On a Theorem of Gausz Concerning the Number of Integral Solutions of the Equation x2 + y2 + z2 = m

2020 ◽  
pp. 31-38
Author(s):  
Hans Peter Rehm
Keyword(s):  
Integral Solutions

Path-integral solutions of wave equations with dissipation

1989 ◽  
Vol 62 (19) ◽  
pp. 2201-2204 ◽  
Author(s):  
Cecile DeWitt-Morette ◽  
See Kit Foong
Keyword(s):  
Path Integral ◽  
Wave Equations ◽  
Solutions Of Wave Equations ◽  
Integral Solutions

scholarly journals Comment on “Exact integral solutions for two-phase flow” by David B. McWhorter and Daniel K. Sunada

1992 ◽  
Vol 28 (5) ◽  
pp. 1477-1478 ◽  
Author(s):  
Z.-X. Chen ◽  
G. S. Bodvarsson ◽  
P. A. Witherspoon
Keyword(s):  
Two Phase Flow ◽  
Phase Flow ◽  
Two Phase ◽  
Integral Solutions

Parametric Deflection Approximations for End-Loaded, Large-Deflection Beams in Compliant Mechanisms

1995 ◽  
Vol 117 (1) ◽  
pp. 156-165 ◽  
Author(s):  
L. L. Howell ◽  
A. Midha
Keyword(s):  
Closed Form ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Compliant Mechanisms ◽  
Elliptic Integral ◽  
Cantilever Beams ◽  
Simple Method ◽  
Body Angle ◽  
Analysis And Design ◽  
Integral Solutions

Geometric nonlinearities often complicate the analysis of systems containing large-deflection members. The time and resources required to develop closed-form or numerical solutions have inspired the development of a simple method of approximating the deflection path of end-loaded, large-deflection cantilever beams. The path coordinates are parameterized in a single parameter called the pseudo-rigid-body angle. The approximations are accurate to within 0.5 percent of the closed-form elliptic integral solutions. A physical model is associated with the method, and may be used to simplify complex problems. The method proves to be particularly useful in the analysis and design of compliant mechanisms.

Integral solutions of Maxwell’s equations

2018 ◽  
pp. 415-437
Author(s):  
Edward J. Rothwell ◽  
Michael J. Cloud
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Integral Solutions

SIMILARITY AND FIRST-INTEGRAL SOLUTIONS FOR AIR AND WATER DIFFUSION IN SOILS AND COMPARISON WITH OPTIMAL RESULTS

Soil Science ◽  
1984 ◽  
Vol 138 (5) ◽  
pp. 321-325 ◽  
Author(s):  
G. C. SANDER ◽  
J. -Y. PARLANGE ◽  
W. L. HOGARTH ◽  
R. D. BRADDOCK
Keyword(s):  
First Integral ◽  
Water Diffusion ◽  
Integral Solutions

scholarly journals On generation and propagation of tsunamis in a shallow running ocean

1978 ◽  
Vol 1 (3) ◽  
pp. 373-390
Author(s):  
Lokenath Debnath ◽  
Uma Basu
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Relative Magnitude ◽  
Ocean Floor ◽  
Surface Elevation ◽  
Free Surface Elevation ◽  
Surface Disturbance ◽  
Fourier And Laplace Transforms ◽  
The Given ◽  
Integral Solutions

A theory is presented of the generation and propagation of the two and the three dimensional tsunamis in a shallow running ocean due to the action of an arbitrary ocean floor or ocean surface disturbance. Integral solutions for both two and three dimensional problems are obtained by using the generalized Fourier and Laplace transforms. An asymptotic analysis is carried out for the investigation of the principal features of the free surface elevation. It is found that the propagation of the tsunamis depends on the relative magnitude of the given speed of the running ocean and the wave speed of the shallow ocean. When the speed of the running ocean is less than the speed of the shallow ocean wave, both the two and the three dimensional free surface elevation represent the generation and propagation of surface waves which decay asymptotically ast−12for the two dimensional case and ast−1for the three dimensional tsunamis. Several important features of the solution are discussed in some detail. As an application of the general theory, some physically realistic ocean floor disturbances are included in this paper.

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