• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.229-238
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• 1993

Let M be an n-dimensional compact Riemannian manifold with boundary .part.M. We consider the Neumann eigenvalue problem on M of the equation (Fig.) where .upsilon. is the unit outward normal vector to the boundary .part.M. due to the importance of Poincare inequality for analysis on manifolds, one wishes to obtain the lower bound of the first non-zero eigenvalue .eta.$_{1}$ of (1.1). For the purpose of applications, it is important to relax the dependency of the lower bound on the geometric quantities. For general compact manifolds with convex boundary, Li-Yau [3] obtained the lower bound of .eta.$_{1}$. Recently, Roger Chen [1] investigated the lower bound of the first Neumann eigenvalue .eta.$_{1}$ on compact manifold M with nonconvex boundary. We investigate the lower bound .eta.$_{1}$ with the same conditions as those of Roger chen. But, using the different auxiliary function, we have the following theorem.

• The Journal of the Acoustical Society of Korea
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• v.18 no.3E
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• pp.30-36
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• 1999

In this paper, we develop a hybrid speaker recognition system [1] enhanced by pre-recognizer and post-recognizer. The pre-recognizer consists of general speech recognition systems and the post-recognizer is a pitch detection system using adapted continuous wavelet transform (ACWT) to improve the performance of the hybrid speaker recognition system. Two schemes to design ACWT is considered. One is the scheme to search basis library covering the whole band of speech fundamental frequency (speech pitch). The other is the scheme to determine which one is the best basis. Information cost functional is used for the criterion for the latter. ACWT is robust enough to classify the pitch of speech very well, even though the speech signal is badly damaged by environmental noises.

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

• Research in Mathematical Education
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• v.17 no.2
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• pp.99-118
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• 2013

The present study focuses on the contribution of a teaching unit to the development of spatial ability of third graders in general and from a gender point of view in particular. The research population consisted of seventy-four pupils: thirty-seven pupils in the experimental group who attended the teaching unit and thirty-seven pupils in the control group. The spatial ability of all the pupils was examined by means of common tests which checked cognitive capabilities of spatial ability. The research findings illustrate an improvement in the spatial ability of the experimental group pupils following the participation in the teaching unit. Moreover, regarding the gender aspect, the findings show that there was no significant differentiation between the spatial ability of third grade boys and the spatial ability of girls of the same age group.

• Honam Mathematical Journal
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• v.33 no.1
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• pp.19-25
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• 2011

Let G be the general linear group GL(n,$\mathbb{C}$), $W_0$ the Weyl group of G and W the extended a neWeyl group of G. Then it is well-known that W is a union of the double cosets $W_{0x}W_0$ as x moves over the set of dominant weights of W. It is also known that each double coset $W_{0x}W_0$ contains a unique element $m_x$ of the shortest length. These shortest length elements belong to what are called the canonical left cells. However, it is still an open problem to find the canonical left cell containing a given $m_x$. One of the mai purposes of this paper is to introduce a new approach to attack this question. In particular, we will present a conjecture which explicitly describes the canonical left cells containing an element $m_x$. We will show that our conjecture is true for some specific types of $m_x$.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.327-340
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ and presented their several generating functions. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.293-300
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• 2020

In this article, we define a (an amply) F_δ-supplemented module in category of R-Mod. The general properties of F_δ-supplemented modules are briefly discussed. Then, concentrating on the F_δ-small submodule, we find the necessary and sufficient condition for F_δ- supplemented modules. Also, we introduce ascending chain condition for F_δ-small submodules of any module and establish a basic theorem for amply F_δ-supplemented modules by using π-projectivity.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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• pp.371-376
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• 2008

Let $P(M,G,{\pi})=:P$ be a principal fibre bundle with structure Lie group G over a base manifold M. In this paper we get the following facts: 1. The tangent bundle TG of the structure Lie group G in $P(M,G,{\pi})=:P$ is a Lie group. 2. The Lie algebra ${\mathcal{g}}=T_eG$ is a normal subgroup of the Lie group TG. 3. $TP(TM,TG,{\pi}_*)=:TP$ is a principal fibre bundle with structure Lie group TG and projection ${\pi}_*$ over base manifold TM, where ${\pi}_*$ is the differential map of the projection ${\pi}$ of P onto M. 4. for a Lie group $H,\;TH=H{\circ}T_eH=T_eH{\circ}H=TH$ and $H{\cap}T_eH=\{e\}$, but H is not a normal subgroup of the group TH in general.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.211-218
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• 2014

In 3-dimensional Euclidean space, the geometric figures of a regular curve are completely determined by the curvature function and the torsion function of the curve, and surfaces are the fundamental curved spaces for pioneering study in modern geometry as well as in classical differential geometry. In this paper, we define parametrizations for surface by using parametric functions whose images are in the normal plane of each point on a given curve, and then obtain some results relating the Gaussian curvature of the surface with curvature and torsion of the given curve. In particular, we find some conditions for the surface to have either nonpositive Gaussian curvature or nonnegative Gaussian curvature.

• East Asian mathematical journal
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• v.28 no.5
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• pp.579-585
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• 2012

Let D be a finite digraph with the vertex set V(D) and arc set A(D). A two-valued function $f:V(D){\rightarrow}\{-1,\;1\}$ defined on the vertices of a digraph D is called a signed 2-independence function if $f(N^-[v]){\leq}1$ for every $v$ in D. The weight of a signed 2-independence function is $f(V(D))=\sum\limits_{v{\in}V(D)}\;f(v)$. The maximum weight of a signed 2-independence function of D is the signed 2-independence number ${\alpha}_s{^2}(D)$ of D. Recently, Volkmann [3] began to investigate this parameter in digraphs and presented some upper bounds on ${\alpha}_{s}^{2}(D)$ for general digraph D. In this paper, we improve upper bounds on ${\alpha}_s{^2}(D)$ given by Volkmann [3].