• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.1016-1019
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• 2002

This paper deals with a fundamental and classical scattering problem by a finite strip. For the analysis of scattered acoustic field, a “single” integral equation is derived. Firstly, the complexity by considering the effect of the mean flow is alleviated by the introduction of Prandtl-Glauert coordinate and the new dependent variable. Secondly, the difficulty of solving the resultant strongly-coupled integral equations which always appear in this kind of 3-part mixed boundary value problem is solved by observing some good properties of the functions in complex domain and manipulating the equations and variables for the use of those properties. The solution can be obtained asymptotically in terms of gamma function and Whittaker function. One aim of this study is the improvement of methodology for the research using integral equations. The other is the basic understanding of scattering by a finite strip related to the linear cascade model of rotating fan blades.

• Journal of the Chungcheong Mathematical Society
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• v.9 no.1
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• pp.69-76
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• 1996

We obtain some properties of reducible differential equations in the sense of Liapunov.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.271-283
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• 2018

In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.185-188
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• 2010

In this note the distribution of roots of cubic equations in contrast to 0 is given, which is useful to discuss eigenvalues for qualitative properties of differential equations.

• Journal of the Korean Chemical Society
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• v.57 no.2
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• pp.176-203
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• 2013

In this work is induced a new topology of solutions of chemical equations by virtue of point-set topology in an abstract stoichiometrical space. Subgenerators of this topology are the coefficients of chemical reaction. Complex chemical reactions, as those of direct reduction of hematite with a carbon, often exhibit distinct properties which can be interpreted as higher level mathematical structures. Here we used a mathematical model that exploits the stoichiometric structure, which can be seen as a topology too, to derive an algebraic picture of chemical equations. This abstract expression suggests exploring the chemical meaning of topological concept. Topological models at different levels of realism can be used to generate a large number of reaction modifications, with a particular aim to determine their general properties. The more abstract the theory is, the stronger the cognitive power is.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.565-589
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• 2004

The present paper concerns the macroscopic overall description of rheologic properties for steel wire and synthetic fibre cables under variable loading actions according to non-linear creep and/or relaxation theory. The general constitutive equations of non-linear creep and/or relaxation of tension elements - cables under one-step and the variable stress or strain inputs using the product and two types of additive approximations of the kernel functions are presented in the paper. The derived non-linear constitutive equations describe a non-linear rheologic behaviour of the cables for a variable stress or strain history using the kernel functions determined only by one-step - constant creep or relaxation tests. The developed constitutive equations enable to simulate and to predict in a general way non-linear rheologic behaviour of the cables under an arbitrary loading or straining history. The derived constitutive equations can be used for the various tension structural elements with the non-linear rheologic properties under uniaxial variable stressing or straining.

• Proceedings of the Korea Concrete Institute Conference
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• 2010.05a
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• pp.337-338
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• 2010

In this study, the test results on creep properties of high strength concrete are shown compared with various prediction equations about creep. So in order to investigate the creep properties of high strength concrete, the application possibility of prediction equations about creep is studied compared with the equations in ACI-209 and CEB/FIP-90 for concrete produced using Portland cement.

• Industrial Engineering and Management Systems
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• v.12 no.1
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• pp.2-8
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• 2013

Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.3
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• pp.189-207
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• 2021

In this paper, we consider the approximate controllability for a class of semilinear integro-differential functional control equations in which nonlinear terms of given equations satisfy quasi-homogeneous properties. The main method used is to make use of the surjective theorems that is similar to Fredholm alternative in the nonlinear case under restrictive assumptions. The sufficient conditions for the approximate controllability is obtain which is different from previous results on the system operator, controller and nonlinear terms. Finally, a simple example to which our main result can be applied is given.

• 한국연소학회:학술대회논문집
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• 2012.11a
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• pp.233-236
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• 2012

In order to estimate the efficiency of an evaporative heat exchanger having mini channel, the equations to calculate heat exchanger properties, those are air temperatures and water temperatures etc, are derived from the governing equations based on the Navier-Stokes equation, even though there are several assumptions to make problem simplify. There are three heat transfer zones at the mini channel heat exchanger depending on the water condition. So, there are three governing equations and solutions to calculate the properties. As a results of this study, the equations to calculate a saturation point and a dry point are derived to evaluate an evaporative heat exchanger having micro channel. It is supposed to predict the performance and evaluate a mini channel heat exchanger.