On Dependence of Lipschitzian Solutions of Nonlinear Functional Inequality on an Arbitrary Function

2000 ◽  
pp. 65-75
Author(s):  
Marek Czerni
Keyword(s):  
Arbitrary Function ◽  
Functional Inequality ◽  
Nonlinear Functional ◽  
Lipschitzian Solutions

Testing Pulse Timing Devices Using Arbitrary Function Generators

2020 ◽  
Vol 54 (5) ◽  
pp. 466-473
Author(s):  
V. A. Bespal’ko ◽  
I. Burak ◽  
A. S. Rybakov
Keyword(s):  
Arbitrary Function ◽  
Pulse Timing ◽  
Function Generators

scholarly journals Reducing a Class of Two-Dimensional Integrals to One-Dimension with an Application to Gaussian Transforms

Atoms ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 53
Author(s):  
Jack C. Straton
Keyword(s):  
Quantum Theory ◽  
Arbitrary Function ◽  
Plane Waves ◽  
Wave Functions ◽  
One Dimension ◽  
Two Dimensional ◽  
Transition Amplitudes ◽  
Multidimensional Integrals ◽  
Coulomb Potentials

Quantum theory is awash in multidimensional integrals that contain exponentials in the integration variables, their inverses, and inverse polynomials of those variables. The present paper introduces a means to reduce pairs of such integrals to one dimension when the integrand contains powers multiplied by an arbitrary function of xy/(x+y) multiplying various combinations of exponentials. In some cases these exponentials arise directly from transition-amplitudes involving products of plane waves, hydrogenic wave functions, and Yukawa and/or Coulomb potentials. In other cases these exponentials arise from Gaussian transforms of such functions.

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