• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.247-260
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• 2011

Let h be a meromorphic function with few poles and zeros. By Nevanlinna's value distribution theory we prove some new properties on the polynomials in h with the coefficients being small functions of h. We prove that if f is a meromorphic function and if $f^m$ is identically a polynomial in h with the constant term not vanish identically, then f is a polynomial in h. As an application, we are able to find the entire solutions of the differential equation of the type $$f^n+P(f)=be^{sz}+Q(e^z)$$, where P(f) is a differential polynomial in f of degree at most n-1, and Q($e^z$) is a polynomial in $e^z$ of degree k $\leqslant$ max {n-1, s(n-1)/n} with small functions of $e^z$ as its coefficients.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.103-109
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• 2012

The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: $$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$ are investigated, where ${\phi}_p(u)={\mid}u{\mid}^{p-2}u$ with $p$ > 1 and ${\alpha}{\in}C^1$, $e{\in}C$ are T-periodic and $g$ is continuous and T-periodic in $t$. By using coincidence degree theory, some existence and uniqueness results are obtained.

• Bulletin of the Korean Mathematical Society
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• v.57 no.3
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• pp.677-690
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• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.933-941
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• 2009

In this paper, we consider p-Laplace equation which models the turbulent flow in a porous medium. Using a continuation principle (cf. [R. $Man{\acute{a}}sevich$ and J. Mawhin, Periodic solutions for nonlinear systems with p-Lplacian-like operators, J. Diff. Equa. 145(1998), 367-393]), we prove the existence of solutions for p-Laplace equation subject to periodic boundary conditions, under some sign and growth conditions for f. With the help of Leray-Schauder degree theory, the multiplicity of periodic solutions for p-Laplace equation is obtained under the similar conditions above and some known results are improved.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.391-395
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• 1996

This paper presents a robust force tracking control of a small-sized SMA gripper with two fingers using shape memory alloy(SMA) actuators. The mathematical governing equation of the proposed system is derived by Hamilton's principle and Lagrangian equation and then, the control system model is integrated with the first-order actuator dynamics. Uncertain system parameters such as time constant of the actuators are also included in the control model. A robust two degree of freedom(TDF) controller using H$_{\infty}$ control theory, which has inherent robustness to model uncertainties and external disturbances, is adopted to achieve end-point force tracking control of the two-finger gripper. Force tracking control performances for desired trajectories represented by sinusoidal and step functions are evaluated by undertaking both simulation and experimental works.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.11
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• pp.4573-4584
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• 2015

The traditional feature extraction algorithms for recognition of communication signals can hardly realize the balance between computational complexity and signals' interclass gathered degrees. They can hardly achieve high recognition rate at low SNR conditions. To solve this problem, a novel feature extraction algorithm based on Holder coefficient was proposed, which has the advantages of low computational complexity and good interclass gathered degree even at low SNR conditions. In this research, the selection methods of parameters and distribution properties of the extracted features regarding Holder coefficient theory were firstly explored, and then interval gray relation algorithm with improved adaptive weight was adopted to verify the effectiveness of the extracted features. Compared with traditional algorithms, the proposed algorithm can more accurately recognize signals at low SNR conditions. Simulation results show that Holder coefficient based features are stable and have good interclass gathered degree, and interval gray relation classifier with adaptive weight can achieve the recognition rate up to 87% even at the SNR of -5dB.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.2
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• pp.273-278
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• 2009

The determination of the associated weights in the theory of ordered weighted averaging (OWA) operators is one of the important issue. Recently, Wang and Parkan [Information Sciences 175 (2005) 20-29] proposed a minimax disparity approach for obtaining OWA operator weights and the approach is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Liu [International Journal of Approximate Reasoning, accepted] showed that the minimum variance OWA problem of Fuller and Majlender [Fuzzy Sets and Systems 136 (2003) 203-215] and the minimax disparity OWA problem of Wang and Parkan always produce the same weight vector using the dual theory of linear programming. In this paper, we give an improved proof of the minimax disparity problem of Wang and Parkan while Liu's method is rather complicated. Our method gives the exact optimum solution of OWA operator weights for all levels of orness, $0\leq\alpha\leq1$, whose values are piecewise linear and continuous functions of $\alpha$.