• Kyungpook Mathematical Journal
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• v.60 no.1
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• pp.185-195
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• 2020

This paper aims to study the 𝒲^⁎-curvature tensor on relativistic space-times. The energy-momentum tensor T of a space-time having a semi-symmetric 𝒲^⋆-curvature tensor is semi-symmetric, whereas the whereas the energy-momentum tensor T of a space-time having a divergence free 𝒲^⋆-curvature tensor is of Codazzi type. A space-time having a traceless 𝒲^⁎-curvature tensor is Einstein. A 𝒲^⁎-curvature flat space-time is Einstein. Perfect fluid space-times which admits 𝒲^⋆-curvature tensor are considered.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.99-106
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• 1984

J. Yeh has recently introduced the concept of conditional Wiener integrals which are meant specifically the conditional expectation E$^{w}$ (Z vertical bar X) of a real or complex valued Wiener integrable functional Z conditioned by the Wiener measurable functional X on the Wiener measure space (A precise definition of the conditional Wiener integral and a brief discussion of the Wiener measure space are given in Section 2). In [3] and [4] he derived some inversion formulae for conditional Wiener integrals and evaluated some conditional Wiener integrals E$^{w}$ (Z vertical bar X) conditioned by X(x)=x(t) for a fixed t>0 and x in Wiener space. Thus E$^{w}$ (Z vertical bar X) is a real or complex valued function on R$^{1}$. In this paper we shall be concerned with the random vector X given by X(x) = (x(s$_{1}$),..,x(s$_{n}$ )) for every x in Wiener space where 0=s$_{0}$ $_{1}$<..$_{n}$ =t. In Section 3 we will evaluate some conditional Wiener integrals E$^{w}$ (Z vertical bar X) which are real or complex valued functions on the n-dimensional Euclidean space R$^{n}$ . Thus we extend Yeh's results [4] for the random variable X given by X(x)=x(t) to the random vector X given by X(x)=(x(s$_{1}$).., x(s$_{n}$ )).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.4
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• pp.393-398
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• 2008

This paper suggests a GPS/INS navigation computer architecture that can be applied to small satellites. In order to implement a GPS/INS navigation system on a small satellite, the extreme environment in space such as radiation, micro-gravity, vacuum, etc. must be considered. In addition, a real-time processing ability is required for the GPS/INS navigation system since the formation flying of multiple small satellites is the ultimate goal. The developed navigation electronics utilizes a PowerPC-type MPC860T that has space environment heritage, and a pair of Atmega128s that has been implemented in KAUSAT-2 and has completed the space environment verification tests. The navigation algorithm is designed to work in VxWorks environment, ported in MPC860T.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.275-285
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• 1997

Let E be a uniformly convex Banach space with a uniformly G$\hat{a}teaux differentiable norm, C a nonempty closed convex subset of $E, T : C \to E$ a nonexpansive mapping, and Q a sunny nonexpansive retraction of E onto C. For $u \in C$ and $t \in (0,1)$, let $x_t$ be a unique fixed point of a contraction $R_t : C \to C$, defined by $R_tx = Q(tTx + (1-t)u), x \in C$. It is proved that if ${x_t}$ is bounded, then the strong $lim_{t\to1}x_t$ exists and belongs to the fixed point set of T. Furthermore, the strong convergence of ${x_t}$ in a reflexive and strictly convex Banach space with a uniformly G$\hat{a}$teaux differentiable norm is also given in case that the fixed point set of T is nonempty.

• Bulletin of the Korean Space Science Society
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• 1994.09a
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• pp.23-23
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• 1994

No Abstract. See Full-text

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.35-41
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• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.541-560
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• 2023

Let T be an m-linear Calderón-Zygmund operator. $T_{{\vec{b}S}}$ is the generalized commutator of T with a class of measurable functions {b_i}^∞_i=1. In this paper, we will give some new estimates for $T_{{\vec{b}S}}$ when {b_i}^∞_i=1 belongs to Orlicz-type space and Lipschitz space, respectively.

• The korean journal of orthodontics
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• v.47 no.6
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• pp.344-352
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• 2017

Objective: The purpose of this study was to compare the changes induced in the pharyngeal airway space by orthodontic treatment with bodily retraction of the mandibular incisors and mandibular setback surgery without extraction. Methods: This retrospective study included 63 adult patients (32 men and 31 women). Thirty-three patients who had been treated via four-bicuspid extraction and bodily retraction of the mandibular incisors (incisor retraction, IR group) were compared with 30 patients who had been treated via mandibular setback surgery (MS group) without extraction. Lateral cephalograms were acquired and analyzed before (T1) and after treatment (T2). Results: The superior pharyngeal airway space did not change significantly in either group during treatment. The middle pharyngeal airway space decreased by $1.15{\pm}1.17mm$ and $1.25{\pm}1.35mm$ after treatment in the IR and MS groups, respectively, and the decrease was comparable between the two groups. In the MS group, the inferior pharyngeal airway space (E-IPW) decreased by $0.88{\pm}1.67mm$ after treatment (p < 0.01). The E-IPW was larger in the MS group than in IR group at T1, but it did not differ significantly between the two groups at T2. No significant correlation was observed between changes in the pharyngeal airway space and the skeletal and dental variables in each group. Conclusions: The middle pharyngeal airway space decreased because of the posterior displacement of the mandibular incisors and/or the mandibular body. The E-IPW decreased only in the MS group because of the posterior displacement of only the mandibular body.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.597-602
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• 1997

Let H be a separable complex Hilbert space and L(H) be the *-algebra of all bounded linear operators on H. For $T \in L(H)$, we construct a pair of semi-positive definite operators $$ $\mid$T$\mid$_r = (T^*T)^{\frac{1}{2}} and $\mid$T$\mid$_l = (TT^*)^{\frac{1}{2}}. $$ An operator T is called a semi-hyponormal operator if $$ Q_T = $\mid$T$\mid$_r - $\mid$T$\mid$_l \geq 0. $$ In this paper, by using a technique introduced by Berberian [1], we show that the approximate point spectrum $\sigma_{ap}(T)$ of a semi-hyponomal operator T is empty.