eye

Title

Date Archived

Creator

Arxiv.org

Jul 20, 2013
by
Maria Rosaria Enea; Donato Saeli

texts

#
eye 245

# favorite 0

# comment 0

There are many ways to construct the field R of real numbers. The most important and famous of these employ Cauchy sequences (Cantor) or cuts (Dedekind) in the field Q of rational numbers. These constructions sometimes overlook important details and often are complicated and cumbersome. In this note, the authors propose an essential, clear and rigorous construction of R from the stucture Q+ of positive rational numbers by the key notion of initial segment.

Source: http://arxiv.org/abs/1203.1283v1

Source: http://arxiv.org/abs/1203.1283v1

Arxiv.org

Jul 20, 2013
by
Alexey Radul; Barak A. Pearlmutter; Jeffrey Mark Siskind

texts

#
eye 92

# favorite 0

# comment 0

We describe an implementation of the Farfel Fortran AD extensions. These extensions integrate forward and reverse AD directly into the programming model, with attendant benefits to flexibility, modularity, and ease of use. The implementation we describe is a "prepreprocessor" that generates input to existing Fortran-based AD tools. In essence, blocks of code which are targeted for AD by Farfel constructs are put into subprograms which capture their lexical variable context, and these...

Source: http://arxiv.org/abs/1203.1450v2

Source: http://arxiv.org/abs/1203.1450v2

Arxiv.org

Jul 20, 2013
by
Donato Saeli; Maurizio Spano

texts

#
eye 102

# favorite 0

# comment 0

Goldbach's comet is the plot of the Goldbach function g(n), in the interval [3, N], with a large positive integer N. The function g(n) counts the number of different ways in which 2n can be expressed as the sum of two odd primes. An account, hopefully satisfying and accessible, is given for the layers that make up the comet. By means of several (sometimes historical) results of Theory of Number, other conjectures, similar to the Goldbach's one, emerge. These are related with sequences of odd...

Source: http://arxiv.org/abs/1203.1282v1

Source: http://arxiv.org/abs/1203.1282v1

Fetching more results

# Posts by Jeff Kaplan

**View more forum posts**