4,785 research outputs found
A Universal Machine for Biform Theory Graphs
Broadly speaking, there are two kinds of semantics-aware assistant systems
for mathematics: proof assistants express the semantic in logic and emphasize
deduction, and computer algebra systems express the semantics in programming
languages and emphasize computation. Combining the complementary strengths of
both approaches while mending their complementary weaknesses has been an
important goal of the mechanized mathematics community for some time. We pick
up on the idea of biform theories and interpret it in the MMTt/OMDoc framework
which introduced the foundations-as-theories approach, and can thus represent
both logics and programming languages as theories. This yields a formal,
modular framework of biform theory graphs which mixes specifications and
implementations sharing the module system and typing information. We present
automated knowledge management work flows that interface to existing
specification/programming tools and enable an OpenMath Machine, that
operationalizes biform theories, evaluating expressions by exhaustively
applying the implementations of the respective operators. We evaluate the new
biform framework by adding implementations to the OpenMath standard content
dictionaries.Comment: Conferences on Intelligent Computer Mathematics, CICM 2013 The final
publication is available at http://link.springer.com
A Factorization Algorithm for G-Algebras and Applications
It has been recently discovered by Bell, Heinle and Levandovskyy that a large
class of algebras, including the ubiquitous -algebras, are finite
factorization domains (FFD for short).
Utilizing this result, we contribute an algorithm to find all distinct
factorizations of a given element , where is
any -algebra, with minor assumptions on the underlying field.
Moreover, the property of being an FFD, in combination with the factorization
algorithm, enables us to propose an analogous description of the factorized
Gr\"obner basis algorithm for -algebras. This algorithm is useful for
various applications, e.g. in analysis of solution spaces of systems of linear
partial functional equations with polynomial coefficients, coming from
. Additionally, it is possible to include inequality constraints
for ideals in the input
The Early Days of Research on Carbonic Anhydrase
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73862/1/j.1749-6632.1984.tb12310.x.pd
NMR experiment factors numbers with Gauss sums
We factor the number 157573 using an NMR implementation of Gauss sums.Comment: 4 pages 5 figure
K-Sign in retrocaecal appendicitis: a case series
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Variations in position of the vermiform appendix considerably changes clinical findings. Retrocaecal appendicitis presents with slightly different clinical features from those of classical appendicitis associated with a normally sited appendix. K-sign looks for the presence of tenderness on posterior abdominal wall in the retrocaecal and paracolic appendicitis. This is the first case report of this kind in the literature. The K-sign has been named, as a mark of respect, after the region of origin of this sign, Kashmir, so called as "Kashmir Sign". The sign being present in view of inflamed appendix crossing above its non palpable position above iliac crest on the posterior abdominal wall and the tenderness is by irritation of posterior peritoneum Case presentation: The author is reporting a case series of four patients in whom a K-sign, a clinical sign, was elicited and found positive on the posterior abdominal wall for presence of tenderness in a specific area bound by the 12th rib superiorly, spine medially, lateral margin of posterior abdominal wall laterally and iliac crest inferiorly and was found to be present in three retrocaecal and one paracolic appendicitis. Each case had tenderness in this specific area o
A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II
We present a semi-decision procedure to tackle first order differential
equations, with Liouvillian functions in the solution (LFOODEs). As in the case
of the Prelle-Singer procedure, this method is based on the knowledge of the
integrating factor structure.Comment: 11 pages, late
Genetic structure and admixture in sheep from terminal breeds in the United States
Selection for performance in diverse production settings has resulted in variation across sheep breeds worldwide. Although sheep are an important species to the United States, the current genetic relationship among many terminal sire breeds is not well characterized. Suffolk, Hampshire, Shropshire and Oxford (terminal) and Rambouillet (dual purpose) sheep (n = 248) sampled from different flocks were genotyped using the Applied Biosystems Axiom Ovine Genotyping Array (50K), and additional Shropshire sheep (n = 26) using the Illumina Ovine SNP50 BeadChip. Relationships were investigated by calculating observed heterozygosity, inbreeding coefficients, eigenvalues, pairwise Wright’s FST estimates and an identity by state matrix. The mean observed heterozygosity for each breed ranged from 0.30 to 0.35 and was consistent with data reported in other US and Australian sheep. Suffolk from two different regions of the United States (Midwest and West) clustered separately in eigenvalue plots and the rectangular cladogram. Further, divergence was detected between Suffolk from different regions with Wright’s FST estimate. Shropshire animals showed the greatest divergence from other terminal breeds in this study. Admixture between breeds was examined using ADMIXTURE, and based on cross-validation estimates, the best fit number of populations (clusters) was K = 6. The greatest admixture was observed within Hampshire, Suffolk, and Shropshire breeds. When plotting eigenvalues, US terminal breeds clustered separately in comparison with sheep from other locations of the world. Understanding the genetic relationships between terminal sire breeds in sheep will inform us about the potential applicability of markers derived in one breed to other breeds based on relatedness
Thermal noise limitations to force measurements with torsion pendulums: Applications to the measurement of the Casimir force and its thermal correction
A general analysis of thermal noise in torsion pendulums is presented. The
specific case where the torsion angle is kept fixed by electronic feedback is
analyzed. This analysis is applied to a recent experiment that employed a
torsion pendulum to measure the Casimir force. The ultimate limit to the
distance at which the Casimir force can be measured to high accuracy is
discussed, and in particular the prospects for measuring the thermal correction
are elaborated upon.Comment: one figure, five pages, to be submitted to Phys Rev
NMR implementation of Factoring Large Numbers with Gau\ss{}Sums: Suppression of Ghost Factors
Finding the factors of an integer can be achieved by various experimental
techniques, based on an algorithm developed by Schleich et al., which uses
specific properties of Gau\ss{}sums. Experimental limitations usually require
truncation of these series, but if the truncation parameter is too small, it is
no longer possible to distinguish between factors and so-called "ghost"
factors. Here, we discuss two techniques for distinguishing between true
factors and ghost factors while keeping the number of terms in the sum constant
or only slowly increasing. We experimentally test these modified algorithms in
a nuclear spin system, using NMR.Comment: 4 pages, 5 figure
Construction of Special Solutions for Nonintegrable Systems
The Painleve test is very useful to construct not only the Laurent series
solutions of systems of nonlinear ordinary differential equations but also the
elliptic and trigonometric ones. The standard methods for constructing the
elliptic solutions consist of two independent steps: transformation of a
nonlinear polynomial differential equation into a nonlinear algebraic system
and a search for solutions of the obtained system. It has been demonstrated by
the example of the generalized Henon-Heiles system that the use of the Laurent
series solutions of the initial differential equation assists to solve the
obtained algebraic system. This procedure has been automatized and generalized
on some type of multivalued solutions. To find solutions of the initial
differential equation in the form of the Laurent or Puiseux series we use the
Painleve test. This test can also assist to solve the inverse problem: to find
the form of a polynomial potential, which corresponds to the required type of
solutions. We consider the five-dimensional gravitational model with a scalar
field to demonstrate this.Comment: LaTeX, 14 pages, the paper has been published in the Journal of
Nonlinear Mathematical Physics (http://www.sm.luth.se/math/JNMP/
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