A comparison of gradient dependent techniques for the minimization of an unconstrained function of several variables

AIAA Journal ◽  
1970 ◽  
Vol 8 (12) ◽  
pp. 2226-2229 ◽  
Author(s):  
TERRY A. STRAETER ◽  
JOHN E. HOGGE
Keyword(s):  
Several Variables ◽  
Function Of Several Variables

On The Factorization of Partial Differential Equations

1987 ◽  
Vol 39 (4) ◽  
pp. 825-834 ◽  
Author(s):  
W. Dale Brownawell
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Nevanlinna Theory ◽  
Algebraic Differential Equation ◽  
List Type ◽  
Variable Result ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Degenerate Cases

In [4] N. Steinmetz used Nevanlinna theory to establish remarkably versatile theorems on the factorization of ordinary differential equations which implied numerous previous results of various authors. (Here factorization is taken in the sense of function composition as introduced by F. Gross in [2].) The thrust of Steinmetz’ central results on factorization is that if g(z) is entire and f(z) is meromorphic in C such that the composite fog satisfies an algebraic differential equation, then so do f(z) and, degenerate cases aside, g(z). In addition, the more one knows about the equation for fog (e.g. degree, weight, autonomy), the more one can conclude about the equations for f and g.In this note we generalize Steinmetz’ work to show the following:a) Steinmetz’ two basic results, Satz 1 and Korollar 1 of [4] can be seen as one-variable specializations of a single two variable result, andb) the function g(z) can itself be allowed to be a function of several variables.

Reactions of Thiyl Radicals. VII. Photolysis of Methyl Sulfide Vapor

1972 ◽  
Vol 50 (6) ◽  
pp. 844-852 ◽  
Author(s):  
P. M. Rao ◽  
A. R. Knight
Keyword(s):  
Wavelength Range ◽  
Sulfur Hexafluoride ◽  
Quantum Yields ◽  
Primary Process ◽  
Methyl Radicals ◽  
Methyl Sulfide ◽  
Thiyl Radicals ◽  
Several Variables ◽  
Bond Scission ◽  
Function Of Several Variables

The photolysis of methyl sulfide vapor has been investigated as a function of substrate pressure, exposure time, and temperature in the wavelength range 2000 to 2300 Å. The effects of added propane, sulfur hexafluoride, and 2-methylpentane have been studied. The principal products of the decomposition are CH4, C2H6, CH3SSCH3, and CH3SH. The data indicate direct C—S bond scission in the primary process giving rise to "hot" CH3 and CH3S radicals. A mechanism in which disproportionation of methylthiyl radicals is a very minor process is proposed.The reactions of CH3 and CH3S radicals with methyl sulfide have been examined also by photolyzing CH3SSCH3 and CH3COCH3 in the presence of CH3SCH3. Quantum yields at 2288 Å have been determined as a function of several variables. A number of rate parameters for the reactions of methyl radicals and methylthiyl radicals have been calculated.

scholarly journals Some precisions on the Fourier-Borel transform and infinite order differential equations

1973 ◽  
Vol 14 (2) ◽  
pp. 161-167 ◽  
Author(s):  
Lawrence Gruman
Keyword(s):  
Entire Function ◽  
Differential Equations ◽  
Infinite Order ◽  
Borel Transform ◽  
Several Variables ◽  
Function Of Several Variables ◽  
Image Position

Let f(z) be an entire function (of several variables). We define the functionwhich is increasing. The orderof f(z) is the constant (perhaps infinite)

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