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Computers have long been used by scientists, engineers, and mathematicians for the solution of numerical problems requiring more calculations than can be reasonably performed ...
We develop a general method for analyzing the renormalization group equations (RGE's) to one-loop and two-loop order in grand unified theories (GUT's) which can have an ...
Nonlinear Programming   (Courseware and Class Materials)
This is an introductory graduate-student course in nonlinear programming. The focus is on theory and algorithmic methods for solving equations and for the related task of ...
When Close Enough Is Close Enough   (MathSource: Packages and Programs)
The following equation is taken from my brother's algebra workbook. Sqrt(5-2*Sqrt(6))=Sqrt(3)-Sqrt(2) He always challenges me to prove these equations like this by ...
Beam Statics Package   (MathSource: Packages and Programs)
The package BeamStatics.m calculates shear force, bending moment, slope, and deflection functions for a straight Euler--Bernoulli beam in static equilibrium. The program is ...
The natural frequencies of annular plates on a aperture of an infinite rigid wall and in contact with a fluid on one side are theoretically obtained by using the added mass ...
Phase diagrams involving solid solutions are calculated by solving sets of non-linear equations. In calculating P-T projections and compatibility diagrams, the equations used ...
Focusing on small size-parameter particles, this paper compares several easily-computable approximations to the Mie equations, including those by Rayleigh, Penndorf and ...
Many interesting solutions of the so-called Basler problem of evaluating the Riemann zeta function zeta(s) when s=2, which was of vital importance to Euler and the Bernoulli ...
A long-wavelength model of polar optical modes coupling the vibration amplitude mu (the relative displacement vector) and the electrostatic potential psi leads to a system of ...
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