• Honam Mathematical Journal
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• v.33 no.2
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• pp.223-229
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• 2011

In investigation of boundary-value problems for certain partial differential equations arising in applied mathematics, we often need to study the solution of system of partial differential equations satisfied by hypergeometric functions and find explicit linearly independent solutions for the system. Here we choose the Exton functions $X_1$ and $X_2$ among his twenty functions to show how to find the linearly independent solutions of partial differential equations satisfied by these functions $X_1$ and $X_2$.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.168-176
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• 2000

Related to the error dynamics of an adaptive system, averaging theorems are developed for coupled differential equations which consist of ordinary differential equations and a parabolic partial differential equation. The results are then applied to the convergence analysis of the parameter estimate errors in the model reference adaptive control of a nonautonomous parabolic partial differential equation with lowly time-varying parameters.

• Journal of the Korean Mathematical Society
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• v.53 no.5
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• pp.1019-1036
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• 2016

In this paper, we study the existence of solutions and $L^2$-regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the non-linear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.355-364
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• 2008

Under pathological stress stimuli, dynamics of a biological system can be changed by alteration of several components such as functional proteins, ultimately leading to disease state. These dynamics in disease state can be modeled using differential equations in which kinetic or system parameters can be obtained from experimental data. One of the most effective ways to restore a particular disease state of biology system (i.e., cell, organ and organism) into the normal state makes optimization of the altered components usually represented by system parameters in the differential equations. There has been no such approach as far as we know. Here we show this approach with a cardiac hypertrophy model in which we obtain the existence of the optimal parameters and construct an optimal system which can be used to find the optimal parameters.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.861-876
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• 2016

The determination of the critical buckling load of multistory structures is important since this load is used in second order analysis. It is more realistic to determine the critical buckling load of multistory structures using the whole system instead of independent elements. In this study, a method is proposed for designating the system critical buckling load of torsion-free structures of which the load-bearing system consists of frames and shear walls. In the method presented, the multistory structure is modeled in accordance with the continuous system calculation model and the differential equation governing the stability case is solved using the differential transform method (DTM). At the end of the study, an example problem is solved to show the conformity of the presented method with the finite elements method (FEM).

• KIEAE Journal
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• v.16 no.6
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• pp.13-19
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• 2016

Purpose: In this study, we examined outdoor air fraction using historical data of actual Air Handling Unit (AHU) in the existing building during intermediate season and analyzed optimal outdoor air fraction by control types for economizer. Method: Control types for economizer which was used in analysis are No Economizer(NE), Differential Dry-bulb Temperature(DT), Diffrential Enthalpy(DE), Differential Dry-bulb Temperature+Differential Enthalpy(DTDE), and Differential Enthalpy+Differential Dry-bulb Temperature (DEDT). In addition, the system heating and cooling load were analyzed by calculating the outdoor air fraction through existing AHU operating method and control types for economizer. Result: Optimized outdoor air fraction through control types was the lowest in March and distribution over 50% was shown in May. In case of DE control type, outdoor air fraction was the highest of other control types and the value was average 63% in May. System heating load was shown the lowest value in NE, however, system cooling load was shown 1.7 times higher than DT control type and 5 times higher than DE control type. For system heating load, DT and DTDE is similar during intermediate season. However, system cooling load was shown 3 times higher than DE and DEDT. Accordingly, it was found as the method to save cooling energy most efficiently with DE control considering enthalpy of outdoor air and return air in intermediate season.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.527-537
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• 2004

This paper deals with the asymptotic behaviour for the semi-linear differential systems x' (t) = A(t)χ + f(t, x). We give a detailed proof of known generalization of Coppel's result about the above mentioned system.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.327-342
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• 2015

By employing a fixed point theorem in a weighted Banach space, we establish the existence of a solution for a system of impulsive singular fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.347-359
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• 2016

In this paper, we show that the solutions to perturbed functional differential system $$y^{\prime}=f(t,y)+{\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$$, have a bounded properties. To show the bounded properties, we impose conditions on the perturbed part ${\int_{t_0}^{t}}g(s,y(s),Ty(s))ds$ and on the fundamental matrix of the unperturbed system y' = f(t, y) using the notion of $t_{\infty}$-similarity.