scholarly journals MOMENT METHOD TREATMENT OF CORRUGATIONS WITH FINS OVER RIDGES AND STRATIFIED COVERS USING DYADIC CAVITY AND MULTILAYER GREEN'S FUNCTIONS FOR STUDIES OF HIGHER-ORDER DIFFRACTION MODES

2020 ◽  
Vol 88 ◽  
pp. 1-18
Author(s):  
Malcolm Ng Mou Kehn
Keyword(s):  
Moment Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Higher Order ◽  
Order Diffraction

POSITIVITY OF GREEN'S FUNCTIONS TO VOLTERRA INTEGRAL AND HIGHER ORDER INTEGRO-DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 07 (04) ◽  
pp. 405-418 ◽  
Author(s):  
M. I. GIL'
Keyword(s):  
Differential Equations ◽  
Integral Equations ◽  
Green's Functions ◽  
Arbitrary Order ◽  
Green’S Functions ◽  
Higher Order ◽  
Volterra Integral Equations ◽  
Differential Delay

We consider Volterra integral equations and arbitrary order integro-differential equations. We establish positivity conditions and two-sided estimates for Green's functions. These results are then applied to obtain stability and positivity conditions for equations with nonlinear causal mappings (operators) and linear integro-differential parts. Such equations include differential, difference, differential-delay, integro-differential and other traditional equations.

MODIFIED HUBBARD DECOUPLING FOR THE EMERY MODEL

1995 ◽  
Vol 09 (25) ◽  
pp. 1635-1641
Author(s):  
LEW GEHLHOFF
Keyword(s):  
Single Particle ◽  
Green's Functions ◽  
Green’S Functions ◽  
Equation Of Motion ◽  
Higher Order ◽  
Exact Results ◽  
Emery Model ◽  
Spin Degeneracy ◽  
Motion Method ◽  
Large Spin

We consider a version of the Emery model with large spin degeneracy N and use the X-operator formulation and the equation-of-motion method to determine the single-particle Green’s functions. We propose a modified Hubbard decoupling technique for the higher-order Green’s functions appearing in this equation of motion. By applying it to the above model in the limit N→∞ we obtain the exact results.

Degeneracy, Derivative Rule, and Green’s Functions of Anisotropic Elasticity

2004 ◽  
Vol 71 (2) ◽  
pp. 273-282 ◽  
Author(s):  
Wan-Lee Yin
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Direct Proof ◽  
Anisotropic Elasticity ◽  
Higher Order ◽  
Zeroth Order ◽  
Isotropic Elasticity ◽  
Anisotropic Elastic ◽  
Analytical Expressions ◽  
Basic Elasticity

Degenerate and extra-degenerate anisotropic elastic materials have repeated material eigenvalues whose multiplicity is greater than the number of independent eigensolutions. Using basic elasticity relations, a simple, direct proof is given to show that higher-order eigensolutions may be obtained from the analytical expressions of the zeroth-order eigensolutions according to the derivative rule. These higher-order eigensolutions contribute to the complexity of the general solutions of degenerate and extra-degenerate materials, and to the analytical difficulties inherent in such cases including isotropic elasticity. For all types of anisotropic materials, the general solution is given specific forms to obtain Green’s functions of several domains with straight or elliptical boundaries. These results, presented in fully explicit expressions, extend Green’s functions of nondegenerate materials to degenerate and extra-degenerate cases that have not been explored previously.

Evaluation of a class of integrals occurring in mathematical physics via a higher order generalization of the principal value

1989 ◽  
Vol 67 (8) ◽  
pp. 759-765 ◽  
Author(s):  
K. T. R. Davies ◽  
R. W. Davies
Keyword(s):  
Single Particle ◽  
Numerical Evaluation ◽  
Green's Functions ◽  
Green’S Functions ◽  
Simple Algorithm ◽  
Mathematical Physics ◽  
Higher Order ◽  
Divergent Integral ◽  
Principal Value

The notion of the principal value of an integral is generalized to treat higher order singularities. The principal value of an integral can be considered the "convergent part" of a divergent integral, an interpretation that is almost trivial for simple poles, but more meaningful for higher order poles. Application of this concept leads to a simple algorithm that may be applied to the evaluation of a class of integrals arising in mathematical physics. Many of these integrals frequently occur in the analytic and numerical evaluation of folding functions arising from the product of single-particle Green's functions.

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