• The Mathematical Education
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• v.21 no.1
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• pp.19-21
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• 1982

In this paper, we define the z-S-closed spaces using the notions of zero-sets and S-closed spaces introduced by T. Thompson, and investigate some properties of these spaces. We also obtain the following results. If a space X is z-S-closed, then every cover of z-regular semiopen sets has a finite proximate subcover. A z-extremally disconnected z-QHC space is z-S-closed, z-S-closed is contagious.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.563-568
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• 2019

This study is concerned with the approximation properties of pairs. For ${\lambda}{\geq}1$, we prove that given a Banach space X and a closed subspace $Z_0$, if the pair ($X,Z_0$) has the ${\lambda}$-bounded approximation property (${\lambda}$-BAP), then for every ideal Z containing $Z_0$, the pair ($Z,Z_0$) has the ${\lambda}$-BAP; further, if Z is a closed subspace of X and the pair (X, Z) has the ${\lambda}$-BAP, then for every separable subspace $Y_0$ of X, there exists a separable closed subspace Y containing $Y_0$ such that the pair ($Y,Y{\cap}Z$) has the ${\lambda}$-BAP. We also prove that if Z is a separable closed subspace of X, then the pair (X, Z) has the ${\lambda}$-BAP if and only if for every separable subspace $Y_0$ of X, there exists a separable closed subspace Y containing $Y_0{\cup}Z$ such that the pair (Y, Z) has the ${\lambda}$-BAP.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.453-468
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• 2022

In this article, we define a module M to be G^z-extending if and only if for each z-closed submodule X of M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We investigate structural properties of G^z-extending modules and locate the implications between the other extending properties. We deal with decomposition theory as well as ring and module extensions for G^z-extending modules. We obtain that if a ring is right G^z-extending, then so is its essential overring. Also it is shown that the G^z-extending property is inherited by its rational hull. Furthermore it is provided some applications including matrix rings over a right G^z-extending ring.

• Honam Mathematical Journal
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• v.2 no.1
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• pp.13-18
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• 1980

모든 기호(記號)는 G.E Bredon의 저(著) Sheaf Theory의 기호(記號)를 따른다. A가 torsion free이며 elementary sheaf이라 하자. 그리고 L을 injective L-module이라 하자 $dim_{\varphi}X<{\infty}$이라면 support의 $family{\varphi}$와 locally subset z에 대하여 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{\varphi}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-p}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ 이며 support의 family c와 compact subset z에 대하여도 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{c}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-y}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ A가 elementary이면 locally closed z와 z에서 closed인 $z^{\prime}$ 그리고 $z^{\prime\prime}=z-z^{\prime}$에 대하여 exact sequence ⋯⋯${\rightarrow}H^{z^{\prime}}_{p}\;(X:A){\rightarrow}H^{z}_{p}(X:A){\rightarrow}H^{z^{\prime\prime}}_{p}\;(X:A){\rightarrow}$⋯⋯ 가 존재(存在)한다.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.3
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• pp.281-293
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• 2008

In the layered medium, the Sommerfeld integral must be evaluated to calculate a space domain Green's function. The real axis integration method provides stable and accurate results over wide ranges of the observation distance and the singnal frequency. But this method has the in efficiency of approximation when the field point z is changed. Also, as the amplitude of z increases, the change of the spectral domain function is more rapidly. Therefore, the approximation is difficult when z becomes larger. In this paper, we propose a method to calculate an accurate closed-form Green's function for microstrip structure by using the closed-loop integration path.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.141-155
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• 2010

In this paper we prove that with some hypothesis the set of k-isomorphism classes of simple closed k-surfaces in ${\mathbf{Z}}^3$ forms a commutative monoid with an operation derived from a digital connected sum, k ${\in}$ {18,26}. Besides, with some hypothesis the set of k-homotopy equivalence classes of closed k-surfaces in ${\mathbf{Z}}^3$ is also proved to be a commutative monoid with the above operation, k ${\in}$ {18,26}.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.481-494
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• 2008

Iteration functions $K_m(z)$ and $U_m(z)$, $m{\geq}2$are defined recursively using the determinant of a matrix. We show that the fixed-iterations of $K_m(z)$ and $U_m(z)$ converge to a simple zero with order of convergence m and give closed form expansions of $K_m(z)$ and $U_m(z)$: To show the convergence, we derive a recursion formula for $L_m$ and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is $L_m(z)/(f^{\prime})^m$, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.

• Fibers and Polymers
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• v.6 no.1
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• pp.89-94
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• 2005

The purpose of this study is to offer acoustical database of warp knitted fabrics by investigating frictional sound properties and physiological responses according to structural parameters such as construction, lap form, and direction of mutual guide bar movement. Fabric sounds of seven warp knitted fabrics are recorded, and Zwicker's psychoacoustic param­eters - loudness(Z), sharpness(Z), roughness(Z), and fluctuation strength(Z) - are calculated. Also, physiological responses evoked by frictional sounds of warp knitted fabrics are measured such as electroencephalogram (EEG), the ratio of high fre­quency to low frequency (HF/LF), respiration rate (RESP), skin conductance level (SCL), and photoplethysmograph (PPG). In case of constructions, frictional sound of sharkskin having higher loudness(Z) and fluctuation strength(Z) increases RESP. By lap form, open lap has louder and larger fluctuating sound than closed lap, but there aren't significant difference of physi­ological responses between open lap and closed lap. In direction of mutual guide bar movement, parallel direction evokes bigger changes of beta wave than counter direction because of its loud, rough, and fluctuating sound. Fluctuation strength(Z) and roughness(Z) are defined as important factors for predicting physiological responses in construction and mutual guide bar movement, respectively.

• Korean Journal of Mathematics
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• v.19 no.4
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• pp.351-365
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• 2011

In the present paper we introduce a new subclass of analytic functions in the unit disc defined by convolution $(f_{\mu})^{(-1)}*f(z)$; where $$f_{\mu}=(1-{\mu})z_2F_1(a,b;c;z)+{\mu}z(z_2F_1(a,b;c;z))^{\prime}$$. Several interesting properties of the class and integral preserving properties of the subclasses are also considered.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.223-233
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• 1998

This paper is concerned with the problem of existence of solutions to the initial value problem u'(t) = A(t, u(t)), u(a) = z in a probabilistic normed space where $A : [a,b)\;{\times}\;D->E$ is continuous, D is a closed subset of a probabilistic normed space E, and $z\;{\in}\;D$. With a dissipative type condition on A, we estabilish sufficient conditions for this initial value problem to have a solution.