• Structural Engineering and Mechanics
• /
• 제4권3호
• /
• pp.227-242
• /
• 1996

An important class of problems in the field of geotechnical engineering may be analyzed with the aid of a simple integro-differential equation. Behavior of "rigid" piles(say concrete piles), "deformable" piles(say gravel piles), pile groups, pile-raft foundations, heavily reinforced earth, flow within circular silos and down drag on cylindrical structures (for example the crusher unit of a mineral processing complex) are the type of situations that can be handled by this type of equation. The equation under consideration has the form; $$\frac{{\partial}w(r,\;z)}{{\partial}z}+f(z){\int}^z_0g({\xi})(\frac{{\partial}^2w(r,\;{\xi})}{{\partial}r^2}+\frac{1}{r}\frac{{\partial}w(r,\;{\xi})}{{\partial}r})d{\xi}+h(r,\;z)=0$$ where w(r, z) is the vertical displacement of a soil particle expressed as a function of the polar cylindrical space coordinates (r, z) and the symbols f, g and h represent soil properties and the loading conditions. The merit of the analysis is its simplicity (both in concept and in application) and the ease with which it can be expressed in a computer code. In the present paper the analysis is applied to investigate the behavior of a single rigid pile to bedrock. The emphasis, however, is placed on developing the equation, the numerical techique used in its evaluation and validation of the technique, hereafter called the ID technique, against a formal program, CRISP, which uses the FEM.

• 응용통계연구
• /
• 제25권1호
• /
• pp.81-87
• /
• 2012

재충전이 있는 연속시간 리스크 모형이 고려된다. 프레미엄은 일정한 율로 들어오고, 보험금 청구는 복합 포아송 과정을 따라 이루어진다. 초기 잉여금 u > 0로 시작하여 잉여금은 프레미엄에 의해 증가하고 보험금 청구에 의해 감소한다. 잉여금의 수준이 ${\tau}$(0 < ${\tau}$ < u)아래로 떨어지면 초기 잉여금 수준까지 재충전이 이루어진다고 가정한다. 재충전이 고려된 리스크 모형에서 잉여금이 없어지는 파산확률을 적미분 방정식을 통해 유도하고, 보험 청구액이 독립적으로 지수분포를 따르는 경우는 파산확률의 명확한 공식이 유도됨을 보인다.

• Advances in aircraft and spacecraft science
• /
• 제7권3호
• /
• pp.215-228
• /
• 2020

As is shown in the paper, the Koltunov-Rzhanitsyn singular kernel of heredity (when constructing mathematical models of the dynamics problem of the hereditary theory of viscoelasticity) adequately describes real mechanical processes, best approximates experimental data for a long period of time. A mathematical model of the problem of the flutter of viscoelastic plates moving in a gas with a high supersonic velocity is given. Using the Bubnov-Galerkin method, discrete models of the problem of the flatter of viscoelastic plates flowed over by supersonic gas flow are obtained. A numerical method is developed to solve nonlinear integro-differential equations (IDE) for the problem of the hereditary theory of viscoelasticity with weakly singular kernels. A general computational algorithm and a system of application programs have been developed, which allow one to investigate the nonlinear dynamic problems of the hereditary theory of viscoelasticity with weakly singular kernels. On the basis of the proposed numerical method and algorithm, nonlinear problems of the flutter of viscoelastic plates flowed over in a gas flow at an arbitrary angle are investigated. In a wide range of changes in various parameters of the plate, the critical velocity of the flutter is determined. It is shown that the singularity parameter α affects not only the oscillations of viscoelastic systems, but the critical velocity of the flutter as well.

• 대한산업공학회지
• /
• 제38권4호
• /
• pp.249-253
• /
• 2012

This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

• 대한수학회지
• /
• 제55권5호
• /
• pp.1269-1283
• /
• 2018

We are concerned with elliptic equations in ${\mathbb{R}}^N$, driven by a non-local integro-differential operator, which involves the fractional Laplacian. The main aim of this paper is to prove the existence of small solutions for our problem with negative energy in the sense that the sequence of solutions converges to 0 in the $L^{\infty}$-norm by employing the regularity type result on the $L^{\infty}$-boundedness of solutions and the modified functional method.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 1993년도 춘계학술대회 논문집
• /
• pp.175-180
• /
• 1993

The nonlinear integro-differential equations of motion of a two-link structurally flexible planar manipulator executing contact tasks are presented. The equations of motion are derived using the extended Hamilton's principle and the Galerkin criterion. Also, Models for the wrist-force sensor and impact that occurs when the manipulator's end point makes contact withthe environment are presented. The dynamic models presented can be used to studythe dynamics of the system and to design controllers.

• 대한수학회보
• /
• 제35권2호
• /
• pp.269-278
• /
• 1998

Let ($G,\;{\upsilon}$) be a bounded smooth domain and reflection vector field on $\partial$G, which points uniformly into G. Under the condition that locally for some coordinate system, ${\mid}{\upsilon^i}{\mid}\;i\;=\;1,{\cdot},{\cdot}$,d - 1, where is constant depending on the Lipschitz constant of G, we have tightness for reflected diffusion with jump on G with reflection $\upsilon$ depending only on c. From this, we obtain some properties of L-harmonic function where L is a sum of Laplacian and integro one.

• 대한수학회지
• /
• 제43권2호
• /
• pp.383-398
• /
• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• Journal of the Korean Data and Information Science Society
• /
• 제23권6호
• /
• pp.1289-1297
• /
• 2012

We consider a general compound Poisson risk model in which the premium rate is surplus dependent. We analyze the joint distribution of the surplus immediately before ruin, the deffcit at ruin and the time of ruin by solving the integro-differential equation for the Gerber-Shiu discounted penalty function.

• Journal of applied mathematics & informatics
• /
• 제30권1_2호
• /
• pp.57-69
• /
• 2012

In this paper, we prove the existence of mild solutions for a first order impulsive neutral differential inclusion with state dependent delay. We assume that the state-dependent delay part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multi-valued maps, a main existence theorem is established.