• 호남수학학술지
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• 제24권1호
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• pp.35-41
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• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.

• 천문학논총
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• 제30권2호
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• pp.229-230
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• 2015

The results of spectral studies of the CTTS type young star RY Tau with spectrograms of the ultraviolet and the visual ranges are presented. We show the first detection of periodic variability of the emission line intensities in UV and visual ranges with a period of 23 days.

• East Asian mathematical journal
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• 제32권1호
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• pp.117-128
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• 2016

In this paper, we study the viscoelastic Kirchhoff type equation with a nonlinear source $$u^{{\prime}{\prime}}-M(x,t,{\parallel}{\bigtriangledown}u(t){\parallel}^2){\bigtriangleup}u+{\int}_0^th(t-{\tau})div[a(x){\bigtriangledown}u({\tau})]d{\tau}+{\mid}u{\mid}^{\gamma}u=0$$. Under the smallness condition with respect to Kirchhoff coefficient and the relaxation function and other assumptions, we prove the uniform decay rate of the Kirchhoff type energy.

• Bulletin of the Korean Chemical Society
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• 제8권5호
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• pp.406-408
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• 1987

It has been shown that the distribution of relaxation times, H(ln $\tau$), in semi-logarithmic time scale can easily be calculated numerically from the derivative of the relaxation function in semilogarithmic scale. In that, ln$\tau$, the abscissa, is divided into N different segments of equal size, then H is considered to be a linear function of ln $\tau$within each segment. The technique has been applied to a Williams-Watts function as well as to the relaxation function obtained by photon correlation spectroscopy from atactic polystyrene glass. It has been demonstrated that the relaxation functions can be precisely reproduced from the calculated distribution functions.

• 대한수학회보
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• 제56권6호
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• pp.1617-1642
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• 2019

In this paper, we study a theory for the structure of ${\tau}_w$-Loewy series of modules over commutative rings, where ${\tau}_w$ is the hereditary torsion theory induced by the so-called w-operation, and explore the relationship between ${\tau}_w$-Loewy modules and w-Artinian modules.

• 대한수학회보
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• 제50권1호
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• pp.241-261
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• 2013

In this paper, we find the coefficients for the Weierstrass ${\wp}(x)$ and ${\wp}^{{\prime}{\prime}}(x)$($x=\frac{1}{2}$, $\frac{\tau}{2}$, $\frac{\tau+1}{2}$)-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan ([23]). Finally, we reprove congruences for the functions ${\mu}(n)$ and ${\nu}(n)$ in Hahn's article [11, Theorems 6.1 and 6.2].

• 대한수학회지
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• 제53권4호
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• pp.895-908
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• 2016

Firstly, we establish spectral mapping theorems for normal eigenvalues (due to Browder) of a $C_0$-semigroup and its generator. Secondly, we discuss relationships between normal eigenvalues of the compact monodromy operator and the generator of the evolution semigroup on $P_{\tau}(X)$ associated with the ${\tau}$-periodic evolutionary process on a Banach space X, where $P_{\tau}(X)$ stands for the space of all ${\tau}$-periodic continuous functions mapping ${\mathbb{R}}$ to X.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2008년도 학술발표회 논문집
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• pp.909-914
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• 2008

미세-점착성 퇴적물로 구성되는 퇴적저면의 침식특성을 해석하기 위해, 고령토 퇴적저면에 대한 침식실험이 환형수조를 이용하여 수행되었다. 현재, 퇴적저면의 침식특성 연구에 대한 국내사례는 전무한 실정으로, 본 연구는 퇴적저면에 대한 침식실험 방법 및 결과의 타당성 검증을 목적으로 한다. 이를 위하여, 본 연구에서는 압밀시간 조건에 따라 4가지의 서로 다른 퇴적저면이 조성되었고, 각 저면별로 저면깊이에 따른 저면밀도의 변화가 우선적으로 정밀 측정되었다. 각 퇴적저면별 침식실험으로부터는, 바닥전단응력(${\tau}_b$)의 변화에 따른 저면 침식깊이(즉, 수층 부유사 농도)의 변화 측정을 통하여, 저면깊이에 따른 저면전단강도(즉, 침식한계전단응력, ${\tau}_S$)의 변화 값들이 정량적으로 분석되었으며, 최종적으로 잉여전단응력(${\tau}_b-{\tau}_S$)과 침식률 간의 관계식이 산정되었다. 퇴적저면 침식특성에 관한 과거 해외 연구 결과와의 비교 검토를 통하여, 본 연구에서 사용 혹은 적용된 실험장치, 실험 방법 및 실험결과가 타당성이 있음이 확인되었다.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.15-26
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• 2012

Some oscillation results are presented for the second-order neutral dynamic equation of mixed type on a time scale unbounded above $$\(r(t)[x(t)+p_1(t)x(t-{\tau}_1)+p_2(t)x(t+{\tau}_2)]^{\Delta}\)^{\Delta}+q_1(t)x(t-{\tau}_3)+q_2(t)x(t+{\tau}_4)=0.$$ These criteria can be applied when $\mathbb{T}=\mathbb{R}$, $\mathbb{T}=h{\mathbb{Z}}$ and $\mathbb{T}=\mathbb{P}_{a,b}$. Two examples are also provided to illustrate the main results.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.903-911
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• 2012

Let $\{u(t)\}$ and $\{u(dt)\}$ be two maximal length sequences of period $2^n-1$. The cross-correlation is defined by $C_d({\tau})=\sum{_{t=0}^{2^n-2}}(-1)^{u(t+{\tau})+v(t)$ for ${\tau}=0,1,{\cdots},2^n-2$. In this paper, we propose a new proof for finding the values and the number of occurrences of each value of $C_d({\tau})$ when $d=2^{k-2}(2^k+3)$, where $n=2k$, $k$ is a positive integer.