• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.461-473
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• 2022

In this paper, we study differential equations arising from the generating functions of the geometric polynomials. We give explicit identities for the geometric polynomials. Finally, we investigate the zeros of the geometric polynomials by using computer.

• Journal of Mechanical Science and Technology
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• v.17 no.9
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• pp.1287-1296
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• 2003

In this paper the dynamic analysis of the Macpherson strut motor-vehicle suspension system is presented. The equations of motion are formulated using a two-step transformation. Initially, the equations of motion are derived for a dynamically equivalent constrained system of particles that replaces the rigid bodies by applying Newton's second law The equations of motion are then transformed to a reduced set in terms of the relative joint variables. Use of both Cartesian and joint variables produces an efficient set of equations without loss of generality For open chains, this process automatically eliminates all of the non-working constraint forces and leads to an efficient solution and integration of the equations of motion. For closed loops, suitable joints should be cut and few cut-joints constraint equations should be included for each closed chain. The chosen suspension includes open and closed loops with quarter-car model. The results of the simulation indicate the simplicity and generality of the dynamic formulation.

• Advances in environmental research
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• v.3 no.2
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• pp.131-149
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• 2014

Two different model selection indices, the Akaike information criterion (AIC) and the coefficient of determination ($R^2$), are used to discriminate competing isotherm equations for aqueous pollutant removal systems. The former takes into account model accuracy and complexity while the latter considers model accuracy only. The five types of isotherm shape in the Brunauer-Deming-Deming-Teller (BDDT) classification are considered. Sorption equilibrium data taken from the literature were correlated using isotherm equations with fitting parameters ranging from two to five. For the isotherm shapes of types I (favorable) and III (unfavorable), the AIC favors two-parameter equations which can easily track these simple isotherm shapes with high accuracy. The $R^2$ indicator by contrast recommends isotherm equations with more than two parameters which can provide marginally better fits than two-parameter equations. To correlate the more intricate shapes of types II (multilayer), IV (two-plateau) and V (S-shaped) isotherms, both indices favor isotherm equations with more than two parameters.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.2
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• pp.115-122
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• 2008

The effects of characteristic condition number on the convergence of preconditioned Euler equations were investigated. The two-dimensional preconditioned Euler equations adopting Choi and Merkle's preconditioning and the temperature preconditioning are considered. Preconditioned Roe's FDS scheme was adopted for spatial discretization and preconditioned LU-SGS scheme was used for time integration. It is shown that the convergence characteristics of the Euler equations are strongly affected by the characteristic condition number, and there is an optimal characteristic condition number for a problem. The optimal characteristic condition numbers for the Choi and Merkle's preconditioning and temperature preconditioning are different.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.789-817
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• 2004

This paper deals with the modal analysis of rotational shell structures by means of the numerical solution technique known as the Generalized Differential Quadrature (G. D. Q.) method. The treatment is conducted within the Reissner first order shear deformation theory (F. S. D. T.) for linearly elastic isotropic shells. Starting from a non-linear formulation, the compatibility equations via Principle of Virtual Works are obtained, for the general shell structure, given the internal equilibrium equations in terms of stress resultants and couples. These equations are subsequently linearized and specialized for the rotational geometry, expanding all problem variables in a partial Fourier series, with respect to the longitudinal coordinate. The procedure leads to the fundamental system of dynamic equilibrium equations in terms of the reference surface kinematic harmonic components. Finally, a one-dimensional problem, by means of a set of five ordinary differential equations, in which the only spatial coordinate appearing is the one along meridians, is obtained. This can be conveniently solved using an appropriate G. D. Q. method in meridional direction, yielding accurate results with an extremely low computational cost and not using the so-called "delta-point" technique.

• Applied Chemistry for Engineering
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• v.32 no.4
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• pp.417-422
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• 2021

In this study, poly isocyanurate foam (PIR), poly urethane foam (PUR), and phenol foam (PF) of organic insulation materials were selected, and investigated using a cone calorimeter, as per ISO 5660-1. Standard materials (PMMA) were used to standardize the fire hazard assessment, and the fire risk was classified and evaluated by Chung's equations-III and IV. The fire performance index-II value of Chung's equations-II was the highest value with PF of 14.77 s²/kW. And the PUR was 0.08 s²/kW, the lowest value of fire performance index-II value. The fire growth index-II value was the lowest value with PF of 0.01 kW/s². And the PUR was 1.14 kW/s², the highest value of fire growth index-II value. The fire performance index-III (FPI-III) of Chung's equations-III had the lowest value for PUR (0.11) and the highest for PF (20.23). The PUR showed the highest value of the fire growth index-III (FGI-III) as 14.25, while the PF exhibited 0.13 regarded as the safest materials. The fire risk index-IV (FRI-IV) value of Chung's equation-IV was in the following order: PUR (130.03) >> PIR (19.13) > PMMA (1.00) > PF (0.01). Therefore, it was concluded that the fire risk associated with PF is the lowest, whereas that associated with PUR is the highest.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Transactions of the Korean Society of Mechanical Engineers
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• v.5 no.3
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• pp.217-222
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• 1981

The stress analysis of two-orthotropic layer, adhesively bonded structures is considered. An orthotropic plate has a through-crack of finite length and is adhesively bounded by a sound orthotropic plate. The problem is resuced to a pair of Fredholm integral equations ofthe second kind. Using a numerical integration scheme to evaluate the intgrals, The integral equations are reduced to a system of algebraic equations. By solving these equations some numerical results for stress intensity factors are presented for various crack lengths.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.3
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• pp.177-190
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• 2011

According to fractional calculus theory and Banach's fixed point theorem, we establish the sufficient conditions for the controllability of impulsive fractional evolution integrodifferential equations in Banach spaces. An example is provided to illustrate the theory.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.847-858
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• 2011

We make use of the simplified Hirota's bilinear method with computer symbolic computation to study a variety of coupled potential KdV (pKdV) equations. Each coupled equation is completely integrable and gives multiple soliton solutions and multiple singular soliton solutions. The phase shifts for all coupled pKdV equations are identical whereas the coefficients of the obtained solitons are not identical. The four coupled pKdV equations are resonance free.