• 대한수학회논문집
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• 제22권4호
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• pp.597-608
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• 2007

We present a general uniqueness result of an endemic state for an S-I-R model with external force of infection. We reduce the problem of finding non-trivial steady state solutions to that of finding zeros of a real function of one variable so that we can easily prove the uniqueness of an endemic state. We introduce an assumption which was usually used to show stability of a non-trivial steady state. It turns out that such an assumption adopted from a stability analysis is crucial for proving the uniqueness as well, and the assumption holds for almost all cases in our model.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권2호
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• pp.59-64
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• 2001

In this paper, we propose an alternate method for determining the uniqueness of the reconstruction of a complex sequence from its phase. Uniqueness constraints could be derived in terms of the zeros of a complex polynomial defined by the DFT of the sequence. However, rooting of complex polynomials of high order is a very difficult problem. Instead of finding zeros of a complex polynomial, the proposed uniqueness criteria show that non-singularity of a matrix can guarantee the uniqueness of the reconstruction of a complex sequence from its phase-only data. It has clear advantage over the rooting method in numerical stability and computational time.

• 대한수학회보
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• 제41권3호
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• pp.483-492
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• 2004

Let : [0, 1] $\times$ [0, $\infty$) $\longrightarrow$ [0, $\infty$) be continuous and a ${\in}$ C([0, 1], [0, $\infty$)),and let ${\xi}_{i}$ $\in$ (0, 1) with 0 < {\xi}$_1$ < ${\xi}_2$ < … < ${\xi}_{m-2}$ < 1, $a_{i}$, $b_{i}$ ${\in}$ [0, $\infty$) with 0 < $\Sigma_{i=1}$ /$^{m-2}$ $a_{i}$ < 1 and $\Sigma_{i=1}$$^{m-2}$ < l. This paper is concerned with the following m-point boundary value problem: $\chi$″(t)＋a(t) (t.$\chi$(t))＝0,t ${\in}$(0,1), $\chi$'(0)＝$\Sigma_{i=1}$ $^{m-2}$ /$b_{i}$$\chi$'(${\xi}_{i}$),$\chi$(1)＝$\Sigma_{i=1}$$^{m-2}$$a_{i}$$\chi$(${\xi}_{i}$). The existence, multiplicity and uniqueness of positive solutions of this problem are discussed with the help of two fixed point theorems in cones, respectively.

• 대한수학회논문집
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• 제30권3호
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• pp.327-337
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• 2015

This paper is concerned with the optimality conditions for optimal control problem of Belousov-Zhabotinskii reaction model. That is, we obtain the optimality conditions by showing the differentiability of the solution with respect to the control. We also show the uniqueness of the optimal control.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.439-448
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• 2007

In the paper, we use the theory of normal family to study the problem on entire function that share a finite non-zero value with their derivatives and prove a uniqueness theorem which improve the result of J.P. Wang and H.X. Yi.

• 충청수학회지
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• 제21권4호
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• pp.543-553
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• 2008

This paper is concerned with the optimal control problem of global press for an adsorbate-induced phase transition model. That is, we show the existence of the optimal control and derive the optimality conditions. Moreover, we obtain the uniqueness of the optimal control.

• East Asian mathematical journal
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• 제29권5호
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• pp.491-501
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• 2013

This paper is concerned with the necessary conditions of the optimal boundary control for some chemotaxis equations. We obtain the existence and the necessary conditions of the optimal boundary control in the space $(H^1(0,T))^2$. Moreover, under some assumptions, we show the uniqueness of the optimal control.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.371-383
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• 2013

In this paper, we investigate the uniqueness problem on entire functions sharing fixed points (ignoring multiplicities). Our main results improve and generalize some results due to Zhang [13], Qi-Yang [10] and Dou-Qi-Yang [1].

• 대한수학회보
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• 제35권1호
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• pp.63-74
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• 1998

Our study is dedicated to the the proof of uniqueness of solution of initially boundary value problem in Elastodynamics of initially stressed bodies with voids. This proof is obtained without recourse either to an energy conservation law or to any boundedness assumptions on the elastic coefficients.

• Journal of applied mathematics & informatics
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• 제37권1_2호
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• pp.133-148
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• 2019

This paper is devoted to studying the sharing value problem for the derivative of a meromorphic function with its shift and q-difference. The results in the paper improve and generalize the recent result due to Qi, Li and Yang.