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 $G$-algebras, are finite factorization domains (FFD for short). Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \in \mathcal{G}$, where $\mathcal{G}$ is any $G$-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 $G$-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 $\mathcal{G}$. 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/