• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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• pp.587-592
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• 1996

In 1950, Nash [5] first proved the existence of equilibrium for games where the player's preferences are representable by continuous quasiconcave utilities and the strategy sets are simplexes. Next Debreu [3] proved the existence of equilibrium for abstract economies. Recently, the existence of Nash equilibrium can be further generalized in more general settings by several athors, e.g. Shafer-Sonnenschein [6], Borglin-Keiding [2], Yannelis-Prabhaker [8]. In the above results, the convexity assumption is very essential and the main proving tools are the continuous selection technique and the existence of maximal elements. Still there have been a number of generalizations and applications of equilibrium existence theorem in generalized games.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.541-547
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• 2000

This paper presents the closed-form forward kinematics of the 6-6 Stewart platform of planar base and moving platform. Based on algebraic elimination method and with one extra linear sensor, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretical one, a correction method is also used. The overall procedure requires so little computation time that it can be efficiently used for realtime applications. In addition, unlike the iterative schemes e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.387-399
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• 2014

We show that in quasi-topological spaces, separation axiom $T_2$ is equivalent to ${\alpha}-T_2$, $T_0$ is equivalent to semi - $T_0$, and semi - $T_{\frac{1}{2}}$ is equivalent to semi - $T_D$. Also, we give characterizations for ${\alpha}-T_1$, semi - $T_1$ and semi - $T_{\frac{1}{2}}$ generalized topological spaces.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.1
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• pp.149-155
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• 2013

In this study, factors that affect the air entrainment within a closed conduit by air drawn in through an air vent are investigated using a hydraulic scale model, which represents a gated circular conduit system connected to the intake tower of an irrigation reservoir. In addition, using data obtained during the hydraulic experiments, experimental equations are developed to estimate the amount of air drawn in through the air vent. In case of pressurized flow conditions downstream of hydraulic jumps, the relationships between $\frac{Q_a}{Q_w}$ and $Fr_g-1$ of the data form a experimental equation, $\frac{Q_a}{Q_w}=0.0304(Fr_g-1)^{1.0622}$; in case of free surface flow conditions, $\frac{Q_a}{Q_w}=0.0271(Fr_g-1)^{1.8205}$. Comparing two data sets observed under the two flow regimes with the results of previous researchers, patterns of the data sets are similar to the results estimated using the equations presented previously, and this indicates that the quality of the data obtained during the hydraulic experiments is ensured. In addition, it is revealed that air entrainment phenomena in the regions close to air vents are affected by the characteristics of supercritical flows downstream of gates. Finally, it is concluded that the equation developed for pressurized flow conditions can be applied to design of air vents.

• 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.

• Economic and Environmental Geology
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• v.49 no.6
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• pp.459-467
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• 2016

Due to the limited areal space for installation, borehole heat exchangers (BHEs) at depths deeper than 300 m are considered for geothermal heating and cooling in the urban area. The deep vertical closed-loop BHEs are unconventional due to the depth and the range of the typical installation depth is between 100 and 200 m in Korea. The BHE in the study consists of 50A (outer diameter 50 mm, SDR 11) PE U-tube pipe in a 150 mm diameter borehole with the depth of 300 m. In order to compensate the buoyancy caused by the low density of PE pipe ($0.94{\sim}0.96g/cm^3$) in the borehole filled with ground water, 10 weight band sets (4.6 kg/set) were attached to the bottom of U-tube. A thermal response test (TRT) and fundamental basic surveys on the thermophysical characteristics of the ground were conducted. Ground temperature measures around $15^{\circ}C$ from the surface to 100 m, and the geothermal gradient represents $1.9^{\circ}C/100m$ below 100 m. The TRT was conducted for 48 hours with 17.5 kW heat injection, 28.65 l/min at a circulation fluid flow rate indicates an average temperature difference $8.9^{\circ}C$ between inlet and outlet circulation fluid. The estimated thermophysical parameters are 3.0 W/mk of ground thermal conductivity and 0.104 mk/W of borehole thermal resistance. In the stepwise evaluation of TRT, the ground thermal conductivity was calculated at the standard deviation of 0.16 after the initial 13 hours. The sensitivity analysis on the borehole thermal resistance was also conducted with respect to the PE pipe diameter and the thermal conductivity of backfill material. The borehole thermal resistivity slightly decreased with the increase of the two parameters.