• Korean Management Science Review
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• v.26 no.1
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• pp.1-5
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• 2009

I study a solution concept which preserves the nice Nash equilibrium properties of two-person zero-sum games, and define a locally competitive equilibrium which is characterized by a saddle point with respect to the coordinates of strategies. I show that a locally competitive equilibrium shares the properties of uniqueness of equilibrium payoffs, interchangeablity of equilibrium strategies and convexity of the equilibrium set.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.455-466
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• 2007

The zero-distribution of the Fourier integral $${\int}^{\infty}_{-{\infty}}\;Q(u)e^{p(u)+^{izu}du$$, where P is a polynomial with leading term $-u^{2m}(m\;{\geq}\;1)$ and Q an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.

• Journal of the Korean Mathematical Society
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• v.49 no.4
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• pp.843-854
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• 2012

In this paper, the iterative Uzawa method with a modified Lagrangian functional is investigated to seek a saddle point for the semicoercive variational Signorini inequality.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.34 no.4
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• pp.191-197
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• 2021

To calculate the induced charge of atoms in molecular dynamics, linear equations for the induced charges need to be solved. As induced charges are determined at each time step, the process involves considerable computational costs. Hence, an efficient method for calculating the induced charge distribution is required when analyzing large systems. This paper introduces the Uzawa method for solving saddle point problems, which occur in linear systems, for the solution of the Lagrange equation with constraints. We apply the accelerated Uzawa algorithm, which reduces computational costs noticeably using the Schur complement and preconditioned conjugate gradient methods, in order to overcome the drawback of the Uzawa parameter, which affects the convergence speed, and increase the efficiency of the matrix operation. Numerical models of molecular dynamics in which two gold nanoparticles are placed under external electric fields reveal that the proposed method provides improved results in terms of both convergence and efficiency. The computational cost was reduced by approximately 1/10 compared to that for the Gaussian elimination method, and fast convergence of the conjugate gradient, as compared to the basic Uzawa method, was verified.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2008.05a
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• pp.677-680
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• 2008

The paper deals with the analysis of radiation characteristics of antenna in the multi-layered media structures. The dyadic Green's function for three layer medium is complex because the Green's functions belonging to the kernel of the integral equation are expressed as Sommerfeld integrals, in which surface wave effects are automatically included. When certain condition are met, the integral can be evaluated approximated by the method of Saddle-point integration. In this study, we propose a method to calculate a radiation pattern for several antennas by using the method of Saddle-point integration. Numerical results show how the radiation characteristics are affected by parameter of dielectric media.

• Wind and Structures
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• v.9 no.4
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• pp.315-330
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• 2006

Flow and scalar dispersion around Cheomseongdae are numerically investigated using a three-dimensional computational fluid dynamics (CFD) model with the renormalization group (RNG) $k-{\varepsilon}$ turbulence closure scheme. Cheomseongdae is an ancient astronomical observatory in Gyeongju, Korea, and is chosen as a model obstacle because of its unique shape, that is, a cylinder-shaped architectural structure with its radius varying with height. An interesting feature found is a mid-height saddle point behind Cheomseongdae. Different obstacle shapes and corresponding flow convergences help to explain the presence of the saddle point. The predicted size of recirculation zone formed behind Cheomseongdae increases with increasing ambient wind speed and decreases with increasing ambient turbulence intensity. The relative roles of inertial and eddy forces in producing cavity flow zones around an obstacle are conceptually presented. An increase in inertial force promotes flow separation. Consequently, cavity flow zones around the obstacle expand and flow reattachment occurs farther downwind. An increase in eddy force weakens flow separation by mixing momentum there. This results in the contraction of cavity flow zones and flow reattachment occurs less far downwind. An increase in ambient wind speed lowers predicted scalar concentration. An increase in ambient turbulence intensity lowers predicted maximum scalar concentration and acts to distribute scalars evenly.

• Proceedings of the KSME Conference
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• 2000.11b
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• pp.404-409
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• 2000

Characteristics of secondary vortices is topologically investigated in the near-wake region of a circular cylinder where the Taylor hypothesis does not hold. The three-dimensional flow fields in the wake-transition regime were measured by a time-resolved PIV. For the analysis in a moving frame of reference, the convection velocity of the Karman vortices is evaluated from the trajectory of vortex center which is defined as the centroid of the vorticity field. Then, a saddle point is obtained by applying the critical point theory. Science the distributions of fluctuating Reynolds stresses defined by triple-decomposition are closely related with the existence of secondary vortices. the physical meaning of them is explained in conjunction with vortex center and saddle point trajectories. Finally, the temporal evolution of streamwise vortex is also discussed.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.837-847
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• 2005

We consider multiobjective fractional programming problems with generalized invexity. An equivalent multiobjective programming problem is formulated by using a modification of the objective function due to Antczak. We give relations between a multiobjective fractional programming problem and an equivalent multiobjective fractional problem which has a modified objective function. And we present modified vector saddle point theorems.

• Ocean Systems Engineering
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• v.13 no.1
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• pp.43-55
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• 2023

In this study, the SCFs in tubular T-joints stiffened with external ring under axial load are studied and discussed. After verification of the present numerical model with the results of several available experimental tests, 156 FE models were generated and analyzed to parametrically evaluate the effect of the joint geometry and the ring geometry on the SCFs. Results indicated that the SCF of the stiffened T-joints at crown point can be down to 24% of the SCF of the corresponding un-reinforced joint at the same point. Also, the effect of the ring on the SCF at saddle point is more remarkable than the effect of the ring on the SCF at crown point. Moreover, against un-reinforced joints under axial load, the SCF at saddle point of the stiffened joint is smaller than the SCF at crown point of that stiffened joint. The ring results in the redistribution of stresses in the ring and metal substrate. Also, the effect of the ring thickness on the decrease of the SCFs is slight and can be ignored. In final step, the geometric parameters affecting the SCFs of the stiffened T-joints are analyzed by multiple nonlinear regression analyses. An accurate formula is proposed for determining the SCFs.

• Proceedings of the ESK Conference
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• 1993.04a
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• pp.145-145
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• 1993

In bicycle design, saddle is the major part which effects the subjective comfort of rider. This study examines the correlation between the subjective comfort and elastic body pressure. The elastic body pressure measuring instrument for free-form surface such as saddle is developed by force sensor register, A/D converter and computer. The subjective comfort is measured quantit- atively by 11-point scale method and the elastic body pressure distribution is obtained through 3 different saddles at 4 postures. The pressure distribution is presented by computerized equi- pressure contour. While mean pressure, standard deviation of pressure, maximum pressure are inversely proportional to subjective comfort, the modified saddle-bearing weight which is the surface integral of pressure is directly proportional. Consequently, standard deviation of pressure is most important characteristic which affects variation of subjective comfort.