• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.889-904
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• 2021

This study is a follow-up study of Kang and Kim (2020). In this study, we derive the sample influence functions of the t-statistic which were not directly derived in previous researches. Throughout these results, we both mathematically examine the relationship between the empirical influence function and the sample influence function, and consider a method to approximate the sample influence function by the empirical influence function. Also, the validity of the relationship between an approximated sample influence function and the empirical influence function is verified by a simulation of a random sample of size 300 from normal distribution. As a result of the simulation, the relationship between the sample influence function which is derived from the t-statistic and the empirical influence function, and the method of approximating the sample influence function through the empirical influence function were verified. This research has significance in proposing both a method which reduces errors in approximation of the empirical influence function and an effective and practical method that evolves from previous research which approximates the sample influence function directly through the empirical influence function by constant revision.

• The Plant Pathology Journal
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• v.19 no.6
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• pp.301-304
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• 2003

Gamma-ray irradiation is known to induce various mutations in plants caused by chromosome alterations. This study investigated disease responses of selected gamma-ray induced rice mutants generated from seven Japonica-type rice cultivars against three plant diseases. Among the tested 22 mutants, three gain-of-function mutants and six loss-of-function mutants against rice blast were obtained, as well as three loss-of-function mutants against bacterial leaf blight (BLB). Two of the loss-of-function mutants were susceptible to both rice blast and BLB. Gain-of-function mutation has not been frequently observed in rice plants, thus, the mutants can be used to identify loci of novel genes for the regulation of disease resistant response.

• The Mathematical Education
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• v.55 no.3
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• pp.335-355
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• 2016

The purpose of this study is to analyze tasks to find intersection points of a function and its inverse function. To do this, we produced a task and 64 people solved the task. As a result, most people had a cognitive conflict related to inverse function. Because of over-generalization, most people regarded intersection points of a function and y=x as intersection points of a function and its inverse. To find why they used the method to find intersection points, we investigated 10 mathematics textbooks. As a result, 23 tasks were related a linear function, quadratic function, or irrational function. 21 tasks were solved by using an equation f(x)=x. 3 textbooks presented that a set of intersection points of a function and its inverse was not equal to a set of intersection points of a function and y=x. And there was no textbook to present that a set of intersection points of a function and its inverse was equal to a set of intersection points of $y=(f{\circ}f)(x)$ and y=x.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.26-29
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• 2002

Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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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.

• Therapeutic Science for Rehabilitation
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• v.6 no.2
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• pp.71-83
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• 2017

Objective: This study was to develop and verify the effects of the exercise-cognitive combined dual-task training program on cognitive function and depression of the elderly with mild cognitive impairment(MCI). Methods: The subjects were randomly assigned to the exercise-cognitive combined dual-task training group(n=32) or single-task training group(n=31). To identify the effects on cognitive function, general cognitive function, frontal lobe function, and attention/working memory were measured. Depression was evaluated using Korean version of Geriatric Depression Scale. The outcome measurements were performed before and after the 8 weeks of intervention(2 days per week). Results: After 8 weeks, general cognitive function, frontal cognitive function, attention/working memory function, depression of the dual-task training group were significantly increased than those of the single-task training group(p<0.05). Conclusion: The results indicated that an exercise-cognitive combined dual-task training for MCI was effective in improving general cognitive function, frontal /executive function, attention/working memory function and reducing depression.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.531-538
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• 2014

Concentric hyperspheres in the n-dimensional Euclidean space $\mathbb{R}^n$ are the level hypersurfaces of a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$. The magnitude $||{\nabla}f||$ of the gradient of such a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ is a function of the function f. We are interested in the converse problem. As a result, we show that if the magnitude of the gradient of a function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with isolated critical points is a function of f itself, then f is either a radial function or a function of a linear function. That is, the level hypersurfaces are either concentric hyperspheres or parallel hyperplanes. As a corollary, we see that if the magnitude of a conservative vector field with isolated singularities on $\mathbb{R}^n$ is a function of its scalar potential, then either it is a central vector field or it has constant direction.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.479-487
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• 2014

In this paper, we obtain some theorems on certain Euler type integrals involving generalized Mittag-Leffler function. Further, we deduce some special cases involving Wiman function, Prabhakar function and exponential and binomial functions.

• Journal of the Korean Data and Information Science Society
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• v.15 no.4
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• pp.899-910
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• 2004

In this paper we have proposed a new loss function, namely, non-linear exponential(NLINEX) loss function, which is quite asymmetric in nature. We obtained the Bayes estimator under exponential(LINEX) and squared error(SE) loss functions. Moreover, a numerical comparison among the Bayes estimators of power function distribution under SE, LINEX, and NLINEX loss function have been made.