• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.993-1015
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• 2012

In this paper, we study the quantum sl($n$) representation category using the web space. Specially, we extend sl($n$) web space for $n{\geq}4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial $P_n(q)$ specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl($n$). Moreover, we correct the false conjecture [30] given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial ($n=0$) and Jones polynomial ($n=2$) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.307-314
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• 2005

In this paper we consider positive solutions of the following difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}},{\frac{B}{x_{n-2}}}],\;A,B\;>\;0$$. We prove that every positive solution is eventually periodic. Also, we present here some results concerning positive solutions of the difference equation $$x_{n+l}\;=\;min[{\frac{A}{x_{n}x_{n-1}{\cdots}x_{n-k}},{\frac{B}{x_{n-(k+2)}{\cdots}x_{n-(2k+2)}}],\;A,B\;>\;0$$.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.217-222
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• 2003

In this paper, we consider the fuzzy differential equations (equation omitted) where F(t, x(t)) is a continuous fuzzy mapping on [0, $\infty$) ${\times}$ E$\^$n/. The purpose of this paper is to prove that the solution ${\Phi}$(t) of the fuzzy differential equations is equiasymptotically stable in the large and uniformly asymptotically stable in the large.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.353-361
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• 2007

In this paper, we prove the existence of multiple solutions for Neumann and periodic problems. Our main tools are recent general multiplicity theorems proposed by B. Ricceri.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.169-182
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• 1996

This paper presents the numerical experiment of a dis-cretized loaded cable with periodic forcing. There appeared to be var-ious type of nonlinear oscillations over a wide range of fequencies and amplitudes for the periodic forcing term. The same forcing term can give rise to large or small oscillation by solving initial value problem and observing the solutions after a long time.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.127-139
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• 2007

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.95-98
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• 1985

In [1], E.B. Lee and L. Markus described a sufficient condition for which the domain of null-controllability of a linear autonomous system is all of R$^{n}$ . The purpose of this note is to extend the result to a certain linear nonautonomous system. Thus we consider a linear control system dx/dt = A(t)x+B(t)u in the Eculidean n-space R$^{n}$ where A(t) and B(t) are n*n and n*m matrices, respectively, which are continuous on 0.leq.t<.inf. and A(t) is a periodic matrix of period .omega.. Admissible controls are bounded measurable functions defined on some finite subintervals of [0, .inf.) having values in a certain convex set .ohm. in R$^{m}$ with the origin in its interior. And we present a sufficient condition for which the domain of null-controllability is all of R$^{n}$ .

• Journal of the Chungcheong Mathematical Society
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• v.19 no.2
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• pp.141-151
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• 2006

We investigate the multiplicity of $2{\pi}$-periodic solutions of the nonlinear Hamiltonian system with almost polynomial and exponential potentials, $\dot{z}=J(G^{\prime}(z)+h(t))$, where $z:R{\rightarrow}R^{2n}$, $\dot{z}=\frac{dz}{dt}$, $J=\(\array{0&-I\\I&o}\)$, I is the identity matrix on $R^n$, $H:R^{2n}{\rightarrow}R$, and $H_z$ is the gradient of H. We look for the weak solutions $z=(p,q){\in}E$ of the nonlinear Hamiltonian system.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.191-201
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• 2005

In this paper, the existence of periodic positive solution and the attractivity are investigated for the rational recursive sequence $x_{n+1} = (A + ax_{n_k})/(b + x{n-l})$, where A, a and b are real numbers, k and l are nonnegative integer numbers.