• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.197-211
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• 2013

We study some stability properties in discrete Volterra equations by employing to change Yoshizawa's results in [13] for the nonlinear equations into results for the nonlinear discrete Volterra equations with unbounded delay.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.473-481
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• 2021

In this paper, we investigate the relations between the growth of meromorphic coefficients and that of meromorphic solutions of complex linear differential-difference equations with meromorphic coefficients of finite logarithmic order. Our results can be viewed as the generalization for both the cases of complex linear differential equations and complex linear difference equations.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.177-189
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• 2024

In this paper, we suggest and analyze new higher order classes of iterative methods for solving nonlinear equations by using variational iteration technique. We present several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.

• Nuclear Engineering and Technology
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• v.16 no.2
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• pp.47-57
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• 1984

Mathematically-rigorous time-volume averaged conservation equations were simplified to established the differential equations of THERMIT-6S, which is a two-fluid 3-D code. The difference equations of THERMIT-6S were obtained by discretizing the proceeding set of differential equations. The spatial discretization is characterized by a first-order spatial scheme, donor cell method, and staggered mesh layout. For time discretization, a first order semi-implicit scheme treats implictly sonic terms and terms relating to local transport phenomena and explicitly convective terms. The results were linearized by the Newton-Raphson method. In order to construct the reduced pressure equation, the linearized equations were manipulated so that all variables are coupled between mesh cells through only the pressure variable. By simulating numerically the OPERA-15 experiment, it was found that THERMIT-6S is a very powerful code in predicting reactor behavior after sodium boiling including flow coastdown, reversal flow and flow oscillation.

• Computers and Concrete
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• v.3 no.4
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• pp.249-260
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• 2006

Self-consolidating concrete (SCC) in the fresh state is known for its excellent deformability, high resistance to segregation, and use, without applying vibration, in congested reinforced concrete structures characterized by difficult casting conditions. Such a concrete can be obtained by incorporating either mineral or chemical admixtures. This paper presents the results of an investigation to asses the applicability of Abram's law in predicting the compressive strength of SCC to any given age. Abram's law is based on the assumption that the strength of concrete with a specific type of aggregate at given age cured at a prescribed temperature depends primarily on the water-to-cement ratio (W/C). It is doubtful that such W/C law is applicable to concrete mixes with mineral or chemical admixtures as is the case for SCC where water to binder ratio (W/B) is used instead of W/C as the basis for mix design. Strength data of various types of SCC mixtures is collected from different sources to check the performance of Abram's law. An attempt has been made to generalize Abram's law by using various optimization methodologies on collected strength data of various SCC mixtures. A set of generalized equations is developed for the prediction of SCC strength at various ages. The performance of generalized equations is found better than original Abram's equations.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.2
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• pp.225-231
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• 2009

In this paper, it is shown that Carson's equation can still be applied for the calculation of the series reactance of transmission lines with no ground return current as well as the one with ground return. It is proved in the following method. First two voltage drop equations for three-phase three wire transmission line are derived, one without considering ground return and the other using Carson's equation. The impedance matrix of the two equations are different from each other. But if we put the condition of zero ground current, $I_a+I_b+I_c=0$, those two equations becomes the identical equations. Therefore even a transmission line is not grounded, its line parameters can still be obtained using the Carson's equation. It has been confused whether or not Carson's equation can be used for an ungrounded system. It is because where ever Carson's equation is shown in the book, it also says that the system has ground return current paths as a premise. It is also verified with EMTP studies on the test circuit.

• Proceedings of the KIEE Conference
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• 1999.07a
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• pp.154-156
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• 1999

A Linear Stepping Motor(LSM) can operate open loop control mode similarly to a rotary stepping motor. The linear motion without any mechanical linkage in the LSM results in several advantages for precise positioning actuators. However, to realize the more stable and higher speed control without hunting, it is necessary to derive an equivalent circuit to explain the steady-state and transisent characteristics in order to find an adequate control rule for high performance control of the LSM. In this paper, magnetic equivalent circuit is obtained, based on the structure of the LSM, and then the electric equivalent circuit of the LSM is derived by solving equations for the magnetic equivalent circuit. The 1-step response characteristic of the LSM is analyzed by the ACSL with the voltage equations, the force equations, the force equations and the kinetic equation.

• Proceedings of the KSR Conference
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• 2008.11b
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• pp.169-178
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• 2008

In this paper, it is shown that Carson's equation can still be applied for the calculation of the series reactance of transmission lines with no ground return current as well as the one with ground return. It is proved in the following method. First two voltage drop equations for three-phase three wire transmission line are derived, one without considering ground return and the other using Carson's equation. The impedance matrix of the two equations are different from each other. But if we put the condition of zero ground current, $I_a+I_b+I_c=0$, those two equations becomes the identical equations. Therefore even a transmission line is not grounded, its line parameters can still be obtained using the Carson's equation. It has been confused whether or not Carson's equation can be used for an ungrounded system. It is because where ever Carson's equation is shown in the book, it also says that the system has ground return current paths as a premise. It is also verified with EMTP studies on the test circuit.

• Applied Chemistry for Engineering
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• v.34 no.2
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• pp.144-152
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• 2023

To evaluate the fire risk of combustible materials, Chung's equations VII, VIII, and IX were newly established. The fire risk index-IX (FRI-IX) and fire risk rating (FRR) were calculated. Ginkgo, dawn redwood, toona, lime, walnut, and polymethylmethacrylate (PMMA) were selected as test specimens. The combustion characteristics were evaluated using a cone calorimeter according to ISO 5660-1. After combustion, the fire performance index-VII (FPI-VII) of the specimens, varied between 15.15 and 182.53 s²/kW, as determined by Chung's equations, and the fire growth index-VII (FGI-VII) varied between 0.0023 and 0.0165 kW/s². The fire performance index-VIII (FPI-VIII) based on PMMA varied between 0.29 and 3.45, and the fire growth index-VIII (FGI-VIII) varied between 2.88 and 20.63. The FRI-IX, which is the fire risk rating, showed dawn redwood has a very high fire risk, with FRI-IX values of 71.14 (fire risk rating: G). Therefore, wood with a large amount of volatile organic compounds and a low bulk density showed a high value of FRI-IX by lowering FPI-VII and FPI-VIII and increasing FGI-VII and FGI-VIII.