to provide necessary conditions based on related homogeneous equations which probably suffice to decide existence in most cases. As part of our investigations we provide complete algorithms for existence of and finding a basis for polynomial solutions of linear differential and difference equations with polynomial coefficients, also rational solutions for such differential equations. Our goal would be a method for decidability of whether any differential equation Mdx+Mdy=0 with polynomial M, N has algebraic solutions(or an undecidability proof). We reduce the question of all solutions algebraic to singularities but have not yet found a definite procedure to find their type. We begin with general results on the set of all polynomial solutions and integrating factors. Consider a differential equation Mdx+Ndy where M, N are nonreal polynomials in x, y with no common factor. When does there exist an integrating factor u which is (i) polynomial (ii) rational? In case (i) the solution F(x, y)=c will be a polynomial. We assume all functions here are complex analytic polynomial in some open set.

• IEIE Transactions on Smart Processing and Computing
• /
• v.4 no.4
• /
• pp.291-296
• /
• 2015

This paper describes the design of a high-speed comparator for high-speed automatic test equipment (ATE). The normal comparator block, which compares the detected signal from the device under test (DUT) to the reference signal from an internal digital-to-analog converter (DAC), is composed of a rail-to-rail first pre-amplifier, a hysteresis amplifier, and a third pre-amplifier and latch for high-speed operation. The proposed continuous comparator handles high-frequency signals up to 800MHz and a wide range of input signals (0~5V). Also, to compare the differences of both common signals and differential signals between two DUTs, the proposed differential mode comparator exploits one differential difference amplifier (DDA) as a pre-amplifier in the comparator, while a conventional differential comparator uses three op-amps as a pre-amplifier. The chip was implemented with $0.18{\mu}m$ Bipolar CMOS DEMOS (BCDMOS) technology, can compare signal differences of 5mV, and operates in a frequency range up to 800MHz. The chip area is $0.514mm^2$.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.253-263
• /
• 2006

In this paper we introduce a new concept, a 'periodicizing' function for the linear differential equation with the periodic forcing function. Moreover, we construct this function, which is closely related with the solution of a difference equation and an indefinite sum. Using this function, we can obtain a representation of solutions from which we see immediately the asymptotic behavior of the solutions.

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

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.18 no.2
• /
• pp.478-493
• /
• 2024

In this paper, the Mixed Integer Linear Programming (MILP) model is improved for searching differential characteristics of block cipher Midori-64, and 4 search strategies of differential path are given. By using strategy IV, set 1 S-box on the top of the distinguisher to be active, and set 3 S-boxes at the bottom to be active and the difference to be the same, then we obtain a 5-round differential characteristics. Based on the distinguisher, we attack 12-round Midori-64 with data and time complexities of 2⁶³ and 2^103.83, respectively. To our best knowledge, these results are superior to current ones.

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.33 no.2
• /
• pp.175-182
• /
• 2023

Differential cryptanalysis is one of the analysis techniques for block ciphers, and uses the property that the output difference with respect to the input difference exists with a high probability. If random data and differential data can be distinguished, data complexity for differential cryptanalysis can be reduced. For this, many studies on deep learning-based neural distinguisher have been conducted. In this paper, a deep learning-based neural distinguisher for PIPO 64/128 is proposed. As a result of experiments with various input differences, the 3-round neural distinguisher for the differential characteristics for 0, 1, 3, and 5-rounds achieved accuracies of 0.71, 0.64, 0.62, and 0.64, respectively. This work allows distinguishing attacks for up to 8 rounds when used with the classical distinguisher. Therefore, scalability was achieved by finding a distinguisher that could handle the differential of each round. To improve performance, we plan to apply various neural network structures to construct an optimal neural network, and implement a neural distinguisher that can use related key differential or process multiple input differences simultaneously.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.485-502
• /
• 2015

A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.