• Communications for Statistical Applications and Methods
• /
• v.16 no.5
• /
• pp.881-889
• /
• 2009

Support vector machines(SVMs) are known as flexible and efficient classifier of multivariate observations, producing a hyperplane or hyperdimensional curved surface in multidimensional feature space that best separates training samples by known groups. As various methodological extensions are made for SVM classifiers in recent years, it becomes more difficult to understand the constructed model intuitively. The aim of this paper is to visualize various SVM classifications tuned by several parameters in reduced dimensions, so that data analysts secure the tangible image of the products that the machine made.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.351-360
• /
• 2006

In this paper, we develop an inexact-Newton method for solving nonsmooth operator equations in infinite-dimensional spaces. The linear convergence and superlinear convergence of inexact-Newton method under some conditions are shown. Then, we characterize the order of convergence in terms of the rate of convergence of the relative residuals. The present inexact-Newton method could be viewed as the extensions of previous ones with same convergent results in finite-dimensional spaces.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.297-310
• /
• 2005

The concept of the Moore-Penrose inverse in an indefinite inner product space is introduced. Extensions of some of the formulae in the Euclidean space to an indefinite inner product space are studied. In particular range-hermitianness is completely characterized. Equivalence of a weighted generalized inverse and the Moore-Penrose inverse is proved. Finally, methods of computing the Moore-Penrose inverse are presented.

• Journal of applied mathematics & informatics
• /
• v.29 no.1_2
• /
• pp.443-450
• /
• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• Korean Journal of Mathematics
• /
• v.21 no.1
• /
• pp.41-53
• /
• 2013

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil-Armendariz property for Ore extensions and skew power series rings.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.439-456
• /
• 1994

Let $\tau$ be a given hereditary torsion theory for left R-module category R-Mod. The class of all $\tau$-torsion left R-modules, denoted by T is closed under homomorphic images, submodules, direct sums and extensions. And the class of all $\tau$-torsionfree left R-modules, denoted by $F$, is closed under submodules, injective hulls, direct products, and isomorphic copies ([3], Proposition 1.7 and 1.10).

• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.521-529
• /
• 1994

This paper studies the realization of irreducible unitary representations of $GL_2(R)$ and $GL_2(C)$ by Bargmann's classification[1]. Since the representations of general matrix groups can be obtained by the extensions of characters of a special linear group, we shall follow to a large extent the pattern of the results in [5], [6], and [8]. This article is divided into two sections. In the first section we describe the realization of principal series and discrete series and complementary series of $GL_2(R)$. The last section is devoted to the derivation of principal series and complementary series of $GL_2(C).

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.4
• /
• pp.641-649
• /
• 2007

We in this note introduce a concept, so called ${\pi}-Armendariz$ ring, that is a generalization of both Armendariz rings and 2-primal rings. We first observe the basic properties of ${\pi}-Armendariz$ rings, constructing typical examples. We next extend the class of ${\pi}-Armendariz$ rings, through various ring extensions.

• Journal of the Korean Mathematical Society
• /
• v.57 no.2
• /
• pp.429-450
• /
• 2020

We prove that wave operators for Schrödinger operators with multi-center local point interactions are scaling limits of the ones for Schrödinger operators with regular potentials. We simultaneously present a proof of the corresponding well known result for the resolvent which substantially simplifies the one by Albeverio et al.

• Communications of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1171-1184
• /
• 2020

This paper presents several fractional generalizations and extensions of known integral inequalities. To obtain these, an extended generalized Mittag-Leffler function and its fractional integral operator are used.