Farm Feed Processing.

12 p

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

Direct Finite First-Order Model Generation with Negative Constraint Propagation Heuristic

An Automated Finite First-Order Model Generator Has Been Developed. the Problem is Viewed as a First-Order Satisfiability Problem. Most Existing Model Generators Reduce the Problem to Propositional Satisfiability by Converting the Input First-Order Clauses into Propositional Clauses. This Generator, Unlike Others, Stores the Input First-Order Clauses and Solves the Problem Directly. It Uses an Exhaustive Backtracking Algorithm with Weight-Based Splitting. a Negative Constraint Propagation is Implemented to Reduce the Number of Decision Points and Thus to Speed Up the Search. © 1997 ACM

A case study in automated theorem proving: A difficult problem about commutators

This paper shows how the automated deduction system OTTER. was used to prove the group theory theorem {chi}{sup 3} = e {implies} [[[y, z], u], v] = e, where e is the identity, and [XI Y] is the commutator {chi}{prime}y{prime}{chi}y. This is a difficult problem for automated provers, and several lengthy searches were run before a proof was found. Problem formulation and search strategy played a key role in the success. I believe that ours is the first automated proof of the theorem

Do ecological differences between taxonomic groups influence the relationship between species’ distributions and climate? A global meta-analysis using species distribution models

Understanding whether and how ecological traits affect species’ geographic distributions is a fundamental issue that bridges ecology and biogeography. While climate is thought to be the major determinant of species’ distributions, there is considerable variation in the strength of species’ climate–distribution relationships. One potential explanation is that species with relatively low dispersal ability cannot reach all geographic areas where climatic conditions are suitable. We tested the hypothesis that species from different taxonomic groups varied in their climate–distribution relationships because of differences in life history strategies, in particular dispersal ability. We conducted a meta-analysis by combining the discrimination ability (AUC values) from 4317 species distribution models (SDMs) using fit as an indication of the strength of the species’ climate–distribution relationship. We found significant differences in the strength of species’ climate–distribution relationships across taxonomic groups, however we did not find support for the dispersal hypothesis. Our results suggest that relevant ecological trait variation among broad taxonomic groups may be related to differences in species’ climate–distribution relationships, however which ecological traits are important remains unclear

An equational characterization of the conic construction of cubic curves

An n-ary Steiner law f(x{sub 1},x{sub 2},{hor_ellipsis},x{sub n}) on a projective curve {Gamma} over an algebraically closed field k is a totally symmetric n-ary morphism f from {Gamma}{sup n} to {Gamma} satisfying the universal identity f(x{sub 1},x{sub 2},{hor_ellipsis},x{sub n-1}, f(x{sub 1},x{sub 2},{hor_ellipsis},x{sub n})) = x{sub n}. An element e in {Gamma} is called an idempotent for f if f(e,e,{hor_ellipsis},e) = e. The binary morphism x * y of the classical chord-tangent construction on a nonsingular cubic curve is an example of a binary Steiner law on the curve, and the idempotents of * are precisely the inflection points of the curve. In this paper, the authors prove that if f and g are two 5-ary Steiner laws on an elliptic curve {Gamma} sharing a common idempotent, then f = g. They use a new rule of inference rule =(gL){implies}, extracted from a powerful local-to-global principal in algebraic geometry. This rule is implemented in the theorem-proving program OTTER. Then they use OTTER to automatically prove the uniqueness of the 5-ary Steiner law on an elliptic curve. Very much like the binary case, this theorem provides an algebraic characterization of a geometric construction process involving conics and cubics. The well-known theorem of the uniqueness of the group law on such a curve is shown to be a consequence of this result

A single-amino-acid change in murine norovirus NS1/2 is sufficient for colonic tropism and persistence

Human norovirus (HuNoV) is the major cause of acute nonbacterial gastroenteritis worldwide but has no clear animal reservoir. HuNoV can persist after the resolution of symptoms, and this persistence may be essential for viral maintenance within the population. Many strains of the related murine norovirus (MNV) also persist, providing a tractable animal model for studying norovirus (NoV) persistence. We have used recombinant cDNA clones of representative persistent (CR6) and nonpersistent (CW3) strains to identify a domain within the nonstructural gene NS1/2 that is necessary and sufficient for persistence. Furthermore, we found that a single change of aspartic acid to glutamic acid in CW3 NS1/2 was sufficient for persistence. This same conservative change also caused increased growth of CW3 in the proximal colon, which we found to be a major tissue reservoir of MNV persistence, suggesting that NS1/2 determines viral tropism that is necessary for persistence. These findings represent the first identified function for NoV NS1/2 during infection and establish a novel model system for the study of enteric viral persistence

Studying Algebraic Structures Using Prover9 and Mace4

In this chapter we present a case study, drawn from our research work, on the application of a fully automated theorem prover together with an automatic counter-example generator in the investigation of a class of algebraic structures. We will see that these tools, when combined with human insight and traditional algebraic methods, help us to explore the problem space quickly and effectively. The counter-example generator rapidly rules out many false conjectures, while the theorem prover is often much more efficient than a human being at verifying algebraic identities. The specific tools in our case study are Prover9 and Mace4; the algebraic structures are generalisations of Heyting algebras known as hoops. We will see how this approach helped us to discover new theorems and to find new or improved proofs of known results. We also make some suggestions for how one might deploy these tools to supplement a more conventional approach to teaching algebra.Comment: 21 pages, to appear as Chapter 5 in "Proof Technology in Mathematics Research and Teaching", Mathematics Education in the Digital Era 14, edited by G. Hanna et al. (eds.), published by Springe