• Communications of the Korean Mathematical Society
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• v.32 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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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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• v.29 no.1
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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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• v.21 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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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.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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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.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.48 no.1
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• pp.64-70
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• 2011

In an H.264/AVC video encoder, the motion estimation at fractional pixel accuracy improves a coding efficiency and image quality. However, it requires additional computation overheads for fractional search and interpolation, and thus, reducing the computation complexity of fractional search becomes more important. This paper proposes a Pixel Re-composition Fractional Motion Estimation (PRFME) algorithm for an H.264/AVC video encoder. Fractional Motion Estimation performs interpolation for the overlapped pixels which increases the computational complexity. PRFME can reduce the computational complexity by eliminating the overlapped pixel interpolation. Compared with the fast full search, the proposed algorithm can reduce 18.1% of computational complexity, meanwhile, the maximum PSNR degradation is less than 0.067dB. Therefore, the proposed PRFME algorithm is quite suitable for mobile applications requiring low power and complexity.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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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 $H(\mathbb{U})$.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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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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• v.58 no.3
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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.