AC-KBO Revisited

Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.Comment: 31 pages, To appear in Theory and Practice of Logic Programming (TPLP) special issue for the 12th International Symposium on Functional and Logic Programming (FLOPS 2014

Dynamics of broken symmetry lambda phi^4 field theory

We study the domain of validity of a Schwinger-Dyson (SD) approach to non-equilibrium dynamics when there is broken symmetry. We perform exact numerical simulations of the one- and two-point functions of lambda phi^4 field theory in 1+1 dimensions in the classical domain for initial conditions where < phi(x) > not equal to 0. We compare these results to two self-consistent truncations of the SD equations which ignore three-point vertex function corrections. The first approximation, which sets the three-point function to one (the bare vertex approximation (BVA)) gives an excellent description for < phi(x) > = phi(t). The second approximation which ignores higher in 1/N corrections to the 2-PI generating functional (2PI -1/N expansion) is not as accurate for phi(t). Both approximations have serious deficiencies in describing the two-point function when phi(0) > .4.Comment: 10 pages, 6 figure

Studies of Physicochemical and Some Heavy Metals in Soil and Lake Sediments

The present work attempts to establish the distribution of Iron, Manganese, Zinc, Copper, Boron and molybdenum and physic-chemical properties of the soil and lake sediments in Bijapur district. The area under study receives domestic raw sewage from surrounding populated neighborhoods through rain water, main tributary of the lake. Concentrations of heavy metals in soil are compared with many guidelines to predict status of pollution. KEYWORDS: Heavy Metals, Lake sediments, Pollution, Soil Samples, etc INTRODUCTION In many developing countries, the expansion of urban centers is of considerable importance for socio-economic growth and this continuously modifies the physical, chemical and biological composition of our living environment MATERIAL AND METHODS Data collection and analysis-10 soil samples (three replicates) were collected at surface level (0-10 cm in depth) were collected from various locations. The collected samples were air dried and sieved into course and fine fractions. Well mixed samples of 2 g each were taken in 250 mL glass beakers and digested with 8 mL of aqua regia on a sand bath for 2 hour

Certification of nontermination proofs using strategies and nonlooping derivations

© 2014 Springer International Publishing Switzerland. The development of sophisticated termination criteria for term rewrite systems has led to powerful and complex tools that produce (non)termination proofs automatically. While many techniques to establish termination have already been formalized—thereby allowing to certify such proofs—this is not the case for nontermination. In particular, the proof checker CeTA was so far limited to (innermost) loops. In this paper we present an Isabelle/HOL formalization of an extended repertoire of nontermination techniques. First, we formalized techniques for nonlooping nontermination. Second, the available strategies include (an extended version of) forbidden patterns, which cover in particular outermost and context-sensitive rewriting. Finally, a mechanism to support partial nontermination proofs further extends the applicability of our proof checker

A ‘quiet revolution’? The impact of Training Schools on initial teacher training partnerships

This paper discusses the impact on initial teacher training of a new policy initiative in England: the introduction of Training Schools. First, the Training School project is set in context by exploring the evolution of a partnership approach to initial teacher training in England. Ways in which Training Schools represent a break with established practice are considered together with their implications for the dominant mode of partnership led by higher education institutions (HEIs). The capacity of Training Schools to achieve their own policy objectives is examined, especially their efficacy as a strategy for managing innovation and the dissemination of innovation. The paper ends by focusing on a particular Training School project which has adopted an unusual approach to its work and enquires whether this alternative approach could offer a more profitable way forward. During the course of the paper, five different models of partnership are considered: collaborative, complementary, HEI-led, school-led and partnership within a partnership

Long-term functional outcome of distal radius fractures is associated with early post-fracture bone stiffness of the fracture region:An HR-pQCT exploratory study

\u3cp\u3eIdentifying determinants of long-term functional outcome after a distal radius fracture is challenging. Previously, we reported on the association between early HR-pQCT measurements and clinical outcome 12 weeks after a conservatively treated distal radius fracture. We extended the follow-up and assessed functional outcome after two years in relation to early HR-pQCT derived bone parameters. HR-pQCT scans of the fracture region were performed in 15 postmenopausal women with a distal radius fracture at 1-2 (baseline), 3-4 weeks and 26 months post-fracture. Additionally, the contralateral distal radius was scanned at baseline. Bone density, micro-architecture parameters and bone stiffness using micro-finite element analysis (μFEA) were evaluated. During all visits, wrist pain and function were assessed using the patient-rated wrist evaluation questionnaire (PRWE), quantifying functional outcome with a score between 0 and 100. Two-year PRWE was associated with torsional and bending stiffness 3-4 weeks post-fracture (R2: 0.49, p = 0.006 and R2: 0.54, p = 0.003, respectively). In contrast, early micro-architecture parameters of the fracture region or contralateral bone parameters did not show any association with long-term outcome. This exploratory study indicates that HR-pQCT with μFEA performed within four weeks after a distal radius fracture captures biomechanical fracture characteristics that are associated with long-term functional outcome and therefore could be a valuable early outcome measure in clinical trials and clinical practice.\u3c/p\u3