• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.387-395
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• 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
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• v.55 no.2
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• pp.473-484
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• 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.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.77-82
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• 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.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.813-828
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• 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
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• v.1 no.1
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• pp.18-24
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• 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 $R_N$.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.193-200
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.139-149
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• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.6C
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• pp.249-257
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• 2012

The reinforced earth method is financially viable. Furthermore, it overcomes environmental limitations and is therefore employed in retaining walls, slopes, foundations, roads, embankments, and other structures. However, in some cases, reinforced retaining walls are not strong enough in the curved sections and can collapse. Such mishaps are believed to occur because of an unsatisfactory analysis of the curved sections of a reinforced retaining wall. Accordingly, with the aim of investigating the workability and structural safety of curved sections of various types, this study investigates the differences in the estimated horizontal displacements of curved sections of various types and subsequently uses this information to study and analyze preliminary data so that appropriate measures can be taken to resolve alignment issues. The results of an experiment reveal that when a load is applied to curved sections of both concave and convex types, the largest horizontal displacement occurs at the center of the section. In the concave form, the earth pressure force is directed inward, whereas in the convex form, this force is directed outward. As a result, the horizontal displacement in convex forms is larger than that in concave forms. Convex reinforced earth structures are subjected to earth pressures as well as lateral earth pressure, therefore horizontal displacements in convex curved sections is larger than that of concave curved sections.

• Journal of the Korean Geosynthetics Society
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• v.18 no.2
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• pp.23-36
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• 2019

In this paper, field measurement of the Block Type Mechanically Stabilized Earth (MSE) wall curved section was performed, and the reinforced area of the curved part is studied through the result. MSE method has been applied to various fields because of easy construction and excellent economic efficiency, so that it can be easily access in our life. However due to lack of compaction and stress concentration phenomenon, cracks and collapse occur in the curve of MSE wall, which is important for safety. The cause of collapse is lack of research on curved section, lack of design criteria, lack of construction due to economical efficiency and shortening of construction period, insufficient compaction space. In this study, therefore, it was examined the existing design and construction standards, analyzed the cause through accident examples of the curved section of the Block Type MSE wall. As a result, the horizontal displacement of the curved section was 90% higher than that of the straight section and 60% higher than that of the concave section. In the case of the convex section in the curved section reinforcement region, the maximum displacement is shown in the H/2 section in the horizontal direction from the center of the MSE wall, and the range of influence from H is shown. In the case of the concave section, the maximum displacement is shown in the center, The minimum displacement was confirmed in H/4 section in the horizontal direction from the center of the MSE wall. As a basic study on the reinforcement area rehabilitation through the actual construction of block type MSE wall, the behaviors of the straight part and the curved part were compared and analyzed. And analyzed the reinforced area in order to reduce the damage of the stress concentration phenomenon and secure the safety.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.11
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• pp.1513-1520
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• 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.