• School Mathematics
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• v.14 no.4
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• pp.565-577
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• 2012

In this study, we investigated the process of constructing the geometrical solutions to quadratic equation, through proportions between lengths of similar triangles in a dynamic environment. To do this, we provided one task to 4 ninth grades students and observed the process of the students' activities and strategies. As a result of this pilot lesson study, our research shows the advantage and possibility of geometrical method in learning and teaching quadratic equation.

• Steel and Composite Structures
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• v.35 no.3
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• pp.449-462
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• 2020

This work aims to study effects of the crack and the surface energy on the free longitudinal vibration of axially functionally graded nanorods. The surface energy parameters considered are the surface stress, the surface density, and the surface Lamé constants. The cracked nanorod is modelled by dividing it into two parts connected by a linear spring in which its stiffness is related to the crack severity. The surface and bulk material properties are considered to vary in the length direction according to the power law distribution. Hamilton's principle is implemented to derive the governing equation of motion and boundary conditions. Considering the surface stress causes that the derived governing equation of motion becomes non-homogeneous while this was not the case in works that only the surface density and the surface Lamé constants were considered. To extract the frequencies of nanorod, firstly the non-homogeneous governing equation is converted to a homogeneous one using an appropriate change of variable, and then for clamped-clamped and clamped-free boundary conditions the governing equation is solved using the harmonic differential quadrature method. Since the present work considers effects of all the surface energy parameters, it can be claimed that this is a comprehensive work in this regard.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.22 no.8
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• pp.573-578
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• 2010

Topological matrix which reflects characteristics of network connectivity has been widely used in efficient solving for complicated flow network. Using topological matrix, one can easily define continuity at each node of flow network and make algorithm to automatically generate continuity equation of matrix form. In order to analyze flow network completely it is required to satisfy energy conservation in closed loops of flow network. Fundamental cycle retrieving algorithm based on graph theory automatically constructs energy conservation equation in closed loops. However, it is often accompanied by NP-complete problem. In addition, it always needs fundamental cycle retrieving procedure for every structural change of flow network. This paper proposes alternative mathematical method to analyze flow network without fundamental cycle retrieving algorithm. Consequently, the new mathematical method is expected to reduce solving time and prevent error occurrence by means of simplifying flow network analysis procedure.

• Korean Journal of Soil Science and Fertilizer
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• v.32 no.4
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• pp.344-356
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• 1999

A new and relatively simple equation for the soil water content-pressure head curve, ${\theta}$(h) is described in this paper. The particular form of the equation enables one to derive closed-form analytical expressions for the relative hydraulic conductivity, Kr, when substituted in the predictive conductivity models of Y. Mualem. Hopmans' equation is presented as an experimental method. The experienced method, $ET_a=K_sK_cET_o$ is introduced to estimate the actual evapotranspiration, $ET_a$(or $ET_c$). Using $ET_c$ and coil water data measured automatically in a weighing lusimeter, $K_s$ and $K_c$ values are estimated. Recently, FAO has introduced calculation procedures for the soil water(stress) coefficient, Ks in "Guidelines for computing crop water requirements".

• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.4
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• pp.252-258
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• 1987

Time periodic finite element solutions for sinusoidally excited electromagnetic field problems in moving media are presented. Solutions by the Galerkin method contain spurious oscillations when grid Peclet number is more than one. To suppress these oscillations an upwind finite element method using two different time periodic test functions is introduced. One is multiplied to second and first-order space derivative terma and the other to the time derivative term. Test functions are obtained from trial functions by adding or subtracting quadratic bias functions with appropriate scaling factors. Phase differences are considered between trial functions and bias functions. For simple interpretations of the phase differences, complex scaling factors are used. The proposed method is developed to give nodally exact solutions for uniform grid spacing in one dimensional problems. Based on the one dimensional results, a two dimensional upwinding scheme is also derived.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.796-801
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• 2002

The goal of this research is the shape design of the valve using a computer simulation. For an analysis a basic mathematical model describing compression cycle is considered as consisting of five sets of coupled equations. These are the volume equation (kinematics), valve dynamic equation (dynamics), ideal gas equation (thermodynamics), Bernoulli equation (fluid dynamics), and dynamic equation of fluid particle based on Helmholtz equation (acoustics). Valve motion is made by the superposition of free vibration modes obtained by the finite element method. That is, the eigenvalues and eigenvectors are the sufficient modeling factors fur the valve in the simulation program. Thus, to design a shape of the valve, shape design sensitivity through chain-ruled derivatives is considered from two sensitivity coefficients, one is the design sensitivity of the capability of compressor with respect to the eigenvalues of the valve, and the other is the design sensitivity of the eigenvalue with respect to the shape change of the valve. In this research, the continuum design sensitivity analysis concepts are used for the latter.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.11a
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• pp.39-44
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• 1996

A nodal transport method based on the F$_{N}$ method is developed for the transport calculation in x- y geometry and tested for benchmark problems. Using transverse integration, the two-dimensional transport equation is converted to one-dimensional equations for x, y-directions and the one-dimensional equations are integrated over azimuthal angle. With proper approximations for the transverse leakage, the one-dimensional equations are discretized by using the F$_{N}$ method without truncation error. At present, isotropic approximation of the transverse with a quadratic or flat shape in spatial variable is tested.ted.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.363-381
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• 2012

This study is aimed at providing an efficient analytical model to obtain pressure- impulse diagram of one-way reinforced concrete slabs subjected to different shapes of air blast loading using single degree of freedom method (SDOF). A tri-linear elastic perfectly plastic SDOF model has been used to obtain the pressure-impulse diagram to correlate the blast pressure and the corresponding concrete flexural damage. In order to capture the response history for the slab, a new approximately SDOF method based on the conventional SDOF method is proposed and validated using published test data. The influences of pulse loading shape on the pressure-impulse diagram are studied. Based on the results, a pressure-impulse diagram generation method using SDOF and an analytical equation for the pressure-impulse diagram is proposed to different damage levels and different blast loading shapes.

• Aerospace Engineering and Technology
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• v.12 no.2
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• pp.147-155
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• 2013

The nominal radiometric calibration equation and additional five algorithms are applied in the infrared channel radiometric calibration for the COMS (Communication, Ocean, Meteorological Satellite) MI (Meteorological Imager). The processing end time of the radiometric calibration is directly related with the start time of geometric calibration processing since the geometric calibration processing is followed by that of the radiometric calibration. This paper describes comparison and analysis results for geometric calibration processing using two types of the radiometric calibration results, outputs from only the nominal radiometric calibration equation and outputs from the complete one (the nominal radiometric calibration equation with additional five algorithms), to propose a method with the earlier start time of the geometric calibration processing. Experimental results show that both of radiometric calibration results, from the nominal radiometric calibration equation with a fast processing speed and from the complete one with accurate radiometric values, can be used in the geometric calibration as the appropriate inputs because those processing results satisfied the requirements of geometric calibration processing accuracy. Thus the radiometric calibration results from the nominal radiometric calibration equation can be used to improve geometric calibration processing time.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.699-713
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• 2022

This paper proposes a hybrid successive over-relaxation iterative method for the numerical solution of a nonlinear diffusion in a one-dimensional porous medium. The considered mathematical model is discretized using a computational complexity reduction scheme called half-sweep finite differences. The local truncation error and the analysis of the stability of the scheme are discussed. The proposed iterative method, which uses explicit group technique and modified successive over-relaxation, is formulated systematically. This method improves the efficiency of obtaining the solution in terms of total iterations and program elapsed time. The accuracy of the proposed method, which is measured using the magnitude of absolute errors, is promising. Numerical convergence tests of the proposed method are also provided. Some numerical experiments are delivered using initial-boundary value problems to show the superiority of the proposed method against some existing numerical methods.