• 호남수학학술지
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• 제39권4호
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.1059-1066
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• 2011

We introduce the concept of fuzzy S-weakly r-M-continuous functions on fuzzy r-minimal spaces, and investigate some characterizations of such functions and the relations between the continuity and fuzzy r-minimal compactness on fuzzy r-minimal spaces.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.993-1001
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• 2010

In this paper, we introduce the concept of fuzzy weakly r-M continuous function on r-minimal structures and investigate characterizations and properties for such functions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권2호
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• pp.124-127
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• 2010

In this paper, we introduce the concepts of fuzzy r-minimal continuous function and fuzzy r-minimal open function between a fuzzy r-minimal space and a fuzzy topological space. We also investigate characterizations and properties for such functions.

• 응용통계연구
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• 제24권3호
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• pp.523-533
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• 2011

위험관리수단으로 시장위험을 정확하게 측정하는 방법 중의 하나로 VaR를 선호한다. 현실생활에서는 단일분포가 아닌 두 개 이상의 다변량분포에 대한 VaR를 추정해야 하는 경우가 많다. 이런 경우에는 VaR를 추정하기 위해 다변량분포를 고려해야 한다. 본 연구는 확률변수들의 종속적 구조를 파악하고 비정규성의 특성을 갖는 다변량 분포함수를 생성하기 위하여 Copula 함수를 사용한다. 여러 산업의 수익률분포에 적합한 Clayton, Gumbel, Frank Copula 함수가 포함된 Archimedean Copula 함수를 추정하여 다변량 수익률 분포함수를 결정하고 이에 대응하는 VaR를 유도한다. 국내의 두 산업체의 자료를 실증예제로 하여 세 종류의 Copula 함수의 모수를 추정하고 이에 대응하는 이변량 분포로부터 VaR와 각각의 주변 분포의 VaR를 구한다. 실제의 VaR를 기준으로 기존 방법으로 구한 VaR와 비교 분석하여 추정의 정확성을 토론한다.

• 대한수학회지
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• 제56권5호
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• pp.1333-1354
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• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

• 대한수학회보
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• 제53권5호
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• pp.1291-1308
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• 2016

In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids {$z{\in}\mathbb{C}^3:{\mid}z_1{\mid}^p+{\mid}z_2{\mid}^q$ < 1, ${\mid}z_1{\mid}^p+{\mid}z_3{\mid}^r$ < 1}. We consider cases p = 6, q = r = 2 and p = q = r = 2. We also investigate the Lu Qi-Keng problem for p = q = r = 2.

• 응용통계연구
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• 제35권5호
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• pp.645-655
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• 2022

본 논문에서는 R에서 시계열 자료 예측을 위한 자동화 함수에 대하여 고찰하고 그 예측 성능을 비교합니다. 대표적인 시계열 예측 방법인 지수 평활 모형과 ARIMA (autoregressive integrated moving average) 모형을 대상으로 하였으며, 이들의 모형화 및 예측 자동화를 가능하게 하는 R의 4가지 자동화 함수인 forecast::ets(), forecast::auto.arima(), smooth::es()와 smooth::auto.ssarima()를 대상으로 하였습니다. 이들의 예측 성능을 비교하기 위하여 3,003가지의 시계열로 구성되어 있는 M3-Competition자료와 3가지의 정확성 척도를 사용하였습니다. 4가지 자동화 함수는 모형화의 다양성 및 편리성, 예측 정확도 및 실행 시간 등에서 각자 장단점이 있음을 확인하였습니다.

• 대한수학회보
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• 제33권3호
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• pp.487-496
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• 1996

Let f(z) be an entire function. Then the order $\rho(f)$ of f is defined by $$ \rho(f) = \overline{lim}_r\to\infty \frac{log r}{log^+ T(r,f)} = \overline{lim}_r\to\infty \frac{log r}{log^+ log^+ M(r,f)}, $$ where T(r,f) is the Nevanlinna characteristic of f (see [4]), $M(r,f) = max_{$\mid$z$\mid$=r} $\mid$f(z)$\mid$$ and $log^+ t = max(log t, 0)$.