• 대한수학회보
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• 제44권4호
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• pp.607-622
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• 2007

We prove four theorems on the uniqueness of non linear differential polynomials sharing one value which improve a result of Yang and Hua, and supplements some results of Lahiri, Xu and Qiu and Banerjee.

• 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.

• 한국산학기술학회논문지
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• 제11권7호
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• pp.2328-2333
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• 2010

직접경계요소법은 음향방사문제 해석에 널리 적용되는 수치해석기법중 하나이지만, 외부 음향방사 문제에 있어서는 방사면 내부공간의 고유주파수 근방에서 비유일성이 나타나게 된다. 이를 해결하기 위한 방법으로 CHIEF 방법이 일반적으로 적용되어 왔으며, 최근 들어서는 ICA-Ring 방법과 같은 새로운 기법이 제안되어 해의 정확도 향상에 기여하고 있다. 본 논문에서는 앞서 언급한 두 가지 비유일성 회피기법들의 특성을 살피고, 각각의 기법 구현을 포함한 직접경계요소법 기반의 수치해석 코드를 작성한다. 또한, 법선방향 균일속도로 진동하는 구의 음향방사문제에 대한 수치해석을 수행하고 그 결과를 해석 해와 비교하여 각각의 기법들에 대한 비유일성 회피 성능을 고찰한다.

• 대한수학회보
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• 제43권1호
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• pp.161-168
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• 2006

We prove two theorems on the uniqueness of nonlinear differential polynomials sharing 1-points, the first of which improves a recent result of Fang-Fang and Lin-Yi.

• 호남수학학술지
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• 제42권4호
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• pp.821-828
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• 2020

In this work, we prove an existence of an inertial manifold for a system of differential equations with a non-self adjoint leading part. The result follows from the existence and uniqueness of negatively bounded solutions. In fact, we show that a sharp spectral condition is sufficient for the proof.

• Kyungpook Mathematical Journal
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• 제51권1호
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• pp.43-58
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• 2011

Using the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain non-linear differential polynomials share the same 1-points. Though the main concern of the paper is to improve a result of Fang [5] but as a consequence of the main result we improve and supplement some former results of Lahiri-Sarkar [16], Fang-Fang[6] et. al.

• 호남수학학술지
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• 제29권4호
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• pp.695-700
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• 2007

We establish two uniqueness theorems for non-constant entire functions which extends results of J. S. Hwang in J. Math. Anal. and its Appl. Vol. 37 (1972) 452-456.

• 대한수학회지
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• 제38권4호
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• pp.781-791
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• 2001

We consider the inverse conductivity problem to identify the unknown conductivity $textsc{k}$ as well as the domain D. We show hat, unlike the case when $textsc{k}$ is known, even a two or three dimensional ball may not be identified uniquely if the conductivity constant $textsc{k}$ is not known. We find a necessary and sufficient condition on the Cauchy data (u│∂Ω, g) for the uniqueness in identification of $textsc{k}$ and D. We also discuss on failure of stability.

• Journal of applied mathematics & informatics
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• 제41권4호
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• pp.849-860
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• 2023

In this research article, we deal with the uniqueness of entire and meromorphic functions when two linear differential polynomial share a non-zero value and obtain some results.