• 대한수학회지
• /
• 제39권3호
• /
• pp.387-395
• /
• 2002

In [11] Kim obtained fixed point theorems for maps defined on some “locally G-convex”subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.

• Kyungpook Mathematical Journal
• /
• 제55권2호
• /
• pp.473-484
• /
• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2001년도 춘계학술대회논문집C
• /
• pp.77-82
• /
• 2001

The 3-lobes blower has been conventionally made by constructing the impeller with the cross-section of simple arc, and has several problems such as noise, vibration and the oscillation of torque. These are caused by the variation of clearance between both impellers rotating in geared. In the present study, an approach for the design of cross-section of impeller has been proposed to prevent the above problems. The whole cross-section is divided into the concave and convex part. The concave zone is designed by simple arc and the convex zone is modified by the condition that some part of convex zone is always in contact with the other impeller during rotating. A sample design has been carried out and it can be seen that the clearance between both impellers is always uniform and the validity of present work has been verified.

• 대한수학회지
• /
• 제36권4호
• /
• pp.813-828
• /
• 1999

In this paper, we give a Peleg type KKM theorem on G-convex spaces and using this, we obtain a coincidence theorem. First, these results are applied to a whole intersection property, a section property, and an analytic alternative for multimaps. Secondly, these are used to proved existence theorems of equilibrium points in qualitative games with preference correspondences and in n-person games with constraint and preference correspondences for non-paracompact wetting of commodity spaces.

• Journal of the Korean Statistical Society
• /
• 제1권1호
• /
• pp.18-24
• /
• 1973

Study on convexity has been improved in many statistical fields, such as linear programming, stochastic inverntory problems and decision theory. In proof of main theorem in Section 3, M. Loeve already proved this theorem with the $r$-th absolute moments on page 160 in [1]. Main consideration is given to prove this theorem using convex theorems with the generalized $t$-th mean when some convex properties hold on a real linear vector space $R_N$, which satisfies all properties of finite dimensional Hilbert space. Throughout this paper $\b{x}_j, \b{y}_j$ where $j = 1,2,......,k,.....,N$, denotes the vectors on $R_N$, and $C_N$ also denotes a subspace of $R_N$.

• 대한수학회보
• /
• 제29권2호
• /
• pp.193-200
• /
• 1992

This paper uses a piecewise ratonal cubic interpolant to solve the problem of shape preserving interpolation for plane curves; scalar curves are also considered as a special case. The results derived here are actually the extensions of the convexity preserving results of Delbourgo and Gregory [Delbourgo and Gregory'85] who developed a $C^{1}$ shape preserving interpolation scheme for scalar curves using the same piecewise rational function. They derived the ocnstraints, on the shape parameters occuring in the rational function under discussion, to make the interpolant preserve the convex shape of the data. This paper begins with some preliminaries about the rational cubic interpolant. The constraints consistent with convex data, are derived in Sections 3. These constraints are dependent on the tangent vectors. The description of the tangent vectors, which are consistent and dependent on the given data, is made in Section 4. the convexity preserving results are explained with examples in Section 5.

• 대한수학회보
• /
• 제26권2호
• /
• pp.139-149
• /
• 1989

pp.Hartman and G. Stampacchia [6] proved the following theorem in 1966: If f:X.rarw. $R^{n}$ is a continuous map on a compact convex subset X of $R^{n}$ , then there exists $x_{0}$ ..mem.X such that $x_{0}$ , $x_{0}$ -x>.geq.0 for all x.mem.X. This remarkable result has been investigated and generalized by F.E. Browder [1], [2], W. Takahashi [9], S. Park [8] and others. For example, Browder extended this theorem to a map f defined on a compact convex subser X of a topological vector space E into the dual space $E^{*}$; see [2, Theorem 2]. And Takahashi extended Browder's theorem to closed convex sets in topological vector space; see [9, Theorem 3]. In Section 2, we obtain some variational inequalities, especially, generalizations of Browder's and Takahashi's theorems. The generalization of Browder's is an earlier result of the first author [8]. In Section 3, using Theorem 1, we improve and extend some known fixed pint theorems. Theorems 4 and 8 improve Takahashi's results [9, Theorems 5 and 9], respectively. Theorem 4 extends the first author's fixed point theorem [8, Theorem 8] (Theorem 5 in this paper) which is a generalization of Browder [1, Theroem 1]. Theorem 8 extends Theorem 9 which is a generalization of Browder [2, Theorem 3]. Finally, in Section 4, we obtain variational inequalities for multivalued maps by using Theorem 1. We improve Takahashi's results [9, Theorems 21 and 22] which are generalization of Browder [2, Theorem 6] and the Kakutani fixed point theorem [7], respectively.ani fixed point theorem [7], respectively.

• 대한토목학회논문집
• /
• 제32권6C호
• /
• pp.249-257
• /
• 2012

보강토 공법은 경제적으로 유리하고 환경적인 제약을 극복하는데 유리하기 때문에 옹벽, 사면, 기초, 도로, 제방 등의 구조물에 실용적으로 적용되고 있다. 하지만 곡선구간에서 충분한 안정성을 확보하지 못한 보강토 옹벽의 붕괴사례가 발생하고 있으며, 이는 보강토 옹벽 곡선구간에 대한 분석이 정립되지 않은데 원인이 있다고 할 수 있다. 따라서 본 연구에서는 곡선구간 형태별 시공성 및 구조적인 안정성을 검토하기 위한 방안으로, 수평변위 측정을 통해 곡선 형태별 수평변위 차이점을 규명하고, 이를 이용하여 곡선구간과 직선구간의 문제점 분석 및 대책강구를 위한 기초자료 연구에 목적을 두고 있다. 실험결과 하중 재하시 오목형과 볼록형 모두 곡선 중앙에서 최대 수평변위가 발생 하였으며, 오목형의 경우 토압을 받는 힘의 방향이 안쪽으로 작용하는 반면에 블록형의 경우는 힘의 방향이 바깥쪽으로 작용하기 때문에 볼록형의 경우가 오목형에 비해 수평변위가 더 발생한 것으로 나타났다. 또한 볼록형의 경우 보강토체의 주동토압 뿐만 아니라 측면토압이 추가로 발생되어 곡선구간에서의 볼록형의 수평변위가 오목형에 비해 더 발생한 것으로 나타났다.

• 한국지반신소재학회논문집
• /
• 제18권2호
• /
• pp.23-36
• /
• 2019

본 논문에서는 블록식 보강토옹벽의 현장계측을 통해 곡선부 보강영역의 변형특성을 분석하였다. 보강토공법은 설계 및 시공이 증가하여 실생활에서 쉽게 접할 수 있게 되었으나, 곡선부의 균열 및 붕괴사례가 빈번히 발생하여 안전에 대한 중요성이 대두되고 있다. 이러한 붕괴원인은 곡선부에 대한 연구 부족과 설계기준의 미흡, 경제성과 공기단축에 의한 시공성 결여, 충분하지 못한 다짐 공간 등에 있다고 할 수 있다. 이에 본 연구에서는 기존 설계 및 시공 기준을 검토하고 블록형 보강토옹벽 곡선부 사고사례를 통해 원인을 분석하였으며, 실제 시공된 블록형 보강토옹벽의 현장계측을 통해 직선부와 곡선부의 거동을 비교 분석하고 곡선부 보강영역의 변형특성을 확인하였다. 그 결과, 먼저 곡선부의 수평변위가 직선부와 비교하여 볼록형에서 최대 90%, 오목형에서 최대 60% 높게 나타났으며, 다음으로 곡선부 보강영역에서 볼록형의 경우 보강토옹벽 중심에서 수평방향으로 H/2구간에서 최대변위를 보이며 H까지의 영향범위를 나타내었으며, 오목형의 경우 중심에서 최대변위를 보이며 수평방향으로 H/4구간에서 최소변위를 확인하였다. 이러한 결과로 형태에 따른 곡선부의 영향범위와 현장적용을 위한 보강영역의 재정립이 필요하다고 판단되며, 본 연구결과가 이를 위한 기초 자료로서 활용 가능할 것으로 판단된다.

• 대한기계학회논문집B
• /
• 제26권11호
• /
• pp.1513-1520
• /
• 2002

Effect of Convex Surface Curvature on the Onset of Nucleate Boiling of Subcooled Fluid Flow in Vertical Concentric Annuli An experimental study has been carried out to investigate the effect of the transverse convex surface curvature of core tubes on heat transfer in concentric annular tubes. Water is used as the working fluid. Three annuli having a different radius of the inner cores, Ri=3.18mm, 6.35mm, and 12.70mm with a fixed ratio of Ri/Ro=0.5 are used over a range of the Reynolds number between about 40,000 and 80,000. The inner cores are made of smooth stainless steel tubes and heated electrically to provide constant heat fluxes throughout the whole length of each test section. Experimental result shows that heat flux values on the onset of nucleate boiling of the smaller inner diameter model is much higher than that of the larger size test model.