On the Complexity of Computing the Logarithm and Square Root Functions on a Complex Domain

2005 ◽  
pp. 349-358 ◽  
Author(s):  
Ker-I Ko ◽  
Fuxiang Yu
Keyword(s):  
Complex Domain ◽  
Square Root ◽  
Root Functions

scholarly journals On the complexity of computing the logarithm and square root functions on a complex domain

2007 ◽  
Vol 23 (1) ◽  
pp. 2-24 ◽  
Author(s):  
Ker-I Ko ◽  
Fuxiang Yu
Keyword(s):  
Complex Domain ◽  
Square Root ◽  
Root Functions

scholarly journals A response analysis of wheat and barley to nitrogen in Finland

1993 ◽  
Vol 2 (6) ◽  
pp. 465-479
Author(s):  
John Sumelius
Keyword(s):  
Functional Form ◽  
Yield Response ◽  
Response Analysis ◽  
Square Root ◽  
Nitrogen Application ◽  
Producer Price ◽  
Root Functions ◽  
Price Increases ◽  
Profit Maximizing ◽  
Better Than

A nonlinear Mitscherlich function was found to be superior to quadratic and square root functions in estimating yield response to nitrogen based on a Finnish sample of barley. Nonnested hypothesis testing (J-test) indicated the Mitscherlich functional form to fit the data better than the quadratic form based on this sample. In the analysis of the crop response for spring wheat the Mitscherlich functional form could not be proved superior by a J-test. The inferred profit maximizing nitrogen fertilization levels based on the Mitscherlich functional form exceeded the quadratic polynomial forms and were lower than the inferred levels using square root specifications. Implementing 100% nitrogen price increases or 50% producer price reductions lowered the profit maximizing nitrogen application doses by 20-24%, according to the Mitscherlich specification.

scholarly journals Definite integrals involving product of logarithmic functions and logarithm of square root functions expressed in terms of special functions

2020 ◽  
Vol 5 (6) ◽  
pp. 5724-5733
Author(s):  
Robert Reynolds ◽  
◽  
Allan Stauffer
Keyword(s):  
Special Functions ◽  
Square Root ◽  
Definite Integrals ◽  
Root Functions ◽  
Logarithmic Functions

scholarly journals Composite Asymptotic Expansions and Difference Equations

2015 ◽  
Vol Volume 20 - 2015 - Special... ◽  
Author(s):  
Augustin Fruchard ◽  
Reinhard Schäfke
Keyword(s):  
Asymptotic Expansion ◽  
Small Parameter ◽  
Difference Equations ◽  
Asymptotic Expansions ◽  
Inverse Function ◽  
Complex Domain ◽  
Square Root ◽  
Step Size ◽  
International Audience

International audience Difference equations in the complex domain of the form y(x+ϵ)−y(x)=ϵf(y(x))/y(x) are considered. The step size ϵ>0 is a small parameter, and the equation has a singularity at y=0. Solutions near the singularity are described using composite asymptotic expansions. More precisely, it is shown that the derivative v′ of the inverse function v of a solution (the so-called Fatou coordinate) admits a Gevrey asymptotic expansion in powers of the square root of ϵ, denoted by η, involving functions of y and of Y=y/η. This also yields Gevrey asymptotic expansions of the so-called Écalle-Voronin invariants of the equation which are functions of epsilon. An application coming from the theory of complex iteration is presented. On considère des équations aux différences dans le plan complexe de la forme y(x+ϵ)−y(x)=ϵf(y(x))/y(x). Le pas de discrétisation ϵ>0 est un petit paramètre, et l'équation a une singularité en y=0. On décrit les solutions près de la singularité en utilisant des développements asymptotiques combinés. Plus précisément, on montre que la dérivée v′ de la fonction réciproque (appelée coordonnée de Fatou) v d'une solution admet un développement asymptotique Gevrey en puissances de la racine carrée de ϵ, notée η, et faisant intervenir des fonctions de y et de Y=y/η. On obtient également des développements asymptotiques Gevrey des invariants d'Écalle-Voronin de l'équation, qui sont des fonctions de ϵ. Une application venant de la théorie de l'itération complexe est présentée.

scholarly journals On the Evaluation of a Definite Integral Involving Nested Square Root Functions

2007 ◽  
Vol 37 (4) ◽  
pp. 1301-1304 ◽  
Author(s):  
M.A. Nyblom
Keyword(s):  
Definite Integral ◽  
Square Root ◽  
Root Functions

The determination and economic analysis of relationships between plant population and yield of main crop potatoes

1968 ◽  
Vol 70 (2) ◽  
pp. 123-129 ◽  
Author(s):  
P. R. Sharpe ◽  
J. B. Dent
Keyword(s):  
Seed Tuber ◽  
Square Root ◽  
Tuber Weight ◽  
Stem Number ◽  
Plant Populations ◽  
Functional Relationships ◽  
Root Functions ◽  
Main Crop ◽  
The Relationship ◽  
Seed Tuber Weight

SUMMARYTwo experiments designed to provide data for the estimation of functional relationships, which may be used to determine economically optimum plant populations and planting patterns in Desire'e potatoes, are described. Functional relationships between the number of main stems per acre and yield per acre were estimated from the results of experiment (i). Experiment (ii) investigated the relationship between stem number per tuber and seed tuber weight. ‘Square root’ functions estimated for seed yield and ware yield from the results of Exp. (i) were used to calculate a total Financial Returns curve. This returns curve, together with the Cobb-Douglas function estimated from the results of Exp. (ii), was used to calculate the stem numbers per acre, which would give maximum returns per acre and economically optimum returns in different cost/price situations.

VLSI module for high-performance multiply, square root and divide

1992 ◽  
Vol 139 (6) ◽  
pp. 505 ◽  
Author(s):  
S.E. McQuillan ◽  
J.V. McCanny
Keyword(s):  
High Performance ◽  
Square Root

Erratum: Realisation of irrational immitances containing a square root

1987 ◽  
Vol 134 (2) ◽  
pp. 94
Author(s):  
J.S. Visser
Keyword(s):  
Square Root
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