• Korean Journal of Mathematics
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• 제6권2호
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• pp.259-279
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• 1998

For the forward-backward semimartingale, we can define the backward semimartingale flow which is generated by the backward canonical stochastic differential equation. Therefore, we define the backward self-similar stochastic processes, and we study the backward self-similar stochastic flows through the canonical stochastic differential equations.

• Journal of the Korean Statistical Society
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• 제33권3호
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• pp.299-302
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• 2004

A Markovian approach is introduced to find the Laplace transform of the forward recurrence time in the renewal process at finite time t > 0. Until now, most works on the forward recurrence time have been done through renewal arguments.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.65-77
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• 2013

In this paper, we develop the operational Tau method for solving nonlinear Volterra integro-differential equations of the second kind. The existence and uniqueness of the problem is provided. Here, we show that the nonlinear system resulted from the operational Tau method has a semi triangular form, so it can be solved easily by the forward substitution method. Finally, the accuracy of the method is verified by presenting some numerical computations.

• International Journal of Aeronautical and Space Sciences
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• 제18권4호
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.215-229
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• 2005

In this paper, constraint aggregation is combined with the adjoint and multiple shooting strategies for optimal control of differential algebraic equations (DAE) systems. The approach retains the inherent parallelism of the conventional multiple shooting method, while also being much more efficient for large scale problems. Constraint aggregation is employed to reduce the number of nonlinear continuity constraints in each multiple shooting interval, and its derivatives are computed by the adjoint DAE solver DASPKADJOINT together with ADIFOR and TAMC, the automatic differentiation software for forward and reverse mode, respectively. Numerical experiments demonstrate the effectiveness of the approach.

• Nuclear Engineering and Technology
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• 제43권6호
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• pp.523-530
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• 2011

In a previous study, the stochastic space-dependent kinetics model (SSKM) based on the forward stochastic model in stochastic kinetics theory and the Ito stochastic differential equations was proposed for treating monoenergetic space-time nuclear reactor kinetics in one dimension. The SSKM was tested against analog Monte Carlo calculations, however, for exemplary cases of homogeneous slab reactors with only one delayed-neutron precursor group. In this paper, the SSKM is improved and evaluated with more realistic and complicated cases regarding several delayed-neutron precursor groups and heterogeneous slab reactors in which the extraneous source or reactivity can be introduced locally. Furthermore, the source level and the initial conditions will also be adjusted to investigate the trends in the variances of the neutron population and fission product levels across the reactor. The results indicate that the improved SSKM is in good agreement with the Monte Carlo method and show how the variances in population dynamics can be controlled.

• 품질경영학회지
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• 제11권2호
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• pp.2-9
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• 1983

As will be seen, this paper is tries that the research on the mathematical structure of Markov process and Markovian sequential decision process (the policy improvement iteration method,) moreover, that it analyze the logic and the characteristic of behavior of mathematical model of Markov process. Therefore firstly, it classify, on research of mathematical structure of Markov process, the forward equation and backward equation of Chapman-kolmogorov equation and of kolmogorov differential equation, and then have survey on logic of equation systems or on the question of uniqueness and existence of solution of the equation. Secondly, it classify, at the Markovian sequential decision process, the case of discrete time parameter and the continuous time parameter, and then it explore the logic system of characteristic of the behavior, the value determination operation and the policy improvement routine.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.863-875
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• 2010

In this paper we apply the martingale approach, which has been widely used in mathematical finance, to investigate the optimal investment problem for an insurer under the criterion of mean-variance. When the risk and security assets are described by the L$\acute{e}$vy processes, the closed form solutions to the maximization problem are obtained. The mean-variance efficient strategies and frontier are also given.

• International Journal of Naval Architecture and Ocean Engineering
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• 제1권2호
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• pp.89-94
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• 2009

The current focus of development in industrial Computational Fluid Dynamics (CFD) is integration of CFD into Computer-Aided product development, geometrical optimisation, robust design and similar. On the other hand, in CFD research aims to extend the boundaries of practical engineering use in "non-traditional" areas. Requirements of computational flexibility and code integration are contradictory: a change of coding paradigm, with object orientation, library components, equation mimicking is proposed as a way forward. This paper describes OpenFOAM, a C++ object oriented library for Computational Continuum Mechanics (CCM) developed by the author. Efficient and flexible implementation of complex physical models is achieved by mimicking the form of partial differential equation in software, with code functionality provided in library form. Open Source deployment and development model allows the user to achieve desired versatility in physical modeling without the sacrifice of complex geometry support and execution efficiency.