• 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.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.1-11
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• 2018

We use Krasnoselskii's fixed point theorem to show that the neutral differential equation $$\frac{d}{dt}[x(t)-a(t)x(\tau(t))]+p(t)x(t)+q(t)x(\tau(t))=0,\;t{\geq}t_0$$, has a positive periodic solution. Some examples are also given to illustrate our results. The results obtained here extend the work of Olach [13].

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.183-193
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• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.4
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• pp.214-220
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• 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.

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

• Steel and Composite Structures
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• v.12 no.2
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• pp.129-147
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• 2012

In this paper, the thermal buckling analysis of rectangular composite laminated plates is investigated using the Differential Quadrature (DQ) method. The composite plate is subjected to a uniform temperature distribution and arbitrary boundary conditions. The analysis takes place in two stages. First, pre-buckling forces due to a temperature rise are determined by using a membrane solution. In the second stage, the critical temperature is predicted based on the first-order shear deformation theory. To verify the accuracy of the method, several case studies were used and the numerical results were compared with those of other published literatures. Moreover, the effects of several parameters such as aspect ratio, fiber orientation, modulus ratio, and various boundary conditions on the critical temperature were examined. The results confirm the efficiency and accuracy of the DQ method in dealing with this class of engineering problems.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.73-82
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• 2019

In this work, we give necessary and sufficient conditions under which every solution of a class of first-order neutral differential equations of the form $$(x(t)+p(t)x({\tau}(t)))^{\prime}+q(t)Hx({\sigma}(t)))=0$$ either oscillates or converges to zero as $t{\rightarrow}{\infty}$ for various ranges of the neutral coefficient p. Our main tools are the Knaster-Tarski fixed point theorem and the Banach's contraction mapping principle.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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• pp.445-454
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• 2022

Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].