• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.837-846
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• 1994

Let A denote a unital normed algebra over a field K = R or C and let e be the identity of A. Given $a \in A$ and $x \in A$ with $\Vert x \Vert = 1$, let $$ V(A, a, x) = {f(ax) : f \in A', f(x) = 1 = \Vert f \Vert}. $$ Then the (Bonsall and Duncan) numerical range of an element $a \in A$ is defined by $$ V(a) = \cup{V(A, a, x) : x \in A, \Vert x \Vert = 1}, $$ where A' denotes the dual of A. In [2], $V(a) = {f(a) : f \in A', f(e) = 1 = \Vert f \Vert}$.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.983-996
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• 1996

In this paper, we show that $\Vert \xi \Vert_r = \Vert \sum_{i \in I}x_i x^*_i \Vert^{\frac{1}{2}}, \Vert \xi \Vert_c = \Vert \sum_{i \in I}x^*_ix_i \Vert^{\frac{1}{2}}$ for $\xi = \sum_{i \in I}x_i e_i$ in $M_n(H)$, that subspaces as Hilbert spaces are subspaces as column and row Hilbert spaces, and that the standard dual of column (resp., row) Hilbert spaces is the row (resp., column) Hilbert spaces differently from [1,6]. We define operator Hilbert spaces differently from [10], show that our definition of operator Hilbert spaces is the same as that in [10], show that subspaces as Hilbert spaces are subspaces as operator Hilbert spaces, and for a Hilbert space H we give a matrix norm which is not an operator space norm on H.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.571-577
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• 1997

We first show that if $\psi : M_n(B(H)) \to M_n (B(H))$ is a $D_n \otimes F(H)$-bimodule map, then there is a matrix $A \in M_n$ such that $\psi = S_A$. Secondly, we show that for an operator space $\varepsilon, A \in M_n$, the Schur product map $S_A : M_n(\varepsilon) \to M_n(\varepsilon)$ and $\phi_A : M_n(\varepsilon) \to \varepsilon$, defined by $\phi_A([x_{ij}]) = \sum^{n}_{i,j=1}{a_{ij}x_{ij}}$, we have $\Vert S_A \Vert = \Vert S_A \Vert_{cb} = \Vert A \Vert_S, \Vert \phi_A \Vert = \Vert \phi_A \Vert_{cb} = \Vert A \Vert_1$ and obtain some characterizations of A for which $S_A$ is contractive.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.439-442
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• 1995

Let ${X_n : n = 1,2,\cdots}$ be a sequence of pairwise independent identically distributed random vectors taking values in a separable Hilbert space H such that $E \Vert X_1 \Vert = \infty$. Let $S_n = X_1 + X_2 + \cdots + X_n$ and for any real $\alpha$ with $0 < \alpha < 1$ define a sequence ${\gamma_n(\alpha)}$ as $\gamma_n(\alpha) = inf {r : P(\Vert S_n \Vert \leq r) \geq \alpha}$. Then $$ lim_{n \to \infty} sup \Vert S_n \Vert/\gamma_n(\alpha) = \infty $$ holds. This is a generalization of Vvedenskaya[2].

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.731-737
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• 1994

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measures on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$- algebras of F. If $r > 0$, let $J = [-r, 0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert_C = sup_{s \in J} $\mid$\gamma(x)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E and F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$ with the norm $\Vert T \Vert = sup {$\mid$T(x)$\mid$_F : x \in E, $\mid$x$\mid$_E \leq 1}$.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.153-166
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• 1992

Consider an unknown regression function f of the response Y on a d-dimensional measurement variable X. It is assumed that f belongs to a tensor Sobolev space. Let T denote a differential operator. Let $\hat{T}_n$ denote an estimator of T(f) based on a random sample of size n from the distribution of (X, Y), and let $\Vert \hat{T}_n - T(f) \Vert_2$ be the usual $L_2$ norm of the restriction of $\hat{T}_n - T(f)$ to a subset of $R^d$. Under appropriate regularity conditions, the optimal rate of convergence for $\Vert \hat{T}_n - T(f) \Vert_2$ is discussed.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.93-107
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• 1995

In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

• The Journal of Korean Society for Radiation Therapy
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• v.21 no.1
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• pp.33-39
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• 2009

Purpose: The aim of this study is to compare patient's body posture and its position at the time of simulation with one at the treatment room using On-board Imaging (OBI) and CT (CBCT). The detected offsets are compared with position errors of Rando Phantom that are practically applied. After that, Rando Phantom's position is selected by moving couch based on detected deviations. In addition, the errors between real measured values of Rando Phantom position and theoretical ones is compared. And we will evaluate target position's accuracy of KV X-ray imaging's 2D and CBCT's 3D one. Materials and Methods: Using the Rando Phantom (Alderson Research Laboratories Inc. Stanford. CT, USA) which simulated human body's internal structure, we will set up Rando Phantom on the treatment couch after implementing simulation and RTP according to the same ways as the real radioactive treatment. We tested Rando Phantom that are assumed to have accurate position with different 3 methods. We measured setup errors on the axis of X, Y and Z, and got mean standard deviation errors by repeating tests 10 times on each tests. Results: The difference between mean detection error and standard deviation are as follows; lateral 0.4+/-0.3 mm, longitudinal 0.6+/-0.5 mm, vertical 0.4+/-0.2 mm which all within 0~10 mm. The couch shift variable after positioning that are comparable to residual errors are 0.3+/-0.1, 0.5+/-0.1, and 0.3+/-0.1 mm. The mean detection errors by longitudinal shift between 20~40 mm are 0.4+/-0.3 in lateral, 0.6+/-0.5 in longitudinal, 0.5+/-0.3 in vertical direction. The detection errors are all within range of 0.3~0.5 mm. Residual errors are within 0.2~0.5 mm. Each values are mean values based on 3 tests. Conclusion: Phantom is based on treatment couch shift and error within the average 5mm can be gained by the diminution detected by image registration based on OBI and CBCT. Therefore, the selection of target position which depends on OBI and CBCT could be considered as useful.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.5
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• pp.137-142
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• 2016

A two-step open system(TOS) was proposed to relay between a healing platform and a repository of personal health documents. TOS was designed by taking into consideration the pubsub service based on large scale connections to monitor a provider's access/request process for health documents in real time. TOS, however, uses WebSocket as a communication protocol in case of pubsub. Given the operational environment of low quality wireless networks for mobile devices that are user terminals in a healing platform, there is a need to add a messaging protocol to support QoS as well as a transmission protocol. As a light messaging protocol optimized for mobile devices, MQTT defines reliable messaging QoS to consider a wireless network situation of low speed/low quality. This study designed an MQTT protocol-based message broker to support QoS in case of large scale connections and pubsub by taking into consideration mobile devices that are user terminals in a healing platform. After designing a model between TOS and MQTT message broker, the study implemented a prototype based on the proposed design and compared it with its counterparts from previous studies based on the performance indicators in a load-test with the MQTT client tool.