• Bulletin of the Korean Chemical Society
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• v.6 no.6
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• pp.337-343
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• 1985

A statistical mechanical approach to elucidate the solvent effects on the high polymer solutions has been carried out on the basis of the simple model of liquids improved by Pak. In our works, the partition function of the polymer solutions is formulated by the lattice model and our simple treatment of liquid structures. For the ideal polymer solutions proposed by Flory, thermodynamic functions of the polymer solutions are obtained and equations of mixing properties and partial molar quantities are derived from the presented partition function of the polymer solutions. Partial molar quantities are calculated for the rubber solutions in carbon disulfide, benzene and carbon tetrachloride. Comparisons have been made between our equations and those of Flory's original paper for partial molar properties of the rubber-benzene system. Comparing the experimental data of the osmotic pressure of polystyrene-cyclohexane system with our calculated values and those of Flory's, our values fit to the agreeable degrees better than those of Flory's.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.201-216
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• 2013

In this note, we consider the Riemann problem for a two-dimensional nonstrictly hyperbolic system of conservation laws. Without the restriction that each jump of the initial data projects one planar elementary wave, six topologically distinct solutions are constructed by applying the generalized characteristic analysis method, in which the delta shock waves and the vacuum states appear. Moreover we demonstrate that the nature of our solutions is identical with that of solutions to the corresponding one-dimensional Cauchy problem, which provides a verification that our construction produces the correct global solutions.

• Journal of Adhesion and Interface
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• v.17 no.4
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• pp.155-162
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• 2016

• Journal of the Korean Mathematical Society
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• v.55 no.5
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• pp.1269-1283
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• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.545-559
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• 2018

In this paper we mainly investigate the properties of the solutions to a type of nonhomogeneous algebraic differential equation in an angular domain. It includes the Borel directions of the solutions, the width of angular domains in which the solutions take its order and the measure of radial distributions of Julia sets of the solutions.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.265-277
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• 2004

This article deals with the number of periodic solutions of the second order polynomial differential equation using the Riccati equation, and applies the property of the solutions of the Riccati equation to study the property of the solutions of the more complicated differential equations. Many valuable criterions are obtained to determine the number of the periodic solutions of these complex differential equations.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.625-637
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• 2010

In this paper, we are concerned with the quasilinear elliptic systems with boundary blow-up conditions in a smooth bounded domain. Using the method of lower and upper solutions, we prove the sufficient conditions for the existence of the positive solution. Our main results are new and extend the results in [Mingxin Wang, Lei Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Analysis(In Press)].

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.19-32
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• 2020

We discuss the coexistence of positive solutions to certain strongly-coupled predator-prey elliptic systems under the homogeneous Dirichlet boundary conditions. The sufficient condition for the existence of positive solutions is expressed in terms of the spectral property of differential operators of nonlinear Schrödinger type which reflects the influence of the domain and nonlinearity in the system. Furthermore, applying the obtained results, we investigate the sufficient conditions for the existence of positive solutions of a predator-prey system with degenerate diffusion rates.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.713-723
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• 2003

We study a limit problem of reflected solutions of parabolic stochastic partial differential equations driven by martingale measures. The existence of solutions is found in an extension of the work with respect to white noise by Donati-Martin and Pardoux [4]. We show that if a certain sequence of driving martingale measures converges, the corresponding solutions also converge in the Skorohod topology.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.