Displaying similar documents to “Energy gaps for exponential Yang-Mills fields”

Schanuel Nullstellensatz for Zilber fields

Paola D'Aquino, Angus Macintyre, Giuseppina Terzo (2010)

Fundamenta Mathematicae

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We characterize the unsolvable exponential polynomials over the exponential fields introduced by Zilber, and deduce Picard's Little Theorem for such fields.

Fields of surreal numbers and exponentiation

Lou van den Dries, Philip Ehrlich (2001)

Fundamenta Mathematicae

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We show that Conway's field of surreal numbers with its natural exponential function has the same elementary properties as the exponential field of real numbers. We obtain ordinal bounds on the length of products, reciprocals, exponentials and logarithms of surreal numbers in terms of the lengths of their inputs. It follows that the set of surreal numbers of length less than a given ordinal is a subfield of the field of all surreal numbers if and only if this ordinal is an ε-number....

Real closed exponential fields

Paola D'Aquino, Julia F. Knight, Salma Kuhlmann, Karen Lange (2012)

Fundamenta Mathematicae

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Ressayre considered real closed exponential fields and “exponential” integer parts, i.e., integer parts that respect the exponential function. In 1993, he outlined a proof that every real closed exponential field has an exponential integer part. In the present paper, we give a detailed account of Ressayre’s construction and then analyze the complexity. Ressayre’s construction is canonical once we fix the real closed exponential field R, a residue field section k, and a well ordering...

The Deformed Trigonometric Functions of two Variables

Marinkovic, Sladjana, Stankovic, Miomir, Mulalic, Edin (2012)

Mathematica Balkanica New Series

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MSC 2010: 33B10, 33E20 Recently, various generalizations and deformations of the elementary functions were introduced. Since a lot of natural phenomena have both discrete and continual aspects, deformations which are able to express both of them are of particular interest. In this paper, we consider the trigonometry induced by one parameter deformation of the exponential function of two variables eh(x; y) = (1 + hx)y=h (h 2 R n f0g, x 2 C n f¡1=hg, y 2 R). In this manner,...