• 대한수학회논문집
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• 제33권4호
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• pp.1159-1170
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• 2018

Recently, Parmar [5] introduced a new extension of the ${\tau}$-Gauss hypergeometric function $_2R^{\tau}_1(z)$. The main object of this paper is to study this extended ${\tau}$-Gauss hypergeometric function and obtain its properties including connection with modified Bessel function of third kind and extended generalized hypergeometric function, several contiguous relations, differential relations, integral transforms and elementary integrals. Various special cases of our results are also discussed.

• 호남수학학술지
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• 제45권2호
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• pp.184-197
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• 2023

For the numerous uses and significance of the Whittaker function in the diverse research areas of mathematical sciences and engineering sciences, This paper aims to introduce an extension of the Whittaker function by using a new extended confluent hypergeometric function of the first kind in terms of the Mittag-Leffler function. We also drive various valuable results like integral representation, integral transform and derivative formula. Further, we also analyze specific known results as a particular case of the main result.

• 대한수학회논문집
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• 제32권2호
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• pp.321-332
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• 2017

In this paper, we generalize the extended Appell's and Lauricella's hypergeometric functions which have recently been introduced by Liu [9] and Khan [7]. Also, we aim at establishing some (presumbly) new integral representations and transforms for the extended generalized Appell's and Lauricella's hypergeometric functions.

• 대한수학회논문집
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• 제29권3호
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• pp.479-487
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• 2014

In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.125-134
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• 2019

Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known results.

• Journal of the Korean Statistical Society
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• 제19권2호
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• pp.113-121
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• 1990

Let ${X_n : n=1,2,\cdots}$ be iid random variables with distribution $P_{\theta}, \theta \in H$ where $H$ is some abstract parameter space. We consider a sequential confidence interval I for the mean $\mu = \mu(\theta)$ of $P_{\theta}$ satisfying $P_{\theta}(\mu \in I) \geq 1-\alpha$ and $P_{\theta}(\mu-\delta(\mu) \in I) \leq \beta$ for all $\theta \in H$ for any given an imprecision real valued function $\delta(\mu) > 0$ and error probabilities $0 < \alpha, \beta < 1$. A one-sided sequential confidence interval is constructed under some restriction of the family {P_{\theta} : \theta \in H}$ and the imprecision function $\delta$. This is extended to the two-sided cases.

• 호남수학학술지
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• 제37권1호
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• pp.113-126
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• 2015

Recently, Liu and Wang generalized Appell's and Lauricella's hypergeometric functions. Motivated by the work of Liu and Wang, the main object of this paper is to present new generalizations of Appell's and Lauricella's hypergeometric functions. Some integral representations, transformation formulae, differential formulae and recurrence relations are obtained for these new generalized Appell's and Lauricella's functions.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.503-507
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• 2006

Let X be a Tychonoff space and ${\sum}(X)$ the set of all the subrings of C(X) that contain $C^*(X)$. For any A(X) in ${\sum}(X)$ suppose $_{{\upsilon}A}X$ is the largest subspace of ${\beta}X$ containing X to which each function in A(X) can be extended continuously. Let us write A(X) ~ B(X) if and only if $_{{\upsilon}A}X=_{{\upsilon}B}X$, thereby defining an equivalence relation on ${\sum}(X)$. We have shown that an A(X) in ${\sum}(X)$ is isomorphic to C(Y ) for some space Y if and only if A(X) is the largest member of its equivalence class if and only if there exists a subspace T of ${\beta}X$ with the property that A(X)={$f{\in}C(X):f^*(p)$ is real for each $p$ in T}, $f^*$ being the unique continuous extension of $f$ in C(X) from ${\beta}X$ to $\mathbb{R}^*$, the one point compactification of $\mathbb{R}$. As a consequence it follows that if X is a realcompact space in which every $C^*$-embedded subset is closed, then C(X) is never isomorphic to any A(X) in ${\sum}(X)$ without being equal to it.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.14-14
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• 2003

Given a sequence ｛ $X_{n}$｝ of independent and identically distributed random variables with F, a sequential procedure for the p-th quantile ξ$_{P}$= $F^{-1}$ (P), 0$\beta$-protection. Some asymptotic properties for the proposed procedure and of an involved stopping time are proved: asymptotic consistency, asymptotic efficiency and asymptotic normality. From one of the results an effect of smoothing based on kernel functions is discussed. The results are also extended to the contaminated case.e.e.

• 한국임상수의학회지
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• 제32권2호
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• pp.191-195
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• 2015

7년령, 중성화 수컷 고양이가 무기력과 식욕부진으로 내원하였다. 실험실 검사는 말초혈액 호중구에서 중등도의 퇴행성 변화, free 및 total thyroxine의 농도 감소 및 혈액배양에서 세균증식이 관찰되었다. 16S ribosomal RNA 및 heat shock protein 60 유전자 검사 결과 세균은 Enterobacter cloacae로 확인되었다. 항생제 최소억제농도 평가결과 16개 항생제에 대한 다약제 내성이 관찰되었다. 중합효소연쇄반응 및 시퀀싱 결과 $bla_{TEM-1}$, $bla_{CTX-M-15}$ 및 플라스미드 유래 $bla_{ACT-1}$ 유전자에 대한 양성 반응이 관찰되었으며, 결과적으로 확인된 세균이 광범위 beta-lactamase 및 ampC beta-lactamase를 합성하는 플라스미드를 보유한 것을 확인하였다. 환자는 1개월 간 항생제와 levothyroxine 치료를 받은 후 증상이 호전되었고, 치료 후 갑상선 기능검사와 혈액배양 결과 이상소견은 소실되었다. 이 증례는 고양이의 지역사회획득 다약제내성 E. cloacae에 의한 정상 갑상샘 질환 증후군의 첫 예이다. 신속한 진단과정과 적절한 항생제 선택에 의해 이환된 고양이는 패혈증으로부터 회복되었다.