• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.559-572
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• 2021

It is well known that every invariant harmonic function on the unit ball of the multi-dimensional complex space has the volume version of the invariant mean value property. In 1993 Ahern, Flores and Rudin first observed that the validity of the converse depends on the dimension of the underlying complex space. Later Lie and Shi obtained the analogues on the unit ball of multi-dimensional real space. In this paper we obtain the half-space analogues of the results of Liu and Shi.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.75-85
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• 2003

Let M be 3 Semi-invariant submanifold of codimension 3 with lift-flat normal connection in a complex projective space. Further, if the mean curvature of M is constant, then we prove that M is a real hypersurface of a complex projective space of codimension 2 in the ambient space.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.376-386
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• 1995

Designs for polynomial approximation to the unknown response function are considered. Optimality criteria are monotone functions of the mean squared error matrix of the least squares estimator. They correspond to the classical A-, D-, G- and Q-optimalities. Optimal first order designs are chosen from the invariant designs and then compared with optimal second order designs.

• 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.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.173-183
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• 2005

The Box-Cox power transformation is generally used for variance stabilization. Recently, Shin and Kang (2001) showed, under the Box-Cox transformation, invariant properties to the original model under the large mean and relatively small variance assumptions in time series analysis. In this paper we obtain some invariant properties in spatial statistics. Spatial statistics, Invariant Property, Variogram, Box-Cox power Transformation.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.979-998
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• 2009

Involving the Ricci curvature and the squared mean curvature, we obtain a basic inequality for a submanifold of an S-space form tangent to structure vector fields. Equality cases are also discussed. As applications we find corresponding results for almost semi-invariant submanifolds, $\theta$-slant submanifolds, anti-invariant submanifold and invariant submanifolds. A necessary and sufficient condition for a totally umbilical invariant submanifold of an S-space form to be Einstein is obtained. The inequalities for scalar curvature and a Riemannian invariant $\Theta_k$ of different kind of submanifolds of a S-space form $\tilde{M}(c)$ are obtained.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.1-9
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• 2003

In this article, we consider a Bayesian estimation method for the geometric mean of $textsc{k}$ exponential parameters, Using the Tibshirani's orthogonal parameterization, we suggest an invariant prior distribution of the $textsc{k}$ parameters. It is seen that the prior, probability matching prior, is better than the uniform prior in the sense of correct frequentist coverage probability of the posterior quantile. Then a weighted Monte Carlo method is developed to approximate the posterior distribution of the mean. The method is easily implemented and provides posterior mean and HPD(Highest Posterior Density) interval for the geometric mean. A simulation study is given to illustrates the efficiency of the method.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.723-732
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• 2016

We characterize proper biharmonic anti-invariant surfaces in 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds with constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of proper biharmonic submanifolds in a certain 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifold. Moreover, we determine 3-dimensional generalized (${\kappa}$, ${\mu}$)-manifolds which admit a certain kind of proper biharmonic foliation.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.851-864
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• 2022

We define a kind of sectional curvature and 𝛿-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.