• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.695-708
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• 2005

Certain observations about formal Dirichlet series whose coefficients are arithmetic functions are made. These include for example algebraic independence and representation as infinite series of logarithms.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.179-194
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• 2020

In this article, we establish some new second main theorems for meromorphic mappings of ℂ^m into ℙⁿ(ℂ), in which the truncated counting functions have different weights. As for application, we deal with the algebraic dependence problem of meromorphic mappings sharing moving hyperplanes in general position.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.149-154
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• 1997

Based on the full Navier-Stokes solutions, the thermohydrodynamic performance of a long journal bearing is investigated. A numerical method based on Galerkin's procedure and B-spline test functions has been presented for solving two-dimensional problems involving fluid flow and heat transfer. For numerical stability the artificial compressibility is employed to the conservation of mass. The discretized algebraic equations are solved by Newton's method. Effects of varying the speed of an inner cylinder to load carrying capacity are investigated. The results indicated that the increase of the speed of an inner cylinder has a significant effect on the temperature profile and ultimately on the performance.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.440-452
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• 1990

Comprehensive numberical computations have been made for four turbulent swirling jets with and without recirculation to critically evaluate the accuracy and universality of several exising turbulence models as well as of the modified k-.epsilon. model proposed in the present study. A numerical scheme based on the full Navier-Stoke equations ha been developed and used for this purpose. Inlet conditions are given by experiments, whenever possible, to minimize the error due to incorrect initial conditions. The standard k-.epsilon. model performs well for the strongly swirling jets with recirculation while it underpredicts the influence of swirl for weakly swirling jets. Rodi's swirl correction and algebraic stress model do not exhibit universality for the swirling jets. The present modified k-.epsilon. model derived from algebraic stress model accounts for anisotropy and streamline curvature effect on turbulence. This model performs consistently better than others for all cases. It may be because these flows have a strong dependence of stresses on the local strain of the mean flow. The predictions of truculence intensities indicate that this model successfully reflect the curvature effect in swirling jets, i.e. the stabilizing and destabilizing effects of swirl on turbulence transport.

• The Proceeding of the Korean Institute of Electromagnetic Engineering and Science
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• v.3 no.2
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• pp.40-45
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• 1992

A simple emission model applicable for low scattering (scattering << absorption) anisotropic layer is developed and applied to the interpretation of measurements of microwave emission from row crops. The vegetation layer of row crops is modeled as a random slab embedded with small spheroid with major axis aligend paralel to the crop-row direction. The total emission is given in a simple algebraic form based on the zero-order radiative transfer theory. The single scattering albedo for spheroid and its polarimetric phase function are presented. The effects of layer azimuthal dependence on emission are accounted for by using an anisotropic albedo in the zero-order transfer theory. The developed emission theory favorably compares with the brightness temperature measured over soybeans canopy.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.215-241
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• 2003

In this paper, solute transport in heterogeneous aquifers using a modified Fokker-Planck equation (MFPE) is investigated. This newly developed mathematical model is characterised with a time-, scale-dependent dispersivity. A two-dimensional finite volume quadrilateral mesh method (FVQMM) based on a quadrilateral background interpolation mesh is developed for analysing the model. The FVQMM transforms the coupled non-linear partial differential equations into a system of differential equations, which is solved using backward differentiation formulae of order one through five in order to advance the solution in time. Three examples are presented to demonstrate the model verification and utility. Henry's classic benchmark problem is used to show that the MFPE captures significant features of transport phenomena in heterogeneous porous media including enhanced transport of salt in the upper layer due to its parameters that represent the dependence of transport processes on scale and time. The time and scale effects are investigated. Numerical results are compared with published results on the some problems.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.