• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.711-730
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• 1994

We consider Gibbs measures on $(R \times W_{0,0})^{Z^\nu}, W_{0,0} = {\omega \in C[0,1] : \omega(0) = \omega(1)}$, which are associated to an interaction between particles in lattice boson systems (quantum unbounded spin systems). In [4], the Gibbs measures were introduced in the study of equilibrium states of interacting lattice boson systems and were characterized by means of the equilibrium conditions. In this paper we utilize the techniques of the stochastic calculus of variations and the infinite dimensional Ito integral to derive stochastic equations which we call the equilibrium equations. We show that under appropriate conditions the equilibrium conditions and the equilibrium equations are equivalent. The lattice boson systems with superstable and regular interactions, which we studied in [4], are typical examples.

• Journal of Advanced Marine Engineering and Technology
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• v.13 no.2
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• pp.21-42
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• 1989

Recently, multi-branced driving systems are often used for power station systems or for marine propulsion systems to save the initial cost, the man power and to improve the energy efficiency. As the multi-branched power system has a very complicated vibrating system, its analyzing method is quite different from the ordinary method for the single straight system. In this study, the multi-branched power system is reduced to derive equations of free vibration and some analytical methods are studied to solve these equations and computer programs are developed to calcuate their numerical solutions. And also, equations of forced-damped vibration of the multi-branched power system which involves diesel engines are derived and their solving methods are studied. Some computer programs are developed to get responses of the forced vibration with damping and their results are synthesized to get resultant responses. Finally, exciting forces of diesel engine and damping forces of power driving systems are appreciated to help field engineers by suggesting reasonable method of estimating their values.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.749-759
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• 2005

We apply a cone theoretic fixed point theorem and obtain conditions for the existence of positive periodic solutions of the system of functional differential equations $$x'(t)\;=\;A(t)x(t)+{\lambda}f(t,\;x(t-\tau(t))$$.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.587-601
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• 2011

In this paper, we prove the existence and uniqueness of mild solution for stochastic functional integrodifferential evolution equations and derive sufficient conditions for the controllability results. As an illustration we consider the controllability for a system governed by a random motion of a string.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.224-243
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• 2022

In this paper, we prove the global existence of classical solutions to the 2D incompressible Boussinesq equations for the micropolar fluid. Furthermore, applying the Fourier splitting methods, we obtain the lager time decay properties.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.3
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• pp.315-321
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• 1988

The input-output relation for nonlinear systems can e explicitly represented by the volterra functional series and it is characterized by the Volterra kernels. A block diagram reduction method is proposed to determine the Volterra kernels for nonlinear differential equations and is compared with the direct substitution techniques. The former method can significantly reduce the computational complexity. A degree of nonlinearity is defined and analyzed for the analysis of nonlinear systems.

• Proceedings of the KSR Conference
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• 1998.05a
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• pp.299-306
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• 1998

Design sensitivity analysis of a mechanical system is an essential tool for design optimization and trade-off studies. This paper presents an efficient algorithm for the design sensitivity analysis of railway vehicle systems, using the direct differentiation method. The cartesian coordinate is employed as the generalized coordinate. The governing equations of the design sensitivity analysis are formulated as the differential equations. Design sensitivity analysis of railway vehicle systems is performed to show the validity and efficiency of the proposed method.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1419-1439
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• 2019

In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.3
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• pp.184-193
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• 2010

In this paper, we investigate the existence and calculation of the expression of periodic solutions for fuzzy differential equations with three types of forcing terms, by using Hukuhara derivative. In particular, Theorems 3.2, 4.2 and 5.2 are the results of existences of periodic solutions for fuzzy differential equations I, II and III, respectively. These results will help us to study phenomena with periodic peculiarity such as wave or sound.