• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.341-352
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• 2019

Let M be an n-dimensional closed Riemannian manifold with metric g, $d{\mu}=e^{-{\phi}(x)}d{\nu}$ be the weighted measure and ${\Delta}_{p,{\phi}}$ be the weighted p-Laplacian. In this article we will study the evolution and monotonicity for the first nonzero eigenvalue problem of the weighted p-Laplace operator acting on the space of functions along the Yamabe flow on closed Riemannian manifolds. We find the first variation formula of it along the Yamabe flow. We obtain various monotonic quantities and give an example.

• 정보처리학회논문지C
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• 제12C권5호
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• pp.673-678
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• 2005

Alamouti 공간시간부호(Space Time Coding)은 UMTS-WCDMA의 표준의 한 부분으로 제안되고 연구되고 있다. 그러나 지금까지 알려진 바로는 이 유명한 부호의 closed-form 비트 에러율(BER)에 대한 공식은 연구된 적이 없다. 본 논문에서는 시뮬레이션을 통한 성능 검증이 시간 소비를 방지하기 위하여 coherent BPSK로 변조된 데이터를 이용하여 시스템 성능 분석시 참고할 수 있는 BER 성능을 수식으로 유도하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권2호
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• pp.151-160
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• 2011

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

• 한국전자파학회논문지
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• 제15권5호
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• pp.499-508
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• 2004

마이크로스트립 구조체를 해석하는데 있어, 행렬 요소를 해석적으로 계산할 수 있는 효율적인 모멘트법이 제안된다. 본 논문의 모멘트법에서는 공간영역 그린함수로 Bessel 함수의 반 무한구간 정적분에 관한 공식에 근거하여 유도된 새로운 형태의 closed-form 그린함수를 사용한다. 본 논문의 모멘트법을 사용할 경우 기존의 모멘트법의 사용에 비해, 계산량 및 계산 속도와 같은 수치계산 효율 측면에서 약 4배 정도로 개선됨을 알 수 있었다. 본 논문이 제안하는 방법의 타당성을 확인하기 위하여 몇 가지 수치해석 결과를 제시한다.

• 대한수학교육학회지:학교수학
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• 제9권1호
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• pp.141-160
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• 2007

본 연구의 목적은 대수 문장제를 해결하기 위하여 학생들이 이전지식이나 경험을 어떻게 적용하는가를 조사하고자 학생들의 풀이과정에 대한 유사성을 일련의 표시(chain of signification) 관점에서 분석하는 것이다. 이를 위하여 본 연구에서는 중학생 3명을 대상으로 사례 연구를 실시하였다. 연구 결과, 학생A나 학생C는 (반)열린 공식을 해법 원리로 생각하여 구체화하는 과정을 일련의 표시로 구성하였다. 학생A와 학생C는 문제를 읽으면서 숫자 정보와 텍스트를 기반으로 정신적 모델을 구성하였으며, 그 의미(기의)와 기록(기표) 과정을 점진적으로 구성함으로써 일련의 표시 과정을 구성하였다. 학생A의 표시과정은 숫자나 문자, 그리고 그리기가 혼합된 것이었다. 그러나 학생C와 학생B는 단지 숫자나 문자만으로 구성하였다. 특히, 학생B는 특정한 문제정보만을 근거로 그 상황을 생각하지 않고, 자신의 알고리즘을 적용하기 위하여 자신이 구성한 규칙을 적용하고자 하는 시행착오에 대한 유사성을 구성하였다.

• 대한수학회지
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• 제52권4호
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• pp.853-868
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• 2015

Let G be a complex semisimple simply connected linear algebraic group. The main result of this note is to give several equivalent criteria for the untwistedness of the twisted cubes introduced by Grossberg and Karshon. In certain cases arising from representation theory, Grossberg and Karshon obtained a Demazure-type character formula for irreducible G-representations as a sum over lattice points (counted with sign according to a density function) of these twisted cubes. A twisted cube is untwisted when it is a "true" (i.e., closed, convex) polytope; in this case, Grossberg and Karshon's character formula becomes a purely positive formula with no multiplicities, i.e., each lattice point appears precisely once in the formula, with coefficient +1. One of our equivalent conditions for untwistedness is that a certain divisor on the special fiber of a toric degeneration of a Bott-Samelson variety, as constructed by Pasquier, is basepoint-free. We also show that the strict positivity of some of the defining constants for the twisted cube, together with convexity (of its support), is enough to guarantee untwistedness. Finally, in the special case when the twisted cube arises from the representation-theoretic data of $\lambda$ an integral weight and $\underline{w}$ a choice of word decomposition of a Weyl group element, we give two simple necessary conditions for untwistedness which is stated in terms of $\lambda$ and $\underline{w}$.

• 경영과학
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• 제25권3호
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• pp.1-12
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• 2008

The Swaption is one of the popular Interest rates derivatives. In spite of such a popularity, the swaption pricing formula is hard to derived within the theoretical consistency. Most of swaption pricing model are heavily depending on the simulation technique. We present a new class of swaption model based on the multi-factor HJM levy-mixture model. A key contribution of this paper is to provide a generalized swaption pricing formula encompassing many market stylize facts. We provide an approximated closed form solution of the swaption price using the Gram-Charlier expansion. Specifically, the solution form is similar to the market models, since our approximation is based on the Lognormal distribution. It can be directly compared with the traditional Black's formula when the size of third and fourth moments are not so large. The proposed extended levy model is also expected to be capable of producing the volatility smiles and skewness.

• ETRI Journal
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• 제16권2호
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• pp.15-25
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• 1994

In this paper we present a new formula which can predict the exact detection probability of a generalized order statistics (GOS) constant false alarm rate (DFAR) detector for a partially correlated Rayleigh target model (0 < $ \rho$< 1) in a closed form, where $\rho$ is the correlation coefficient between returned pulses. By simply substituting a set of specific coefficient into the derived formula, one can obtain the detection probability of any kind of CFAR detector. Detectors may include the order statistics CFAR detector, the censored mean level detector, and the trimmed mean CFAR detector, but are not necessarily restricted to them. The numerical result for the first order Markov correlation model as applied to some of the detectors shows that as $\rho$ increases from zero to one, higher signal-to-noise ratio is required to achieve the same detection probability.

• 대한수학회보
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• 제50권3호
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• pp.929-934
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• 2013

In this short note we discuss degrees of twisted Alexander polynomials and demonstrate an explicit example of a closed 3-manifold which is related to the degree formula due to Friedl, Kim and Kitayama.

• 호남수학학술지
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• 제42권1호
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• pp.49-62
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• 2020

In this paper, we consider interesting binomial and alternating binomial triple sums evaluated in multiplication forms in terms of the Fibonacci and Lucas numbers.