Determination of the Eigenfunctions of a Homogeneous Integral Equation with Non-symmetric Kernel

1975 ◽  
Vol 22 (9) ◽  
pp. 761-766 ◽  
Author(s):  
A. Hardy ◽  
F. Pasqualetti ◽  
L. Ronchi
Keyword(s):  
Integral Equation ◽  
Symmetric Kernel ◽  
Homogeneous Integral Equation

On the limiting behaviour of a basic stochastic process

1972 ◽  
Vol 9 (1) ◽  
pp. 202-207
Author(s):  
İzzet Şahin ◽  
Oussama Achou
Keyword(s):  
Stochastic Process ◽  
Integral Equation ◽  
Stochastic Processes ◽  
Integral Equations ◽  
Mixed Type ◽  
Limiting Distributions ◽  
State Dependent ◽  
Limiting Behaviour ◽  
Rate Of Decline

Determination of the limiting distributions for a class of mixed-type stochastic processes with state-dependent rates of decline is reduced to the solution of a class of integral equations. For the case where the rate of decline is proportional to the state, some results are obtained by solving the integral equation of the process through Fuchs' method.

Approximation of the Strain Field Associated With an Inhomogeneous Precipitate—Part 1: Theory

1980 ◽  
Vol 47 (4) ◽  
pp. 775-780 ◽  
Author(s):  
W. C. Johnson ◽  
Y. Y. Earmme ◽  
J. K. Lee
Keyword(s):  
Integral Equation ◽  
Strain Field ◽  
Equivalent Stress ◽  
Taylor Series Expansion ◽  
Transformation Strain ◽  
Coherent Precipitate ◽  
Precipitate Shape ◽  
Polynomial Series ◽  
Elastic Strain Field

Two independent methods are derived for the calculation of the elastic strain field associated with a coherent precipitate of arbitrary morphology that has undergone a stress-free transformation strain. Both methods are formulated in their entirety for an isotropic system. The first method is predicated upon the derivation of an integral equation from consideration of the equations of equilibrium. A Taylor series expansion about the origin is employed in solution of the integral equation. However, an inherently more accurate means is also developed based upon a Taylor expansion about the point of which the strain is to be calculated. Employing the technique of Moschovidis and Mura, the second method extends Eshelby’s equivalency condition to the more general precipitate shape where the constrained strain is now a function of position within the precipitate. An approximate solution to the resultant system of equations is obtained through representation of the equivalent stress-free transformation strain by a polynomial series. For a given order of approximation, both methods reduce to the determination of the biharmonic potential functions and their derivatives.

On the harmonic oscillations of a rigid body on a free surface

1965 ◽  
Vol 21 (3) ◽  
pp. 427-451 ◽  
Author(s):  
W. D. Kim
Keyword(s):  
Integral Equation ◽  
Free Surface ◽  
Rigid Body ◽  
Potential Problem ◽  
Harmonic Oscillation ◽  
Added Mass ◽  
The Body ◽  
Rigorous Solution ◽  
Damping Coefficients

The present paper deals with the practical and rigorous solution of the potential problem associated with the harmonic oscillation of a rigid body on a free surface. The body is assumed to have the form of either an elliptical cylinder or an ellipsoid. The use of Green's function reduces the determination of the potential to the solution of an integral equation. The integral equation is solved numerically and the dependency of the hydrodynamic quantities such as added mass, added moment of inertia and damping coefficients of the rigid body on the frequency of the oscillation is established.

Sign in / Sign up

Export Citation Format

Share Document