• Kyungpook Mathematical Journal
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• 제32권2호
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• pp.167-175
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• 1992

• East Asian mathematical journal
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• 제7권2호
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• pp.109-117
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• 1992

• Kyungpook Mathematical Journal
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• 제30권1호
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• pp.55-58
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• 1990

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권3호
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• pp.189-200
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• 2010

A numerical method is proposed and analyzed to approximate a mathematical model of age-dependent population dynamics with spatial diffusion. The model takes a form of nonlinear and nonlocal system of integro-differential equations. A finite difference method along the characteristic age-time direction is considered and primal mixed finite elements are used in the spatial variable. A priori error estimates are derived for the relevant variables.

• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.423-432
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• 2016

In this paper, we stochastically analyze the continuous time surplus process in a risk model which involves a continuous type investment. It is assumed that the investment of the surplus to other business is continuously made at a constant rate, while the surplus process stays over a given sufficient level. We obtain the stationary distribution of the surplus level and/or its moment generating function by forming martingales from the surplus process and applying the optional sampling theorem to the martingales and/or by establishing and solving an integro-differential equation for the distribution function of the surplus level.

• Journal of the Korean Data and Information Science Society
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• 제25권4호
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• pp.915-920
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• 2014

We consider a continuous time surplus process with investments the sizes of which are independent and identically distributed. It is assumed that an investment of the surplus to other business is made, if and only if the surplus reaches a given sufficient level. We establish an integro-differential equation for the distribution function of the surplus and solve the equation to obtain the moment generating function for the stationary distribution of the surplus. As a consequence, we obtain the first and second moments of the level of the surplus in an infinite horizon.

• 응용통계연구
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• 제25권5호
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• pp.813-820
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• 2012

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.

• Communications for Statistical Applications and Methods
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• 제20권6호
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• pp.475-480
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• 2013

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

• 제어로봇시스템학회논문지
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• 제16권1호
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• pp.18-24
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• 2010

In this paper, we address an active ranging system based on laser structured light image for mobile robot application. Since the burdensome correspondence problem is avoidable, the structured light image processing has efficient computation in comparison with the conventional stereo image processing. By using a cylindrical lens in the laser generation, it is possible to convert a point laser into a stripe laser without motorized scan in the proposed system. In order to achieve robustness against environmental illumination noise, we propose an efficient integro-differential image processing algorithm. The proposed system has embedded image processing module and transmits distance data to reduce the computational burden in main control system.