On numerical evaluation of double integrals of an analytic function of two complex variables

1986 ◽  
Vol 26 (4) ◽  
pp. 521-526 ◽  
Author(s):  
G. V. Milovanović ◽  
B. P. Acharya ◽  
T. N. Pattnaik
Keyword(s):  
Analytic Function ◽  
Numerical Evaluation ◽  
Complex Variables ◽  
Double Integrals

Approximation of double integrals of analytic functions of two complex variables

Computing ◽  
1986 ◽  
Vol 37 (4) ◽  
pp. 357-364 ◽  
Author(s):  
B. P. Acharya ◽  
T. Mohapatra
Keyword(s):  
Analytic Functions ◽  
Complex Variables ◽  
Double Integrals

Linear forms in algebraic points of Abelian functions. II

1976 ◽  
Vol 79 (1) ◽  
pp. 55-70 ◽  
Author(s):  
D. W. Masser
Keyword(s):  
Analytic Function ◽  
Maximum Modulus ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Maximum Modulus Principle ◽  
Linear Forms ◽  
Extrapolation Procedure ◽  
Abelian Functions

In this paper we continue to develop the apparatus needed for the proof of the theorem announced in (11). We retain the notation of (11) together with the assumptions made there about the field of Abelian functions. This section deals with properties of more general functions holomorphic on Cn. When n = 1 the extrapolation procedure in problems of transcendence is essentially the maximum modulus principle together with the act of dividing out zeros of an analytic function. For n > 1, however, this approach is not possible, and some mild theory of several complex variables is required. This was first used in the context of transcendence by Bombieri and Lang in (2) and (12), and we now give a brief account of the basic constructions of their papers.

Improvement of Punch Profiles for Elastic Circular Contacts

2006 ◽  
Vol 128 (3) ◽  
pp. 486-492 ◽  
Author(s):  
Marilena Glovnea ◽  
Emanuel Diaconescu
Keyword(s):  
Carrying Capacity ◽  
Numerical Evaluation ◽  
Pressure Profile ◽  
Electrical Contacts ◽  
Machine Design ◽  
Load Carrying Capacity ◽  
Uniform Pressure ◽  
Pressure Distributions ◽  
Load Carrying ◽  
Double Integrals

Machine design and electrical contacts involve frequently elastic circular contacts subjected to normal loads. Depending on geometry, these may be Hertzian or surface contacts. Both possess highly nonuniform pressure distributions which diminish contact load carrying capacity. The achievement of a uniform pressure distribution would be ideal to improve the situation, but this violates stress continuity. Instead, the generation of a uniform pressure over most of contact area can be sought. Generally, equivalent punch profile which generates this pressure is found by numerical evaluation of double integrals. This paper simplifies the derivation of punch profile by using an existing correspondence between a polynomial punch surface and elastically generated pressure. First, an improved pressure profile is proposed seeking to avoid high Huber-Mises-Hencky stresses near contact surface. Then, this is approximated by the product between typical Hertz square root and an even polynomial, which yields directly the punch profile. Formulas for normal approach and central pressure are derived.

scholarly journals ESTIMATES FOR MAHLER’S MEASURE OF A LINEAR FORM

2004 ◽  
Vol 47 (2) ◽  
pp. 473-494 ◽  
Author(s):  
Fernando Rodriguez-Villegas ◽  
Ricardo Toledano ◽  
Jeffrey D. Vaaler
Keyword(s):  
Linear Form ◽  
Numerical Evaluation ◽  
Complex Variables ◽  
Mahler Measure ◽  
Subject Classification ◽  
Primary 11C08

AbstractLet $L_{\bm{a}}(\bm{z})=a_1z_1+a_2z_2+\cdots+a_Nz_N$ be a linear form in $N$ complex variables $z_1,z_2,\dots,z_N$ with non-zero coefficients. We establish several estimates for the logarithmic Mahler measure of $L_{\bm{a}}$. In general, we show that the logarithmic Mahler measure of $L_{\bm{a}}(\bm{z})$ and the logarithm of the norm of $\bm{a}$ differ by a bounded amount that is independent of $N$. We prove a further estimate which is useful for making an approximate numerical evaluation of the logarithmic Mahler measure.AMS 2000 Mathematics subject classification: Primary 11C08; 11Y35; 26D15

Sign in / Sign up

Export Citation Format

Share Document