• 대한수학회논문집
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• 제36권1호
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• pp.41-50
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• 2021

This paper devoted to obtain some fractional integral properties of generalized Bessel function using pathway fractional integral operator. We also find the pathway transform of the generalized Bessel function in terms of Fox H-function.

• Nuclear Engineering and Technology
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• 제44권6호
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• pp.597-610
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• 2012

The passive auxiliary feedwater system (PAFS) is one of the advanced safety features adopted in the APR+, which is intended to completely replace the conventional active auxiliary feedwater system. With an aim of validating the cooling and operational performance of PAFS, an experimental program is in progress at KAERI, which is composed of two kinds of tests; the separate effect test and the integral effect test. The separate effect test, PASCAL ($\underline{P}$AF$\underline{S}$ $\underline{C}$ondensing Heat Removal $\underline{A}$ssessment $\underline{L}$oop), is being performed to experimentally investigate the condensation heat transfer and natural convection phenomena in PAFS. A single, nearly-horizontal U-tube, whose dimensions are the same as the prototypic U-tube of the APR+ PAFS, is simulated in the PASCAL test. The PASCAL experimental result showed that the present design of PAFS satisfied the heat removal requirement for cooling down the reactor core during the anticipated accident transients. The integral effect test is in progress to confirm the operational performance of PAFS, coupled with the reactor coolant systems using the ATLAS facility. As the first integral effect test, an FLB (feedwater line break) accident was simulated for the APR+. From the integral effect test result, it could be concluded that the APR+ has the capability of coping with the hypothetical FLB accident by adopting PAFS and proper set-points of its operation.

• Journal of Microbiology and Biotechnology
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• 제22권7호
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• pp.939-946
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• 2012

Antibiotic production with Streptomyces sindenensis MTCC 8122 was optimized under submerged fermentation conditions by artificial neural network (ANN) coupled with genetic algorithm (GA) and Nelder-Mead downhill simplex (NMDS). Feed forward back-propagation ANN was trained to establish the mathematical relationship among the medium components and length of incubation period for achieving maximum antibiotic yield. The optimization strategy involved growing the culture with varying concentrations of various medium components for different incubation periods. Under non-optimized condition, antibiotic production was found to be $95{\mu}g/ml$, which nearly doubled ($176{\mu}g/ml$) with the ANN-GA optimization. ANN-NMDS optimization was found to be more efficacious, and maximum antibiotic production ($197{\mu}g/ml$) was obtained by cultivating the cells with (g/l) fructose 2.7602, $MgSO_4$ 1.2369, $(NH_4)_2PO_4$ 0.2742, DL-threonine 3.069%, and soyabean meal 1.952%, for 9.8531 days of incubation, which was roughly 12% higher than the yield obtained by ANN coupled with GA under the same conditions.

• Kyungpook Mathematical Journal
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• 제45권2호
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• pp.281-292
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• 2005

In this paper a nonlinear alternative of Leray-Schauder type is proved in a Banach algebra involving three operators and it is further applied to a functional nonlinear integral equation of mixed type $$x(t)=k(t,x({\mu}(t)))+[f(t,x({\theta}(t)))]\(q(t)+{\int}_0{^{\sigma}^{(t)}}v(t,s)g(s,x({\eta}\(s)))ds\)$$ for proving the existence results in Banach algebras under generalized Lipschitz and $Carath{\acute{e}}odory$ conditions.

• 호남수학학술지
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• 제29권1호
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• pp.9-18
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• 2007

In this paper we establish the existence theorem of the operator-valued function space integral $K_{\lambda}(F)$ for $\lambda\in\mathbb{C}_{+,\lambda_0}^\sim$ where F is of the form (1.1). Our result is a generalization for Johnson and Skoug result in [8].

• 한국방사선학회논문지
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• 제5권4호
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• pp.217-221
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• 2011

$^{237}Np$ is very important material in the fission products of nuclear reactors. Resonance integral(RI) tests of this material is necessary to check between the experiments and the evaluated data. Such feedback to the evaluated data is very important to correct data and improve of codes. The RI for the $^{237}Np(n,{\gamma})^{238}Np$ reaction were measured by using the 46-MeV electron linear accelerator (linac) at the Research Reactor Institute, Kyoto University (KURRI). The measurement was performed in the energy region from 0.005 eV and 10 keV. RI obtained as 804.7 barns, compared with those of the evaluated data in JENDL-4.0 and Mughabghab.

• 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.

• 한국수학교육학회지시리즈A:수학교육
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• 제23권1호
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• pp.35-38
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• 1984

• 충청수학회지
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• 제20권3호
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.

• 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.