• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.429-445
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• 2004

In this paper we investigate the generalized Hyers-Ulam-Rassias stability for a functional equation of the form $f(\varphi(x,y)){\;}={\;}\phi(x,y)f(x,y)$, where x, y lie in the set S. As a consequence we obtain stability in the sense of Hyers, Ulam, Rassias, Gavruta, for some well-known equations such as the gamma, beta and G-function type equations.

• Journal of the Korean Statistical Society
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• v.31 no.3
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• pp.379-389
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• 2002

For two normal distribution with unknown means and unknown variances, a sequential procedure for estimating the difference of two normal means which satisfies both the coverage probability condition and the $\beta$-protection is proposed under some smoothness of variable imprecision function, and the asymptotic normality of the proposed stopping time after some centering and scaling is given.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.119-130
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• 2024

In this paper we discuss on the growth properties of composite entire and meromorphic functions on the basis of generalized (α, β, γ) order and generalized (α, β, γ) type comparing to their corresponding left and right factors.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.49-60
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• 2016

In this paper, we investigate the high order difference counterpart of $Br{\ddot{u}}ck^{\prime}s$ conjecture, and we prove one result that for a transcendental entire function f of finite order, which has a Borel exceptional function a whose order is less than one, if ${\Delta}^nf$ and f share one small function d other than a CM, then f must be form of $f(z)=a+ce^{{\beta}z}$, where c and ${\beta}$ are two nonzero constants such that $\frac{d-{\Delta}^na}{d-a}=(e^{\beta}-1)^n$. This result extends Chen's result from the case of ${\sigma}(d)$ < 1 to the general case of ${\sigma}(d)$ < ${\sigma}(f)$.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.695-703
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• 2015

Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function $_2F_1$, Some interesting special cases of our main results are also considered.

• BMB Reports
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• v.40 no.3
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• pp.419-425
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• 2007

In vitro directed evolution through DNA shuffling is a powerful molecular tool for creation of new biological phenotypes. E. coli $\beta$-galactosidase and $\beta$-glucuronidase are widely used, and their biological function, catalytic mechanism, and molecular structures are well characterized. We applied an in vitro directed evolution strategy through DNA shuffling and obtained five mutants named YG6764, YG6768, YG6769, YG6770 and YG6771 after two rounds of DNA shuffling and screening, which exhibited more $\beta$-glucuronidase activity than wild-type $\beta$-galactosidase. These variants had mutations at fourteen nucleic acid sites, resulting in changes in ten amino acids: S193N, T266A, Q267R, V411A, D448G, G466A, L527I, M543I, Q626R and Q951R. We expressed and purified those mutant proteins. Compared to the wild-type protein, five mutant proteins exhibited high $\beta$-glucuronidase activity. The comparison of molecular models of the mutated and wildtype enzymes revealed the relationship between protein function and structural modification.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.425-431
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• 2006

In this paper, by introducing three parameters A, B and ${\lambda}$, and estimating the weight coefficient, we give a new extension of Hardy-Hilbert's inequality with a best constant factor, involving the Beta function. As applications, we consider its equivalent inequality.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.93-111
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• 1993

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.493-505
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• 2017

Maximum likelihood estimation (MLE) of the generalized extreme value distribution (GEVD) is known to sometimes over-estimate the positive value of the shape parameter for the small sample size. The maximum penalized likelihood estimation (MPLE) with Beta penalty function was proposed by some researchers to overcome this problem. But the determination of the hyperparameters (HP) in Beta penalty function is still an issue. This paper presents some data adaptive methods to select the HP of Beta penalty function in the MPLE framework. The idea is to let the data tell us what HP to use. For given data, the optimal HP is obtained from the minimum distance between the MLE and MPLE. A bootstrap-based method is also proposed. These methods are compared with existing approaches. The performance evaluation experiments for GEVD by Monte Carlo simulation show that the proposed methods work well for bias and mean squared error. The methods are applied to Blackstone river data and Korean heavy rainfall data to show better performance over MLE, the method of L-moments estimator, and existing MPLEs.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.317-323
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• 2015

The purpose of the present paper is to study certain radii problems for the function $$f(z)=\[{\frac{z^{1-{\gamma}}}{{\gamma}+{\beta}}}\(z^{\gamma}[D^nF(z)]^{\beta}\)^{\prime}\]^{1/{\beta}}$$, where ${\beta}$ is a positive real number, ${\gamma}$ is a complex number such that ${\gamma}+{\beta}{\neq}0$ and the function F(z) varies various subclasses of analytic functions with fixed second coefficients. Relevant connections of the results presented herewith various well-known results are briefly indicated.