• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.223-238
• /
• 1994

A random vector $\b{X} = (X_1,\cdots,X_n)$ is weakly associated if and only if for every pair of partitions $\b{X}_1 = (X_{\pi(1)},\cdots,X_{\pi(k)}), \b{X}_2 = (X_{\pi(k+1),\cdots,X_{\pi(n)})$ of $\b{X}, P(\b{X}_1 \in A, \b{X}_2 \in B) \geq P(\b{X}_1 \in A)\b{P}(\b{X}_2 \in B)$ whenever A and B are open upper sets and $\pi$ is a permutation of ${1,\cdots,n}$. In this paper, we develop notions of weak positive dependence, which are weaker than a positive version of negative association (weak association) but stronger than positive orthant dependence by arguments similar to those of Shaked. We also illustrate some concepts of a particular interest. Various properties and interrelationships are derived.

• Proceedings of the Korean Institute of Communication Sciences Conference
• /
• 2004.11a
• /
• pp.351-351
• /
• 2004

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.129-134
• /
• 2005

Lpt X be a reduced Stein space and L a holomorphic line bundle on X. L is spanned by its global sections and the associated holomorphic map $h_L\;:\;X{\to}P(H^0(X, L)^{\ast})$ is an embedding. Choose any locally convex vector topology ${\tau}\;on\;H^0(X, L)^{\ast}$ stronger than the weak-topology. Here we prove that $h_L(X)$ is sequentially closed in $P(H^0(X, L)^{\ast})$ and arithmetically Cohen -Macaulay. i.e. for all integers $k{\ge}1$ the restriction map ${\rho}_k\;:\;H^0(P(H^0(X, L)^{\ast}),\;O_{P(H^0(X, L)^{\ast})}(k)){\to}H^0(h_L(X),O_{hL_(X)}(k)){\cong}H^0(X, L^{\otimes{k}})$ is surjective.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.387-398
• /
• 2016

Let X be a vector space over a field K of real or complex numbers and $k{\in}{\mathbb{N}}$. We prove the superstability of the following generalized Golab-Schinzel type equation $f(x_1+{\limits\sum_{i=2}^p}x_if(x_1)^kf(x_2)^k{\cdots}f(x_{i-1})^k)={\limits\prod_{i=1}^pf(x_i),x_1,x_2,{\cdots},x_p{\in}X$, where $f:X{\rightarrow}K$ is an unknown function which is hemicontinuous at the origin.

• The Journal of Korean Society for Radiation Therapy
• /
• v.20 no.1
• /
• pp.45-53
• /
• 2008

Purpose: We are trying to analyze 130 patients' conditions by using our Helical Tomotherapy, which was installed in our center in Oct. 2007. We will be statistically approach this examination and analyze so that we will be able to figure out adaptive plans according to the change in place of the tumor, GTV (gross tumor volume), total amount of time it took, vector (${\upsilon}=\surd$x2+y2+z2) and the change in size of the tumor. Materials and Methods: Objectives were the patients who were medicated with Tomotherapy in our medical center since Oct. 2007 August 2008. The Average age of the patients were 53 years old (Minimum 25 years old, Maximum 83 years old). The parts of the body we operated were could be categorized as Head&neck (n=22), Chest (n=47), Abdomen (n=25), Pelvis (n=11), Bone (n=25). MVCT had acted on 2702 times, and also had acted on our adaptive plan toward patients who showed big difference in the size of tumor. Also, after equalizing our gained MVCT and kv-CT we checked up on the range of possible mistake, using x, y, z, roll and vector. We've also investigated on Set-up, MVCT, average time of operation and target volume. Results: Mean time on table was 22.8 minutes. Mean treatment time was 13.26 minutes. Mean correction (mm) was X=-0.7, Y=-1.4, Z=5.77, roll=0.29, vector=8.66 Head&neck patients had 2.96 mm less vector value in movement than patients of Chest, Abdomen, Bone. In increasing order, Head&neck, Bone, Abdomen, Chest, Pelvis showed the vector value in movement. Also, there were 27 patients for adaptive plan, 39 patients, who had long or multiple tumor. We could know that When medical treatment is one cure plan, it takes 32 minutes, and when medical treatment is two cure plan, it takes 40 minutes that one medical treatment takes 21 minutes, and the other medical treatment takes 19 minutes. Conclusion:With our basic tools, we could bring more accurate IMRT with MVCT. Also, through our daily image, we checked up on the change in tumor so that adaptive plan could work. It was made it possible to take the cure of long or multiple tumor, the cure in a nearby OAR, and the complicated cure that should make changes of gradient dose distribution.

• Journal of IKEEE
• /
• v.17 no.4
• /
• pp.459-468
• /
• 2013

Under nonlinear characteristics of frames, we propose the frame interpolation using GRNN to enhance the visual picture quality. By full search with block size of 128x128~1x1 to reduce blocky artifact and image overlay, we select the frame having block of minimum error and re-estimate the nonlinear moving vector using GRNN. We compare our scheme with forward(backward) motion compensation, bidirectional motion compensation when the object movement is large or the object image includes zoom-in and zoom-out or camera focus has changed. Experimental results show that the proposed method provides better performance in subjective image quality compared to conventional MCFI methods.

• Journal of Mechanical Science and Technology
• /
• v.15 no.7
• /
• pp.895-905
• /
• 2001

This paper presents vector fields, three dimensional mean velocities, turbulent intensities, turbulent kinetic energy and Reynolds shear stresses measured in the X-Y plane of the gas swirl burner with a cone type baffle plate by using an X-type hot-wire probe. This experiment is carried out at the flow rates of 350 and 450ℓ/min which are equivalent to the combustion air flow rate necessary to release 15,000 kcal/hr in a gas furnace. The results show that the maximum axial mean velocity component exists around the narrow slits situated radially on the edge of a burner. Therefore, there is some entrainment of ambient air in the outer region of a burner. The maximum values of turbulent intensities occur around the narrow slits and in front of a burner up to X/R=1.5. Moreover, the turbulent intensity components show a relatively large value in the inner region due to the flow diffusion and mixing processes between the inclined baffle plate and the swirl vane. Consequently, the combustion reaction is expected to occur actively near these regions.

• Bulletin of the Korean Mathematical Society
• /
• v.41 no.3
• /
• pp.541-557
• /
• 2004

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by (x * y) ＋ (x * $y^{-1}$) - 2 (x) - 2 (y) =<${\varphi}$(x,y), (x*y*z)＋ (x)＋ (y)＋ (z)－ (x*y)－ (y*z)－ (z*x)＝${\varphi}$(x, y, z), where (G,*) is a group, X is a real or complex Hausdorff topological vector space, and is a function from G into X.

• Journal of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.367-373
• /
• 1994

Let us consider the Cauchy problem $$ {\rho_t + \upsilon \cdot \nabla\rho = 0 {\rho[\upsilon_t + (\upsilon \cdot \nabla)\upsilon] + \nabla p + \rho f {div \upsilon = 0 (1.1) {\rho$\mid$_t = 0 = \rho_0(x) {\upsilon$\mid$_t = 0 = \upsilon_0(x) $$ in $Q_T = R^3 \times [0,T]$, where $f(x,t), \rho_0(x) and \upsilon_0(x)$ are given, while the density $\rho(x,t)$, the velocity vector $\upsilon(x,t) = (\upsilon^1(x,t),\upsilon^2(x,t),\upsilon^3(x,t))$ and the pressure p(x,t) are unknowns. The equations $(1.1)_1 - (1.1)_3$ describe the motion of a nonhomogeneous ideal incompressible fluid.

• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1125-1140
• /
• 2018

Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.