Bhabha first-order wave equations. VI. Exact, closed-form, Foldy-Wouthuysen transformations and solutions

1977 ◽  
Vol 15 (2) ◽  
pp. 433-444 ◽  
Author(s):  
R. A. Krajcik ◽  
Michael Martin Nieto
Keyword(s):  
Closed Form ◽  
Wave Equations ◽  
First Order

First-Order Acoustic Wave Equations and Scattering by Atmospheric Turbules.

1997 ◽  
Author(s):  
George H. Goedecke ◽  
Michael DeAntonio ◽  
Harry J. Auvermann
Keyword(s):  
Acoustic Wave ◽  
Wave Equations ◽  
First Order

scholarly journals Note on constructing a family of solvable sine-type difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ahmed El-Sayed Ahmed ◽  
Bratislav Iričanin ◽  
Witold Kosmala ◽  
Stevo Stević ◽  
Zdeněk Šmarda
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
First Order ◽  
Solvable In Closed Form

AbstractWe obtain a family of first order sine-type difference equations solvable in closed form in a constructive way, and we present a general solution to each of the equations.

scholarly journals Wave Equations and Symmetric First-order Systems in Case of Low Regularity

2013 ◽  
pp. 283-296
Author(s):  
Clemens Hanel ◽  
Günther Hörmann ◽  
Christian Spreitzer ◽  
Roland Steinbauer
Keyword(s):  
Wave Equations ◽  
Low Regularity ◽  
First Order

Jerk Limited Input Shapers

2004 ◽  
Vol 126 (1) ◽  
pp. 215-219 ◽  
Author(s):  
Tarunraj Singh
Keyword(s):  
Time Delay ◽  
Closed Form ◽  
Transfer Functions ◽  
Filter Design ◽  
Limited Time ◽  
Design Technique ◽  
Closed Form Solutions ◽  
First Order ◽  
Damped Systems

The focus of this paper is on the design of jerk limited input shapers (time-delay filters). Closed form solutions for the jerk limited time-delay filter for undamped systems is derived followed by the formulation of the problem for damped systems. Since the jerk limited filter involves concatenating an integrator to a time-delay filter, a general filter design technique is proposed where smoothing of the shaped input can be achieved by concatenating transfer functions of first order, harmonic systems, etc.

Staggered-Grid High-Order Differencemethod for the First-Order Elastic Wave Equations

2000 ◽  
Vol 43 (3) ◽  
pp. 441-449 ◽  
Author(s):  
Liang-Guo DONG ◽  
Zai-Tian MA ◽  
Jing-Zhong CAO
Keyword(s):  
Elastic Wave ◽  
Wave Equations ◽  
High Order ◽  
Staggered Grid ◽  
First Order ◽  
Elastic Wave Equations
Sign in / Sign up

Export Citation Format

Share Document