• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.133-144
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• 2017

In this paper, we study ruled surfaces in 3-dimensional Euclidean and Minkowski space in terms of their Gauss map. We obtain classification theorems for these type of surfaces whose Gauss map G satisfying ${\Box}G=f(G+C)$ for a constant vector $C{\in}{\mathbb{E}}^3$ and a smooth function f, where ${\Box}$ denotes the Cheng-Yau operator.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.825-838
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• 1998

We prove that if a real hypersurface with constant mean curvature of a complex space form satisfying ▽$_{ξ/}$S = 0 and Sξ = $\sigma$ξ for a smooth function $\sigma$, then the structure vector field ξ is principal, where S denotes the Ricci tensor of the hypersurface.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.37-52
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• 2000

This paper is concerned with the impulsive Cauchy problem (equation omitted) where u is a possibly discontinuous vector-valued function and f, $g_{i}$ : $IR^{n}$ -> $IR^{n}$ are suitably smooth functions. We show that the input-output map is Lipschitz continuous and investigate compactness of reachable sets.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.589-600
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• 2016

In this paper, we propose a new incremental gradient method for solving a regularized minimization problem whose objective is the sum of m smooth functions and a (possibly nonsmooth) convex function. This method uses an adaptive stepsize. Recently proposed incremental gradient methods for a regularized minimization problem need O(mn) storage, where n is the number of variables. This is the drawback of them. But, the proposed new incremental gradient method requires only O(n) storage.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.239-245
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• 2011

In this paper, we will study the tension field of the function related to a Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ with totally geodesic fibres. In case that the Riemannain submersion ${\pi}\;:\;N{\rightarrow}M$ particularly has a smooth map $f\;:\;M{\rightarrow}N$ which happens to be a section, we will show that tension field ${\tau}(f)$ of the energy functional can be decomposed into the horizontal and vertical parts.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.479-488
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• 2024

Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is C¹-smooth on [0, ∞), vanishes at zero, and is positive on (0, ∞). A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.

• Korean Journal of Biological Psychiatry
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• v.23 no.4
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• pp.148-156
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• 2016

Objectives According to previous studies, the cannabinoid receptor 1 (CNR1) gene could be an important candidate gene for schizophrenia. Some studies have linked the (AAT)n trinucleotide repeat polymorphism in CNR1 gene with the risk of schizophrenia. Meanwhile, smooth pursuit eye movement (SPEM) has been regarded as one of the most consistent endophenotypes of schizophrenia. In this study, we investigated the association between the (AAT)n trinucleotide repeats in CNR1 gene and SPEM abnormality in Korean patients with schizophrenia. Methods We measured SPEM function in 167 Korean patients with schizophrenia (84 male, 83 female) and they were divided according to SPEM function into two groups, good and poor SPEM function groups. We also investigated allele frequencies of (AAT)n repeat polymorphisms on CNR1 gene in each group. A logistic regression analysis was performed to find the association between SPEM abnormality and the number of (AAT)n trinucleotide repeats. Results The natural logarithm value of signal/noise ratio (Ln S/N ratio) of the good SPEM function group was $4.34{\pm}0.29$ and that of the poor SPEM function group was $3.21{\pm}0.70$. In total, 7 types of trinucleotide repeats were identified, each containing 7, 10, 11, 12, 13, 14, and 15 repeats, respectively. In the patients with $(AAT)7$ allele, the distributions of the good and poor SPEM function groups were 18 (11.1%) and 19 (11.0%) respectively. In the patients with $(AAT)_{10}$ allele, $(AAT)_{11}$ allele, $(AAT)_{12}$ allele, $(AAT)_{13}$ allele, $(AAT)_{14}$ allele and $(AAT)_{15}$ allele, the distributions of good and poor SPEM function groups were 13 (8.0%) and 12 (7.0%), 4 (2.5%) and 6 (3.5%), 31 (19.8%) and 35 (20.3%), 51 (31.5%) and 51 (29.7%), 36 (22.2%) and 45 (26.2%), 9 (5.6%) and 4 (2.3%) respectively. As the number of (AAT) n repeat increased, there was no aggravation of abnormality of SPEM function. Conclusions There was no significant aggravation of SPEM abnormality along with the increase of number of (AAT)n trinucleotide repeats in the CNR1 gene in Korean patients with schizophrenia.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.276-279
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• 2005

A review of how the functions of two or more independent variables can be approximated by using fuzzy systems is provided in this paper. We start with an exact represention of a linear interpolation function of two independent variables by using a fuzzy system. Next, we describe how this function can be approximated by another fuzzy system with a lesser number or with a desired number of output fuzzy sets. Thus, a reduction of the storage needed is achieved by storing the fuzzy rules or equivalently the output fuzzy set numbers instead of storing the whole discrete function values. A description on how the cubic spl me interpolation function can be represented exactly by using the fuzzy system method is provided, along with a few examples where fuzzy rule tables with a size of 7$\times$7 provide a representation of the functions with relative errors of the order of $10^{2}$ or less.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.1 s.178
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• pp.174-184
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• 2006

In order to fill the holes with complex shapes in the large polygon model, a new approach which is based on the implicit surface interpolation method combined with domain decomposition method is presented. In the present study, a surface is constructed by creating smooth implicit surface from the incomplete polygon model through which the surface should pass. In the method an implicit surface is defined by a radial basis function, a continuous scalar-valued function over the domain $R^3$ The generated surface is the set of all points at which this scalar function takes on the value zero and is created by placing zero-valued constraints at the vertices of the polygon model. In this paper the well-known domain decomposition method is used in order to treat the large polygon model. The global domain of interest is divided into smaller domains where the problem can be solved locally. LU decomposition method is used to solve a set of small local problems and their local solutions are combined together using the weighting coefficients to obtain a global solution. In order to show the validity of the present study, various hole fillings are carried out fur the large and complex polygon model of arbitrary topology.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1045-1054
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• 2012

Support vector machine is known to be the very useful statistical method in classification and nonlinear function estimation. In this paper we propose a monotone support vector regression (SVR) for the estimation of monotonically decreasing function. The proposed monotone SVR is applied to smooth the Kaplan-Meier estimate of survival function. Experimental results are then presented which indicate the performance of the proposed monotone SVR using survival functions obtained by exponential distribution.