• 대한수학회논문집
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• 제32권3호
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• pp.677-688
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• 2017

The composition of Jacobi type finite classes of the classical orthogonal polynomials with two generalized Riemann-Liouville fractional derivatives are considered. The outcomes are expressed in terms of generalized Wright function or generalized hypergeometric function. Similar composition formulas are also obtained by considering the generalized Riemann-Liouville and $Erd{\acute{e}}yi-Kober$ fractional integral operators.

• 대한수학회보
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• 제60권4호
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• pp.1061-1070
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• 2023

In this paper, we study products of composition, multiplication and differentiation acting on the fractional Cauchy spaces and mapping into the Zygmund space. Characterizations are provided for boundedness and compactness of these operators.

• Korean Journal of Mathematics
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• 제29권1호
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• pp.91-103
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• 2021

In this paper we have established inequalities for a unified integral operator by using convexity of composition of two functions. The obtained results are directly connected to bounds of various fractional and conformable integral operators which are already known in literature. A generalized Hadamard integral inequality is obtained which further leads to its various versions for associated fractional integrals. Further, some implicated results are discussed.

• East Asian mathematical journal
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• 제21권2호
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• pp.191-203
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• 2005

In the present paper we first establish some basic results for a substantially more general class of functions defined below. The results include simple differentiation and fractional calculus operators(integration and differentiation of arbitrary orders) for this class of functions. These results are then invoked in determining similar properties for the generalized Wright's hypergeometric functions. Further, norm estimate of a certain class of integral operators whose kernel involves the generalized Wright's hypergeometric function, and its composition(and other related properties) with the fractional calculus operators are also investigated.

• 대한수학회지
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• 제48권5호
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• pp.969-984
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• 2011

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

• 대한수학회논문집
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• 제36권2호
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• pp.267-276
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• 2021

The aim of the present investigation is to establish the composition formulas for the pathway fractional integral operator connected with Hurwitz-Lerch zeta function and extended Wright-Bessel function. Some interesting special cases have also been discussed.

• 대한전자공학회논문지SP
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• 제48권1호
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• pp.64-70
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• 2011

본 논문은 H.264/AVC 비디오 코덱의 부화소 움직임 추정 연산을 효율적으로 줄일 수 있는 화소 재구성 알고리즘을 제안한다. 부화소 움직임 추정 연산은 보다 정확한 움직임 벡터를 찾을 수 있어 비디오 코덱에 널리 사용되지만, 추가적인 보간 및 탐색 연산으로 인해 부호화가의 연산량을 증가시키는 문제점이 있다. 본 논문은 화소 재구성 알고리즘을 이용한 부화소 움직임 추정기를 제안 하였다. 일반적인 부화소 움직임 추정기는 보간 시 같은 화소를 중복하여 보간한다. 이러한 중복 보간은 연산량을 증가 시키는 원인이 된다. 화소 재구성 알고리즘은 화소의 중복 보간을 제거하여 부화소 움직임 추정기의 연산량을 감소시킨다. 제안한 알고리즘은 고속 전역 부화소 탐색 알고리즘과 비교하여 보간 시 연산량이 18.1% 감소하였으며, PSNR 감소는 평균 0.067dB로 화질의 열화는 매우 미비했다. 그러므로 제안한 알고리즘은 저전력의 고효율을 요구하는 모바일 응용에 적합하다.

• 대한수학회보
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• 제48권6호
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• pp.1119-1124
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• 2011

In the present paper, we study the chaotic property of weighted composition operators acting on the holomorphic function space $H(\mathbb{U})$.

• 대한수학회논문집
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• 제38권3호
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of Applied Biological Chemistry
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• 제58권3호
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• pp.209-218
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• 2015

Fructooligosaccharides have been mainly produced by microbial fructosyltransferases (FTase) enzymes. The present work focuses on the optimization of medium composition and cultivation parameters affecting FTase produced by Penicillium aurantiogriseum AUMC 5605 in shake flask cultivation. FTase production was optimized in two steps using DeMeo's fractional factorial design. A 1.46-fold increase in FTase production (105.4 U/mL) was achieved using the optimized culture medium consisting of (g/L): sucrose, 600; yeast extract, 10; $K_2HPO_4$, 5; $MgSO_4{\cdot}7H_2O$, 0.5; $(NH_4)_2SO_4$, 1.0 and KCl, 0.5. The obtained results showed that the maximum FTase enzyme activity was produced at initial cultivation pH values ranging from 6.0-6.5, at agitation speed of 200 rpm and using vegetative fungal cells as inoculum. Moreover, results showed that optimization of medium composition and some cultivation parameters resulted in an increase of about 93.7% in the enzyme activity than the nonoptimized cultivation conditions after 96 h of cultivation. Additionally, maximum production and specific production rates recorded 2340 U/L/h and 102 U/L/h/g cells, respectively.