• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.45-48
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• 2002

Consider the mean distance of Brownian motion on Riemannian manifolds. We obtain the first three terms of the asymptotic expansion of the mean distance by means of Stochastic Differential Equation(SDE) for Brownian motion on Riemannian manifold. This method proves to be much simpler for further expansion than the methods developed by Liao and Zheng(1995). Our expansion gives the same characterizations as the mean exit time from a small geodesic ball with regard to Euclidean space and the rank 1 symmetric spaces.

• Journal of Korean Society for Quality Management
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• v.26 no.4
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• pp.101-110
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• 1998

The mean residual life function is the expected remaining life of an item at age $\chi$. The problem of trend change in the mean residual life is great interest in the reliability and survival analysis. In this paper we develop a new test statistic for testing whether or not the mean residual life changes its trend based on a complete sample. Monte Carlo simulations are conducted to compare the perfor mance of our test statistic with that of previously known tests.

• Journal of Veterinary Clinics
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• v.16 no.2
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• pp.253-256
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• 1999

The influence of essential oils from aboriginal softwoods as Pinus densiflora, Pinus koraiensis, Chamaecyparis obtusa and Chamaecyparis pisifera on the motor coordination, pulse, mean blood artery pressure and pain reducing test was investigated in mice and rats. The motor coordination of mouse was not induced by the inhalation of each oil. Furthermore, these oils did not alter the changes of the mean blood pressure and pulse rate. Chamaecyparis pisifera trand to reduce the mean blood pressure. The abdominal pain induced by acetic acid was reduced only by an essential oil from Pinus koraiensis in mouse.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.511-521
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• 2010

In this paper, we define the one-sided fuzzy set and we calculate the mean value and variance, defined by C. Carlsson and R. $Full{\acute{e}}r$, of this fuzzy set. And we obtain a result that, in some special case, the mean of the product of two fuzzy sets is the product of means of each fuzzy sets. This result can be considered as the similar result which is well-known in the independence of events in probability theory.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.287-304
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• 2016

In this paper, we consider the problem of existence of conformal metrics with prescribed mean curvature on the unit ball of ${\mathbb{R}}^n$, $n{\geq}3$. Under the assumption that the order of flatness at critical points of prescribed mean curvature function H(x) is ${\beta}{\in}[1,n-2]$, we give precise estimates on the losses of the compactness and we prove new existence result through an Euler-Hopf type formula.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1327-1334
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• 2012

In this paper, using analytic method and the properties of the Legendre's symbol, we prove an exact calculating formula on the $2m$-th power mean value of the generalized quadratic Gauss sums for $m{\geq}2$. This solves a conjecture of He and Zhang [On the 2k-th power mean value of the generalized quadratic Gauss sums, Bull. Korean Math. Soc. 48 (2011), no. 1, 9-15].

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.611-622
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• 2023

The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that q is a prime.

• Journal of the Korean Data and Information Science Society
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• v.13 no.1
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• pp.147-156
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• 2002

In this paper, we study the properties of the modified winsorized mean to estimate the mean of a two-truncation parameter population. Under some mild conditions, the estimator is found to be strongly consistent and asymptotically unbiased even though the sample is doubly type II censored.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.99-107
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• 2005

In this paper we consider the asymptotic mean squared error of positive part James-Stein estimators. In the normal-normal example, estimators of the mean squared error of these estimators are provided which are correct asymptotically up to O($m^{-l}$). Asymptotic estimators of the MSE's which correct up to O($m^{-l}$) are also provide. Here, m denotes the number of strata. A simulation study is undertaken to evaluate the performance of these estimators.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.647-659
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• 2007

Relationships between the Ricci curvature and the squared mean curvature and between the shape operator associated with the mean curvature vector and the sectional curvature function for slant submanifolds of an S-space-form are proved, particularizing them to invariant and anti-invariant submanifolds tangent to the structure vector fields.