• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.439-448
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• 2023

We introduce several higher-order (p, q)-differential equation of which are related to (p, q)-Bernoulli polynomials. We also find some relations between (p, q)-Bernoulli, (p, q)-Euler, and (p, q)-Genocchi polynomials.

• Structural Engineering and Mechanics
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• v.7 no.2
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• pp.181-202
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• 1999

Dynamic response of axisymmetric arbitrary laminated composite cylindrical shell of finite length, using three-dimensional elasticity equations are studied. The shell is simply supported at both ends. The highly coupled partial differential equations are reduced to ordinary differential equations (ODE) with variable coefficients by means of trigonometric function expansion in axial direction. For cylindrical shell under dynamic load, the resulting differential equations are solved by Galerkin finite element method, In this solution, the continuity conditions between any two layer is satisfied. It is found that the difference between elasticity solution (ES) and higher order shear deformation theory (HSD) become higher for a symmetric laminations than their unsymmetric counterpart. That is due to the effect of bending-streching coupling. It is also found that due to the discontinuity of inplane stresses at the interface of the laminate, the slope of transverse normal and shear stresses aren't continuous across the interface. For free vibration analysis, through dividing each layer into thin laminas, the variable coefficients in ODE become constants and the resulting equations can be solved exactly. It is shown that the natural frequency of symmetric angle-ply are generally higher than their antisymmetric counterpart. Also the results are in good agreement with similar results found in literatures.

• International Journal of Highway Engineering
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• v.17 no.5
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• pp.1-10
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• 2015

PURPOSES : A finite difference model considering snow melting process on porous asphalt pavement was derived on the basis of heat transfer and mass transfer theories. The derived model can be applied to predict the region where black-ice develops, as well as to predict temperature profile of pavement systems where a de-icing system is installed. In addition, the model can be used to determined the minimum energy required to melt the ice formed on the pavement. METHODS : The snow on the porous asphalt pavement, whose porosity must be considered in thermal analysis, is divided into several layers such as dry snow layer, saturated snow layer, water+pavement surface, pavement surface, and sublayer. The mass balance and heat balance equations are derived to describe conductive, convective, radiative, and latent transfer of heat and mass in each layer. The finite differential method is used to implement the derived equations, boundary conditions, and the testing method to determine the thermal properties are suggested for each layer. RESULTS: The finite differential equations that describe the icing and deicing on pavements are derived, and we have presented them in our work. The framework to develop a temperature-forecasting model is successfully created. CONCLUSIONS : We conclude by successfully creating framework for the finite difference model based on the heat and mass transfer theories. To complete implementation, laboratory tests required to be performed.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1773-1778
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• 2006

Steady-state natural convection heat transfer characteristics from cylinders in a multiply-connected bounded region are clarified. A spectral finite difference scheme (spectral decomposition of the system of partial differential equations, semi-implicit time integration) is applied in numerical analysis, with a boundary-fitted conformal coordinate system through a Jacobian elliptic function with a successive transformation to formulate a system of governing equations in terms of a stream function, vorticity and temperature. Multiplicity of the domain is expressed explicitly.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.147-154
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• 2013

We analyze queueing model with priority scheduling by supplementary variable method. Customers are classified into two types (type-1 and type-2 ) according to their characteristics. Customers of each type arrive by independent Poisson processes, and all customers regardless of type have same general service time. The service order of each type is determined by the queue length of type-1 buffer. If the queue length of type-1 customer exceeds a threshold L, the service priority is given to the type-1 customer. Otherwise, the service priority is given to type-2 customer. Method of supplementary variable by remaining service time gives us information for queue length of two buffers. That is, we derive the differential difference equations for our queueing system. We obtain joint probability generating function for two queue lengths and the remaining service time. Also, the mean queue length of each buffer is derived.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• Journal of The Korean Society of Agricultural Engineers
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• v.58 no.1
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• pp.81-90
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• 2016

The Agricultural Systems Application Platform (ASAP) provides bottom-up modelling and simulation environment for agricultural engineer. The purpose of this study is to expand usability of the ASAP to the second order partial differential equations: elliptic equations, parabolic equations, and hyperbolic equations. The ASAP is a general-purpose simulation tool which express natural phenomenon with capsulized independent components to simplify implementation and maintenance. To use the ASAP in continuous problems, it is necessary to solve partial differential equations. This study shows usage of the ASAP in elliptic problem, parabolic problem, and hyperbolic problem, and solves of static heat problem, heat transfer problem, and wave problem as examples. The example problems are solved with the ASAP and Finite Difference method (FDM) for verification. The ASAP shows identical results to FDM. These applications are useful to simulate the engineering problem including equilibrium, diffusion and wave problem.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.1
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• pp.112-119
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• 2001

Design sensitivity is an important is an important device in improving a mechanical system design. A continuum design consists of the shape and orientation design. This research develops the shape and orientation design sensitivity method. The configura-tion design variables of multibody systems define the shape and orientation changes. The equations of motion are directly differentiated to obtain the governing equations for the design sensitivity. The governing equation of the design sensitivity is formulated as an over determined differential algebraic equation and treated as ordinary differential equations on mani-folds. The material derivative of a domain functional is performed to obtain the sensitivity due to shape and orientation changes. The configuration design sensitivities of a fly-ball governor system and a spatial four bar mechanism are obtained using the proposed method and are validated against those obtained from the finite difference method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.109-116
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• 1998

The method of vibration analysis used is the one developed by the senior author. He developed and reported, in 1974, a simple but exact method of calculating the natural frequency of beam and tower structures with irregular cross-sections and attached mass/masses. Since 1989, this method has been extended to two-dimensional problems with several types of given conditions and has been reported at several international conferences. This method uses the deflection influence surfaces. The finite difference method is used for this purpose, in this paper. In order to reduce the pivotal points required, the three simultaneous partial differential equations of equilibrium with three dependent variables, w, M$_{x}$, and $M_{y}$, are used instead of the one forth order partial differential equation. By neglecting the M$_{x}$ terms, the size of the matrices needed to solve the resulting linear equations are reduced to two thirds of the "non-modified" equations.tions.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.229-241
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• 2007

Multi-term fractional differential equations have been used to simulate fractional-order control system. It has been demonstrated the necessity of the such controllers for the more efficient control of fractional-order dynamical system. In this paper, the multi-term fractional ordinary differential equations are transferred into equivalent a system of equations. The existence and uniqueness of the new system are proved. A fractional order difference approximation is constructed by a decoupled technique and fractional-order numerical techniques. The consistence, convergence and stability of the numerical approximation are proved. Finally, some numerical results are presented to demonstrate that the numerical approximation is a computationally efficient method. The new method can be applied to solve the fractional-order control system.