• Honam Mathematical Journal
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• v.32 no.3
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• pp.493-514
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• 2010

The resultant and discriminant of composite polynomials were studied by McKay and Wang using some algebraic properties. In this paper we study the resultant and discriminant of iterate polynomials. We shall use elementary computations of matrices and block matrix determinants; this could provide not only the values but also the visual structure of resultant and discriminant from elementary matrix calculation.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.663-677
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• 2010

We investigate efficient method for the computation of resultant and discriminant of polynomials. The aim of this paper is to provide not only those values but also visual structure from elementary matrix calculation.

• Journal of The Korean Society of Manufacturing Technology Engineers
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• v.9 no.2
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• pp.72-79
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• 2000

A new optimal tool design model which can be minimized the resultant cutting forces under the constrains of variables was developed. The resultant cutting forces are used as the objective function and tool angles are used as the variables. Cutting experiments of tool wear and chip length using the new and conventional tools wee carried out. Tool life of optimized cutter are more increased than those of conventional cutter by 2.29 times and 2.52 times at light and at heavy cutting conditions respectively. Chip length of optimized cutter are more increased than those of conventional cutter It is considered that the decrease of the resultant cutting forces is the cause that an effective rake and shear angles by the shape of optimal cutter.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.26 no.2
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• pp.99-105
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• 2012

This paper deals with the experimental results of the frequency-dependent resultant ground impedance of vertical ground electrodes installed with a regular n-polygon. In order to propose an effective method of installing the vertically-driven multiple ground electrodes used to obtain the low ground impedance, the resultant ground impedance of ground electrodes installed with a regular n-polygon were measured as functions of the number of ground electrodes and the frequency of test currents and the results were discussed based on the potential interferences among ground electrodes. As a consequence, the effect of potential interference on the resultant ground impedance of vertical ground electrodes is frequency-dependent and it is significant in the low frequency of a few hundreds [Hz]. The resultant ground impedance of multiple vertical ground electrodes is not decreased in linearly proportion to the number of ground electrodes due to the overlapped potential interferences. Also the distributed-parameter circuit model considering the potential interference, the frequency-dependent relative permittivity and resistivity of soil was proposed. The simulated results of the frequency-dependent resultant ground impedance of multiple vertical ground electrodes are in good agreement with the measured data.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.25 no.12
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• pp.107-112
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• 2011

Multiple ground rods are commonly used to obtain the low ground impedance, but they will not reduce the ground impedance unless the spacings between the ground rods are sufficient. This paper presents the experimental results of frequency-dependent resultant ground impedance of two ground rods in parallel. The resultant ground impedance of two ground rods in parallel were measured as functions of the spacing and length of ground rods and the frequency of test currents and were discussed based on the potential interferences. As a consequence, the frequency-dependent ground impedance of single ground rod and two combined ground rods give capacitive. It was found that the effect of potential interference on the ground impedance is directly associated with the frequency-dependent ground impedance and is strong in low frequency. Also, in order to reduce the increasing rate of resultant ground impedance of two ground rods due to potential interference to within 10(%), two ground rods in parallel will be placed over one rod length apart.

• Structural Engineering and Mechanics
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• v.40 no.1
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• pp.29-48
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• 2011

Under large storm loads sections of a long pipeline on the seabed can be uplifted. Numerically this loss of contact is extremely difficult to simulate, but accounting for uplift and any subsequent recontact behaviour is a critical component in pipeline on-bottom stability analysis. A simple method numerically accounting for this uplift and reattachment, while utilising efficient force-resultant models, is provided in this paper. While force-resultant models use a plasticity framework to directly relate the resultant forces on a segment of pipe to the corresponding displacement, their historical development has concentrated on precisely modelling increasing capacity with penetration. In this paper, the emphasis is placed on the description of loss of penetration during uplifting, modelled by 'strain-softening' of the force-resultant yield surface. The proposed method employs uplift and reattachment criteria to determine the pipe uplift and recontact. The pipe node is allowed to become free, and therefore, the resistance to the applied hydrodynamic loads to be redistributed along the pipeline. Without these criteria, a localised failure will be produced and the numerical program will terminate due to singular stiffness matrix. The proposed approach is verified with geotechnical centrifuge results. To further demonstrate the practicability of the proposed method, a computational example of a 1245 m long pipeline subjected to a large storm in conditions typical of offshore North-West Australia is discussed.

• Journal of the Society of Naval Architects of Korea
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• v.48 no.2
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• pp.141-146
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• 2011

This study numerically carried out the propeller open water test(POW) by solving Navier-Stokes equations governing the three-dimensional unsteady incompressible viscous flow with the turbulence closure model of the ${\kappa}-{\omega}$ SST model. Numerical simulations are performed at various range of advance ratios. Corresponding to Reynolds numbers of $5.89{\times}105{\sim}6.47{\times}105$ based on free stream velocity and the chord length at 0.7 propeller radius. The present results give a good agreement with those of the experiment. The propeller induced vortical structures have been analyzed by visualizing the resultant vorticity. As the advance ratio increases, the magnitude and length of the resultant vorticity decrease significantly. As the main focus of present study, the numerical model to present the ($r-{\theta}$) plane-averaged resultant vorticity along the streamwise direction for various advance ratios has been suggested.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2211-2224
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• 1994

On face milling operation a new optimal cutter, which can minimize the resultant cutting forces, was designed from the cutting force model. Cutting experiments were carried out and the cutting forces of the new and conventional cutters were analyed in time and frequency domains. The resultant cutting forces were used as the objective function and cutter angles as the variables. A new optimal cutter design model which can minimize the resultant cutting forces under the constraints of variables was developed and its usefulness was proven. The cutting forces in feed direction of the newly designed cutter are reduced in comparison with those from the conventional cutter. The magnitudes of an insert frequency component of cutting force from the newly designed cutter are reduced than those from conventional cutter and the fluctuations of cutting force are also reduced.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.4
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• pp.713-724
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• 2011

We investigate the irreducibility of iterate and composite polynomials. For this purpose discriminant and resultant are computed by means of the norm function.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.149-161
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• 2013

The history of finding solutions of linear equations went back to some thousand years ago, and has been steadily developed to solve systems of higher degree polynomials. The method to eliminate variables came into use around the 17th and 18th century. This technique has been extended to the resultant theory that was laid in the 19th century by outstanding mathematicians as Euler, Sylvester, and B$\acute{e}$zout. In this paper we discuss the historical reflection about the development of solving system of polynomials. We add a special emphasis on E. B$\acute{e}$zout who gave the first account on the resultant which is a generalization of discriminant and Gauss elimination method.