COMPARING AND ZILBER’S EXPONENTIAL FIELDS: ZERO SETS OF EXPONENTIAL POLYNOMIALS

2014 ◽  
Vol 15 (1) ◽  
pp. 71-84 ◽  
Author(s):  
P. D’Aquino ◽  
A. Macintyre ◽  
G. Terzo
Keyword(s):  
Analytic Function ◽  
Function Theory ◽  
Research Programme ◽  
Exponential Functions ◽  
Exponential Polynomials ◽  
Zero Sets ◽  
Diophantine Geometry ◽  
Complex Exponential ◽  
Identity Theorem

We continue the research programme of comparing the complex exponential with Zilberś exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for $\mathbb{C}$ using analytic function theory, for example, the Identity Theorem.

scholarly journals New Trends on Analytic Function Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-1
Author(s):  
Serap Bulut ◽  
Stanislawa Kanas ◽  
Pranay Goswami
Keyword(s):  
Analytic Function ◽  
Function Theory

scholarly journals On the Relation between a Cluster set Introduced by Constantinescu and Cornea, and the Fine Cluster set of Cartan, Brelot, and Naïm

1965 ◽  
Vol 8 (1) ◽  
pp. 59-71
Author(s):  
H. L. Jackson
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Limit Theorems ◽  
Function Theory ◽  
Angular Limit ◽  
Boundary Limit ◽  
Cluster Set ◽  
Almost Everywhere ◽  
Bounded Holomorphic Function ◽  
Bounded Holomorphic

The field of boundary limit theorems in analytic function theory is usually considered to have begun about 1906, with the publication of Fatou's thesis [8]. In this remarkable memoir a theorem is proved, that now bears the author's name, which implies that any bounded holomorphic function defined on the unit disk possesses an angular limit almost everywhere (Lebesgue measure) on the frontier. Outstanding classical contributions to this field can be attributed to F. and M. Riesz, R. Nevanlinna, Lusin, Privaloff, Frostman, Plessner, and others.

Approximation of Lightning Current Waveforms Using Complex Exponential Functions

2016 ◽  
Vol 58 (5) ◽  
pp. 1686-1689 ◽  
Author(s):  
Mirko Yanque Tomasevich ◽  
Antonio C. S. Lima ◽  
Robson F. S. Dias
Keyword(s):  
Exponential Functions ◽  
Lightning Current ◽  
Complex Exponential

Solution of Plane Problems of Elasticity Utilizing Partitioning Concepts

1973 ◽  
Vol 40 (3) ◽  
pp. 767-772 ◽  
Author(s):  
O. L. Bowie ◽  
C. E. Freese ◽  
D. M. Neal
Keyword(s):  
Analytic Function ◽  
Power Series ◽  
Collocation Method ◽  
Stress Function ◽  
Function Theory ◽  
Series Expansions ◽  
Two Dimensional ◽  
Numerical Examples ◽  
Power Series Expansions

A partitioning plan combined with the modified mapping-collocation method is presented for the solution of awkward configurations in two-dimensional problems of elasticity. It is shown that continuation arguments taken from analytic function theory can be applied in the discrete to “stitch” several power series expansions of the stress function in appropriate subregions of the geometry. The effectiveness of such a plan is illustrated by several numerical examples.

The Rapid Tearing of a Half Plane

1985 ◽  
Vol 52 (1) ◽  
pp. 51-56
Author(s):  
J. P. Dempsey ◽  
E. B. Smith
Keyword(s):  
Stress Intensity ◽  
Analytic Function ◽  
Conformal Mapping ◽  
Crack Propagation ◽  
Function Theory ◽  
Elastic Half Space ◽  
Intensity Factors ◽  
Crack Propagation Velocity ◽  
Crack Bifurcation ◽  
Mechanical Disturbances

The surface of an elastic half space is subjected to sudden antiplane mechanical disturbances. Crack initiation and subsequent crack instability are examined via two idealized problems; the first is concerned with instantaneous crack bifurcation and the second with instantaneous skew crack propagation. In either problem, crack propagation occurs at a constant subsonic velocity under an angle κπ with the normal to the surface. For the externally applied disturbances that are considered here, and for contstant crack-tip velocities, the particle velocity and τθz are functions of r/t and θ only, which allows Chaplygin’s transformation and conformal mapping to be used. The problems can then be solved using analytic function theory. For various values of the angle of crack propagation, the dependence of the elastodynamic stress intensity factors on the crack propagation velocity is investigated. For certain specific geometries, fully analytical solutions are derived to provide check cases.

Mathematics of the 19th Century: Geometry/Analytic Function Theory

1999 ◽  
Vol 30 (2) ◽  
pp. 159
Author(s):  
John Ewing ◽  
A. N. Kolmogorov ◽  
A. P. Yushkevich ◽  
Roger Cooke
Keyword(s):  
Analytic Function ◽  
19Th Century ◽  
Function Theory ◽  
The 19Th Century
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