• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.8 no.3
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• pp.338-350
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• 1996

A numerical analysis is carried out to study the two-dimensional steady state natural convection from vertical wires immersed in cold pure water. The surface of the wire is $0^{\circ}C$ unifrom temperature. Results of the analysis are presented for free stream temperature from $0^{\circ}C$ to $25^{\circ}C$ and the aspect ratio N from $5.26{\times}10^{-3}$ to $1.0{\times}10^{-3}$. The effects of the density extremum and aspect ratio on the flow pattern and the heat transfer characteristics are discussed As the aspect ratio N becomes larger, in the range of $1.0^{\circ}C{\leq}T_{\infty}{\leq}4.4^{\circ}C$ and $6{^{\circ}C}{\leq}T_{\infty}{\leq}17^{\circ}C$, the effect of Pr number on the heat transfer is shown to be more significant than the aspect ratio. Investigating into the effect of the density extremum on the heat transfer from wires, the new heat transfer correlations are suggested with the relation of average Nu mumber vs. modified Ra number. Here, the coefficient values C of correlations are presented as the function of density extremum parameter $R^*$. The effects of the density extremum parameter are also discussed.

• Structural Engineering and Mechanics
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• v.46 no.1
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• pp.39-51
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• 2013

An extremum method is presented to predict the wrinkling characteristics of the inflated cone in bending. The wrinkling factor is firstly defined so as to obtain the wrinkling condition. The initial wrinkling location is then determined by searching the maximum of the wrinkling factor. The critical wrinkling load is finally obtained by determining the ratio of the wrinkling moment versus the initial wrinkling location. The extremum method is proposed based on the assumption of membrane material of beam wall, and it is extended to consider beam wall with thin-shell material in the end. The nondimensional analyses show that the initial wrinkling location is closely related to the taper ratio. When the taper ratio is higher than the critical value, the initial wrinkles will be initiated at a different location. The nondimensional critical wrinkling load nonlinearly increases as the taper ratio increases firstly, and then linearly increases after the critical taper ratio. The critical taper ratio reflects the highest load-carrying efficiency of the inflated cone in bending, and it can be regarded as a measure to optimize the geometry of the inflated cone. The comparative analysis shows fairly good agreement between analytical and numerical results. Over the whole range of the comparison, the mean differences are lower than 3%. This gives confidence to use extremum method for bending-wrinkling analysis of inflated conical cantilever beam.

• International Journal of Computer Science & Network Security
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• v.24 no.1
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• pp.1-8
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• 2024

In contemporary education, the rapid advancement of digital technologies elevates demands for integrating the latest tools into the learning process. Mathematical analysis, as a discipline, benefits from computer mathematics in distance education, enhancing practical aspects and enabling individualized learning. This article addresses the integration of the Maple computer mathematics system into higher education, specifically in teaching "Mathematical Analysis." Emphasizing its role in distance learning, computer mathematics optimizes the educational environment, reducing the time required for knowledge acquisition. The article showcases the application of Maple in finding extremum points and introduces an educational software simulator, enabling students to practice the method. The simulator, developed within Maple, facilitates self-checking and enhances the study of functions. Conclusions drawn from the study highlight the positive impact of these tools on distance education, affirming Maple's role in enhancing professional training and information culture among higher education students.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.33-38
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• 2008

For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. Paraxial boundary conditions(PBCs) which are kinds of absorbing boundary conditions based on paraxial approximations of the scalar and elastic wave equations not only lead to well-posed problem but also are stable and computationally inexpensive. But the complex mathematical forms of PBCs with partial derivatives complicate the application of those to finite element analysis. In this paper a penalty functional is newly proposed for applying PBCs into finite element analysis and the existence and uniqueness of the extremum of the proposed functional is demonstrated. The numerical verification of the efficiency is carried out through comparing PBCs with a viscous boundary condition.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.587-598
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• 1997

A numerical model for masonry is proposed by following an internal variable approach originally developed in the field of elastic-plastic analysis. The general features of the theoretical framework are discussed by focussing on finite element models applicable to incremental elastic-plastic problems. An extremum property is derived and its implications in terms of convergence for convenient algorithms are briefly discussed, by including the case of softening materials and damage effects. Next, a numerical model is presented, which is suitable for masonry, can be developed according to the same internal variable formulation and enjoys similar properties. Some numerical results are presented and compared with the response of a masonry shear wall subjected to pseudodynamic tests.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.12
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• pp.1210-1218
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• 2011

GA (Genetic Algorithms) are efficient for searching for global optima but may have some problems such as premature convergence, convergence to local extremum and divergence. These phenomena are related to the evolutionary operators. As population diversity converges to low value, the search ability of a GA decreases and premature convergence or converging to local extremum may occur but population diversity converges to high value, then genetic algorithm may diverge. To guarantee that genetic algorithms converge to the global optima, the genetic operators should be chosen properly. In this paper, we analyze the effects of the selection operator, crossover operator, and mutation operator on convergence properties, and propose the sweeping method of mutation probability and elitist propagation rate to maintain the diversity of the GA's population for getting out of the premature convergence. Results of simulation studies verify the feasibility of using these sweeping operators to avoid premature convergence and convergence to local extrema.

• Bulletin of the Society of Naval Architects of Korea
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• v.23 no.2
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• pp.27-32
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• 1986

This paper describes an application of the adaptive finite element computations to a free surface flow problem in a canal. A-posteriori error estimates for the adaptive finite element computations are based on the dual extremum principles. Previously the dual extremum principles were applied to compute the upper and lower bounds of the added mass of two-dimensional cylinders in a canal[1,2]. However, the present method improves the convergence of the computed results by utilizing the local error estimates and by applying the adaptive meshes in the finite element computations. In a test result using triangular elements it is shown that the numerical error in the adaptive finite elements reduces quadratically compared with that in a uniform mesh subdivision.

• Transactions of Materials Processing
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• v.23 no.3
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• pp.139-144
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• 2014

In the current study, we present a new model for predicting width spread of a slab with a dog-bone shaped cross section during rolling in the roughing train of a hot strip mill. The approach is based on the extremum principle for a rigid plastic material and a three dimensional admissible velocity field. The upper bound theorem is used for calculating the width spread of the slab. The prediction accuracy of the proposed model is examined through comparison with the predictions from 3-D finite element (FE) process simulations.

• Transactions of Materials Processing
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• v.23 no.3
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• pp.145-150
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• 2014

Precision control of the slab is crucial for product quality and production economy in hot strip mills. The current study presents a new model for predicting width spread of a slab with a rectangular cross section during roughing. The model is developed on the basis of the extremum principle for a rigid plastic material and a three dimensional admissible velocity field. This model incorporates the effect of process variables such as the shape factor and the ratio of width to thickness. We compare the results of this model to 3-D finite element (FE) process simulations and also to results from a previous study.

• Journal of Advanced Navigation Technology
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• v.18 no.2
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• pp.170-177
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• 2014

Genetic Algorithms are robust search and optimization techniques but have some problems such as premature convergence and convergence to local extremum. As population diversity converges to low value, the search ability decreases and converges to local extremum but population diversity converges to high value, then the search ability increases and converges to global optimum or genetic algorithm may diverge. To guarantee that genetic algorithms converge to the global optima, the genetic operators should be chosen properly. In this paper, we propose the genetic operators with the hybrid function of the average Hamming distance and the fitness value to maintain the diversity of the GA's population for escaping from the premature convergence. Results of simulation studies verified the effects of the mutation operator for maintaining diversity and the other operators for improving convergence properties as well as the feasibility of using proposed genetic operators on convergence properties to avoid premature convergence and convergence to local extremum.