• Kyungpook Mathematical Journal
• /
• v.61 no.3
• /
• pp.645-660
• /
• 2021

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.1
• /
• pp.19-30
• /
• 2019

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

• Bulletin of the Korean Chemical Society
• /
• v.12 no.2
• /
• pp.170-177
• /
• 1991

A lattice mean field theory is developed to investigate the conformational properties of monolayer amphiphiles at the air-water interface. By generalizing Dill and Cantor's method and by extending Whittington's recurrence equation, we derive the supermatrix recurrence equation which is applied to calculation of various segment density profiles and order parameter, etc. In deriving the equation, we incorporated the chain stiffness effect and the chain connectivity which are distinguished features of linear chain molecule. Our result shows that, as the surface coverage $\sigma$ increases the chain ordering process with respect to vertical axis of the lattice system becomes dominant.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
• /
• v.14 no.4
• /
• pp.293-299
• /
• 1985

This paper describes an economical prediction procedure for heat transfer phenomenon through a channel containing an abrupt asymmetric expansion in flow cross-seetional area. Numerical solutions for the flow field are obtained by the finite difference numerical method applied to the modified boundary layer equations. Modified boundary energy equation is used to analyze heat transfer as modified boundary momentum equation. Predictions of the method compare very favorable with exprimental data. Results of this study by modified boundary layer equation are as follows : 1. The computation time required for the scheme is at least an order of magnitude less than for the numerical solution of the full Navier-stokes and Energy eguations. 2. In laminar flow, the maximum heat transfer occurs downstream of the reattachment point.

• Journal of the Korean Mathematical Society
• /
• v.35 no.3
• /
• pp.793-802
• /
• 1998

We apply the generalization of Levy's infinitesimal equation $\delta$X(t) = $\psi$(X(s), s $\leq$ t, $Y_{t}$, t, dt), $t\in R^1$, for a random field X (C) indexed by a contour C or by a more general set. Assume that the X(C) is homogeneous in x, say of degree n, then we can appeal to the classical theory of variational calculus and to the modern theory of white noise analysis in order to discuss the innovation for the X (C.)

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.22 no.8
• /
• pp.1121-1131
• /
• 1998

The present study is numerically investigated for the high-pressure effects on the vaporization process in the convection-dominating flow field. Numerical results agree well with the available experimental data. The fuel droplet vaporization characterization is parametrically studied for the wide range of the operating conditions encountered with the high-pressure combustion process of turbocharged diesel engines.

• Journal of the Korean Mathematical Society
• /
• v.42 no.6
• /
• pp.1311-1322
• /
• 2005

We consider the several plane sector domains which are bonded together along common edges with vertex at the origin. Such domains appear in electric conducting problem with multi-layered heterogeneous media. Our aim is to give a structure theorem of the singularities of the electric field at the corner. Also, we provide a regularity theorem for the electric field.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.62 no.9
• /
• pp.1260-1263
• /
• 2013

Plane wave scattering from a spherical resonator is calculated by solving the combined field integral equation (CFIE) with Rao-Wilton-Glisson (RWG) basis functions and the moment method. The calculations show that magnetic and electric dipoles are found at resonant modes. These characteristics are confirmed by radiation patterns in the far field region. In addition, an analysis of a magnetodielectric sphere is discussed.

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.25-34
• /
• 1995

S. Tachibana [10] has defined a confornal Killing tensor in a n-dimensional Riemannian manifold M by a skew symmetric tensor $u_[ji}$ satisfying the equation $$ \nabla_k u_{ji} + \nabla_j u_{ki} = 2\rho_i g_{kj} - \rho_j g_{ki} - \rho_k g_{ji}, $$ where $g_{ji}$ is the metric tensor of M, $\nabla$ denotes the covariant derivative with respect to $g_{ji}$ and $\rho_i$ is a associated covector field of $u_{ji}$. In here, a covector field means a 1-form.

• 전기의세계
• /
• v.22 no.4
• /
• pp.11-16
• /
• 1973

This paper presents an optimum control of the field resistance for the self-excited DC shunt generator to keep a constant terminal voltage in case of the load change or the torque variation in the system. The non-linearity of the system is linearized by applying the small signal technique and the linearized equation is solved by the maximum principle with the digital computer. The optimal control value of the field resistance for the step error of the generator output voltage is obtained and the transient voltage characteristics in the system are investigated.