• 한국군사과학기술학회지
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• 제1권1호
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• pp.128-144
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• 1998

일반적인 선형 탄성해석 경계 요소법이 초 고속 회전과 정상 열전도에 의한 열 탄성 효과가 고려된 문제에 적용되었다. 축대칭 경계 요소법 구성이 요약되었고, 등가 경계 적분 방정식의 물체력 핵 함수의 체적 적분 전환방법에 일반화된 내적과 벡터 연산법 개념이 도입되었다. 고차 경계 요소 적용을 위한 이산화 수치 해석법이 요약되었고, 소형 젯트 엔진(ADD 500)의 터어빈 로우터 디스크의 해석 결과가 유한 요소해와 비교되었다.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.725-734
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• 2019

The aim of this paper is to establish two general finite integral formulas involving the product of Galué type Struve functions and Srivastava's polynomials. The results are given in terms of generalized (Wright's) hypergeometric functions. These results are obtained with the help of finite integrals due to Oberhettinger and Lavoie-Trottier. Some interesting special cases of the main results are also considered. The results presented here are of general character and easily reducible to new and known integral formulae.

• East Asian mathematical journal
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• 제34권3호
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• pp.295-303
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• 2018

Gautam et al. [9] introduced the multivariable A-function, which is very general, reduces to yield a number of special functions, in particular, the multivariable H-function. Here, first, we aim to establish two very general integral formulas involving product of the general class of Srivastava multivariable polynomials and the multivariable A-function. Then, using those integrals, we find a solution of partial differential equations of heat conduction at zero temperature with radiation at the ends in medium without source of thermal energy. The results presented here, being very general, are also pointed out to yield a number of relatively simple results, one of which is demonstrated to be connected with a known solution of the above-mentioned equation.

• 대한수학회논문집
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• 제34권2호
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• pp.523-532
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• 2019

Integrals involving a finite product of the generalized Bessel functions have recently been studied by Choi et al. [2, 3]. Motivated by these results, we establish certain unified integral formulas involving a finite product of the generalized k-Bessel functions. Also, we consider some integral formulas of the (p, q)-extended Bessel functions $J_{{\nu},p,q}(z)$ and the Delerue hyper-Bessel function which are proved in terms of (p, q)-extended generalized hypergeometric functions, and the generalized Wright hypergeometric functions, respectively.

• 대한수학회보
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• 제58권4호
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• pp.1003-1019
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• 2021

In this paper, we introduce a class of maximal functions along twisted surfaces in ℝⁿ×ℝ^m of the form {(𝜙(|v|)u, 𝜑(|u|)v) : (u, v) ∈ ℝⁿ×ℝ^m}. We prove L^p bounds when the kernels lie in the space L^q (𝕊^n-1×𝕊^m-1). As a consequence, we establish the L^p boundedness for such class of operators provided that the kernels are in L log L(𝕊^n-1×𝕊^m-1) or in the Block spaces B^0,0_q (𝕊^n-1×𝕊^m-1) (q > 1).

• 호남수학학술지
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• 제43권4호
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• pp.597-612
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• 2021

Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

• 대한수학회논문집
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• 제31권1호
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• pp.115-129
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• 2016

Fractional calculus operators have been investigated by many authors during the last four decades due to their importance and usefulness in many branches of science, engineering, technology, earth sciences and so on. Saigo et al. [9] evaluated the fractional integrals of the product of Appell function of the third kernel $F_3$ and multivariable H-function. In this sequel, we aim at deriving the generalized fractional differentiation of the product of Appell function $F_3$ and multivariable H-function. Since the results derived here are of general character, several known and (presumably) new results for the various operators of fractional differentiation, for example, Riemann-Liouville, $Erd\acute{e}lyi$-Kober and Saigo operators, associated with multivariable H-function and Appell function $F_3$ are shown to be deduced as special cases of our findings.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• 대한수학회보
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• 제53권4호
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• pp.1071-1085
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• 2016

For $b{\in}L^1_{loc}({\mathbb{R}}^n)$, let ${\mathcal{I}}_{\alpha}$ be the bilinear fractional integral operator, and $[b,{\mathcal{I}}_{\alpha}]_i$ be the commutator of ${\mathcal{I}}_{\alpha}$ with pointwise multiplication b (i = 1, 2). This paper shows that if the commutator $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 is bounded from the product Morrey spaces $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to the Morrey space $L^{q,{\lambda}}({\mathbb{R}}^n)$ for some suitable indexes ${\lambda}$, ${\lambda}_1$, ${\lambda}_2$ and $p_1$, $p_2$, q, then $b{\in}BMO({\mathbb{R}}^n)$, as well as that the compactness of $[b,{\mathcal{I}}_{\alpha}]_i$ for i = 1 or 2 from $L^{p_1,{\lambda}_1}({\mathbb{R}}^n){\times}L^{p_2,{\lambda}_2}({\mathbb{R}}^n)$ to $L^{q,{\lambda}}({\mathbb{R}}^n)$ implies that $b{\in}CMO({\mathbb{R}}^n)$ (the closure in $BMO({\mathbb{R}}^n)$of the space of $C^{\infty}({\mathbb{R}}^n)$ functions with compact support). These results together with some previous ones give a new characterization of $BMO({\mathbb{R}}^n)$ functions or $CMO({\mathbb{R}}^n)$ functions in essential ways.

• 대한수학회논문집
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• 제32권2호
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• pp.305-319
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• 2017

Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.