• Nuclear Engineering and Technology
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• v.16 no.1
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• pp.1-10
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• 1984

General time-volume averaged conservation equations and jump conditions for two-phase flows are derived here. The time-averaged equations for a single phase region in two-phase flow are obtained from local instant balance equations by a technique often used for single phase turbulent flow equations. The results obtained by integrating the time averaged equations over a flow volume are spatially averaged twice; first, they are averaged over a single phase region of the k-th phase and then averaged over the total volume of the k-th phase, in a flow volume. The mass, momentum, and energy conservation equations are obtained from the general time-volume averaged equations. The advantages of the present model are explained by comparing it with Ishii's model (1) and Banerjee's model (2). Finally, the assumptions and approximate terms of the equations of the THERMIT-6S are clarified.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.

• Animal Bioscience
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• v.34 no.2
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• pp.306-311
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• 2021

Objective: The objectives were to develop prediction equations for digestible energy (DE) and metabolizable energy (ME) of feed ingredients and diets for pigs based on chemical composition and to evaluate the accuracy of the equations using in vivo data. Methods: A total of 734 data points from 81 experiments were employed to develop prediction equations for DE and ME in feed ingredients and diets. The CORR procedure of SAS was used to determine correlation coefficients between chemical components and energy concentrations and the REG procedure was used to generate prediction equations. Developed equations were tested for the accuracy according to the regression analysis using in vivo data. Results: The DE and ME in feed ingredients and diets were most negatively correlated with acid detergent fiber or neutral detergent fiber (NDF; r = -0.46 to r = -0.67; p<0.05). Three prediction equations for feed ingredients reflected in vivo data well as follows: DE = 728+0.76×gross energy (GE)-25.18×NDF (R2 = 0.64); ME = 965+0.66×GE-24.62×NDF (R2 = 0.60); ME = 1,133+0.65×GE-29.05×ash-23.17×NDF (R2 = 0.67). Conclusion: In conclusion, the equations suggested in the current study would predict energy concentration in feed ingredients and diets.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1043-1057
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• 2000

This paper is devoted to the investigation of mixed Fourier-Bessel transformation (※Equations, See Full-text) We apply the method of [6] which provides the estimate for weighted L(sub)$\infty$-norm of the spherical mean of │f│$^2$ via its weighted L$_1$-norm (generally it is wrong without the requirement of the non-negativity of f). We prove that in the case of Fourier-Bessel transformatin the mentioned method provides (in dependence on the relation between the dimension of the space of non-special variables n and the length of multiindex ν) similar estimates for weighted spherical means of │f│$^2$, the allowed powers of weights are also defined by multiindex ν. Further those estimates are applied to partial differential equations with singular Bessel operators with respect to y$_1$, …, y(sub)m and we obtain the corresponding estimates for solutions of the mentioned equations.

• International Journal of Automotive Technology
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• v.6 no.4
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• pp.375-381
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• 2005

This paper presents linear algebraic equations in the form of recursive formula to compute elastokinematic characteristics of a suspension system. Conventional methods of elastokinematic analysis are based on nonlinear kinematic constrant equations and force equilibrium equations for constrained mechanical systems, which require complicated and time-consuming implicit computing methods to obtain the solution. The proposed linearized elastokinematic equations in the form of recursive formula are derived based on the assumption that the displacements of elastokinematic behavior of a constrained mechanical system under external forces are very small. The equations can be easily computerized in codes, and have the advantage of sharing the input data of existing general multi body dynamic analysis codes. The equations can be applied to any form of suspension once the type of kinematic joints and elastic components are identified. The validity of the method has been proved through the comparison of the results from established elastokinematic analysis software. Error estimation and analysis due to piecewise linear assumption are also discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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• pp.791-799
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT was performed through discretization of equations of motion and boundary condition. Structural model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations(Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence are investigated and pertinent conclusions are derived.

• Journal of Educational Research in Mathematics
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• v.12 no.3
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• pp.389-408
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• 2002

This paper is based on a teaching experiment research conducted in a differential equations course at Ewha Womans University. The purpose of this paper lies in seeking a new direction in the teaching and learning of college mathematics by applying RME's theoretical essence to the teaching of differential equations. For this purpose, the emergent procedure had to be carefully considered before to analyzing the existing problems in teaching differential equations and alternative access to reformed differential equations. Methods of developmental research, ideas concerning teaching procedure and instructional design are offered. This research demonstrates that a deeper understanding of differential equations by students can be achieved with the instructional design which reflects the RME theory.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.317-324
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• 2016

Since Jiuzhang Suanshu, mathematical structures in the traditional East Asian mathematics have been revealed by practical problems. Since then, polynomial equations are mostly the type of $p(x)=a_0$ where p(x) has no constant term and $a_0$ is a positive number. This restriction for the polynomial equations hinders the systematic development of theory of equations. Since tianyuanshu (天元術) was introduced in the 11th century, the polynomial equations took the form of p(x) = 0, but it was not universally adopted. In the mean time, East Asian mathematicians were occupied by kaifangfa so that the concept of zeros of polynomials was not materialized. We also show that Suanxue Qimeng inflicted distinct developments of the theory of equations in three countries of East Asia.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Journal of Biosystems Engineering
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• v.23 no.4
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• pp.335-342
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• 1998

The objectives of this study were to evaluate respiration characteristics and develop empirical respiratory rate equations for short gain rough rice. The carbon dioxide concentrations generated from mush rice at four level temperatures(10, 20, 30, 4$0^{\circ}C$) and 4 level moisture contents(17.2, 21.5, 25.9, 31.6％, d.b.) were measured by gas chromatography. The respiratory rates' increased exponentially with gain temperature and also with moisture content The relationship between respiratory rate and gain temperature fitted the Arrehenius' and Core's equations very well. Two empirical respiratory rate equations were presented as a function of gain temperature and moisture content. The values of determination coefficient for the developed respiratory rate equations were 0.999, and the result of t-test showed that there were no significant differences between predicted and measured respiratory rates on significance level of 1%. Therefore, it appeared that respiratory rates predicted by the respiratory rate equations agreed well with measured values. An equation for predicting dry matter losses of rough rice during storage was presented by modifying the respiratory rate equations based on chemical reaction of decomposition of carbohydrate.