• 대한수학회지
• /
• 제38권6호
• /
• pp.1235-1243
• /
• 2001

We obtain bounds relating to Eulers formula for the case of a function with higher-order convexity properties. These are used to derive estimates of the error involved in the use of the trapezoidal formula for integrating such a function.

• 전기의세계
• /
• 제27권2호
• /
• pp.53-63
• /
• 1978

The problem of optimally controlling a time-delay control system to a function as the final target is inverstigated. Necessary conditions are presented in the form of Pontryagin's maximum principle, and it is further shown that they are also sufficient for linear systems with a convex cost functional. Several examples are given to illustrate the results.

• 대한수학회보
• /
• 제59권4호
• /
• pp.993-1010
• /
• 2022

In this paper, we establish some radius results and inclusion relations for starlike functions associated with a petal-shaped domain.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제9권1호
• /
• pp.1-7
• /
• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• Communications for Statistical Applications and Methods
• /
• 제22권1호
• /
• pp.69-80
• /
• 2015

In this paper, the probability that a given point is covered by a random convex hull generated by independent and identically-distributed random points in a plane is studied. It is shown that such probability can be expressed in terms of an integral that can be approximated numerically by function-evaluations over the grid-points in a 2-dimensional space. The new integral representation allows such probability be computed efficiently. The computational burdens under the proposed integral representation and those in the existing literature are compared. The proposed method is illustrated through numerical examples where the random points are drawn from (i) uniform distribution over a square and (ii) bivariate normal distribution over the two-dimensional Euclidean space. The applications of the proposed method in statistics are are discussed.

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.409-421
• /
• 2018

Let X be a complex manifold of dimension n $n{\geqslant}2$ and let ${\Omega}{\Subset}X$ be a weakly q-convex domain with smooth boundary. Assume that E is a holomorphic line bundle over X and $E^{{\otimes}m}$ is the m-times tensor product of E for positive integer m. If there exists a strongly plurisubharmonic function on a neighborhood of $b{\Omega}$, then we solve the ${\bar{\partial}}$-problem with support condition in ${\Omega}$ for forms of type (r, s), $s{\geqslant}q$ with values in $E^{{\otimes}m}$. Moreover, the solvability of the ${\bar{\partial}}_b$-problem on boundaries of weakly q-convex domains with smooth boundary in $K{\ddot{a}}hler$ manifolds are given. Furthermore, we shall establish an extension theorem for the ${\bar{\partial}}_b$-closed forms.

• 전자공학회논문지C
• /
• 제34C권7호
• /
• pp.51-60
• /
• 1997

Prototype based methods are commonly used in cluster analysis and the results may be highly dependent on the prototype used. In this paper, we propose a fuzzy clustering method that involves adaptively expanding convex polytopes. Thus, the dependency on the use of prototypes can be eliminated. The proposed method makes it possible to effectively represent an arbitrarily distributed data set without a priori knowledge of the number of clusters in the data set. Specifically, nonlinear membership functions are utilized to determine whether a new cluster is created or which vertex of the cluster should be expanded. For this, the membership function of a new vertex is assigned according to not only a distance measure between an incoming pattern vector and a current vertex, but also the amount how much the current vertex has been modified. Therefore, cluster expansion can be only allowed for one cluster per incoming pattern. Several experimental results are given to show the validity of our mehtod.

• 대한기계학회논문집
• /
• 제12권4호
• /
• pp.916-925
• /
• 1988

본 연구에서는 이에 대한 현상을 이해하기 위한 노력의 일환으로 반원호가 유 동방향에 오목하게 놓여있는 경우와 볼록하게 놓여있는 두 특수한 경우에 대해 Re수를 0.1부터 50까지 증가시켜가며 수치해를 구하여 박리점, 와류길이, 그리고 와도와 유선 들을 중점적으로 조사하였다.

• 호남수학학술지
• /
• 제35권1호
• /
• pp.37-49
• /
• 2013

Consider a non-degenerate open convex cone C with vertex the origin in the $n$2-dimensional Euclidean space $E^n$. We study volume properties of strictly convex hypersurfaces in the cone C. As a result, for example, if the volume of the region of an elliptic cone C cut off by the tangent hyperplane P of M at $p$ is independent of the point $p{\in}M$, then it is shown that the hypersurface M is part of an elliptic hyperboloid.

• Journal of the Korean Data and Information Science Society
• /
• 제25권2호
• /
• pp.455-464
• /
• 2014

Unlabeled examples are easier and less expensive to obtain than labeled examples. Semisupervised approaches are used to utilize such examples in an eort to boost the predictive performance. This paper proposes a novel semisupervised classication method named transductive least squares support vector machine (TLS-SVM), which is based on the least squares support vector machine. The proposed method utilizes the dierence convex algorithm to derive nonconvex minimization solutions for the TLS-SVM. A generalized cross validation method is also developed to choose the hyperparameters that aect the performance of the TLS-SVM. The experimental results conrm the successful performance of the proposed TLS-SVM.