Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Equivalence between Redfield- and master-equation approaches for a time-dependent quantum system and coherence control

We present a derivation of the Redfield formalism for treating the dissipative dynamics of a time-dependent quantum system coupled to a classical environment. We compare such a formalism with the master equation approach where the environments are treated quantum mechanically. Focusing on a time-dependent spin-1/2 system we demonstrate the equivalence between both approaches by showing that they lead to the same Bloch equations and, as a consequence, to the same characteristic times T(1) and T(2) (associated with the longitudinal and transverse relaxations, respectively). These characteristic times are shown to be related to the operator-sum representation and the equivalent phenomenological-operator approach. Finally, we present a protocol to circumvent the decoherence processes due to the loss of energy (and thus, associated with T(1)). To this end, we simply associate the time dependence of the quantum system to an easily achieved modulated frequency. A possible implementation of the protocol is also proposed in the context of nuclear magnetic resonance.

GLOBALIZATION OF TWISTED PARTIAL ACTIONS

Let A be a unital ring which is a product of possibly infinitely many indecomposable rings. We establish a criteria for the existence of a globalization for a given twisted partial action of a group on A. If the globalization exists, it is unique up to a certain equivalence relation and, moreover, the crossed product corresponding to the twisted partial action is Morita equivalent to that corresponding to its globalization. For arbitrary unital rings the globalization problem is reduced to an extendibility property of the multipliers involved in the twisted partial action.

Equivalence between hot tensile and creep testing data for Kanthal A1 alloy

Hot tensile and creep tests were carried out on Kanthal A1 alloy in the temperature range from 600 to 800 degrees C. Each of these sets of data were analyzed separately according to their own methodologies, but an attempt was made to find a correlation between them. A new criterion proposed for converting hot tensile data to creep data, makes possible the analysis of the two kinds of results according to usual creep relations like: Norton, Monkman-Grant, Larson-Miller and others. The remarkable compatibility verified between both sets of data by this procedure strongly suggests that hot tensile data can be converted to creep data and vice-versa for Kanthal A1 alloy, as verified previously for other metallic materials.

A test of the hypothesis of ecological equivalence in an Australian subtropical rain forest

We tested the hypothesis that tree species in a subtropical rain forest in south-east Queensland are ecologically equivalent and therefore have identical environmental requirements for their regeneration. We assessed the evidence that juveniles of species differed in their distributions in treefall gap microsites and along gradients of light availability, soil pH, soil PO4-P availability and soil NO3-N availability. Pairwise comparisons were made on a subset of the common species selected on the basis that they showed a relatively high level of positive association, and would therefore, a priori, be expected to have similar regeneration requirements. Detailed comparisons between the species failed to demonstrate evidence for species differentiation with respect to their tolerance of the disturbance associated with gap microsites or to the gradient of NO3-N availability. However, species differed markedly in their distributions along the soil pH gradient and along the gradients of light availability and soil PO4-P availability. The overall level of ecological differentiation between the species is high: seven out of the 10 possible species pairings showed evidence for ecological differentiation. Such niche differentiation amongst the juveniles of tree species may play an important role in maintaining the species richness of rain-forest communities.

Mid-point for open-ended income category and the effect of equivalence scales on the income-health relationship

To estimate the mid-point of an open-ended income category and to assess the impact of two equivalence scales on income-health associations. Data were obtained from the 2010 Brazilian Oral Health Survey ( Pesquisa Nacional de Saúde Bucal – SBBrasil 2010). Income was converted from categorical to two continuous variables ( per capita and equivalized) for each mid-point. The median mid-point was R$ 14,523.50 and the mean, R$ 24,507.10. When per capita income was applied, 53% of the population were below the poverty line, compared with 15% with equivalized income. The magnitude of income-health associations was similar for continuous income, but categorized equivalized income tended to decrease the strength of association.

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Approved Drug Products with Theurapeutic Equivalence Evaluation - 34th edition

The publication, Approved Drug Products with Therapeutic Equivalence Evaluations (the List, commonly known as the Orange Book), identifies drug products approved on the basis of safety and effectiveness by the Food and Drug Administration (FDA) under the Federal Food, Drug, and Cosmetic Act (the Act). Drugs on the market approved only on the basis of safety (covered by the ongoing Drug Efficacy Study Implementation [DESI] review [e.g., Donnatal® Tablets and Librax® Capsules] or pre-1938 drugs [e.g., Phenobarbital Tablets]) are not included in this publication. The main criterion for the inclusion of any product is that the product is the subject of an application with an effective approval that has not been withdrawn for safety or efficacy reasons. Inclusion of products on the List is independent of any current regulatory action through administrative or judicial means against a drug product. In addition, the List contains therapeutic equivalence evaluations for approved multisource prescription drug products. These evaluations have been prepared to serve as public information and advice to state health agencies, prescribers, and pharmacists to promote public education in the area of drug product selection and to foster containment of health care costs. Therapeutic equivalence evaluations in this publication are not official FDA actions affecting the legal status of products under the Act.

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

Does Ricardian Equivalence Hold When Expectations are not Rational?

This paper considers the Ricardian Equivalence proposition when expectations are not rational and are instead formed using adaptive learning rules. We show that Ricardian Equivalence continues to hold provided suitable additional conditions on learning dynamics are satisfied. However, new cases of failure can also emerge under learning. In particular, for Ricardian Equivalence to obtain, agents’ expectations must not depend on government’s financial variables under deficit financing.

Egalitarian equivalence under asymmetric information

We propose a definition of egalitarian equivalence that extends Pazner and Schmeidler's (1978) concept to environments with incomplete information. If every feasible allocation rule can be implemented by an incentive compatible mechanism (as, for instance, in the case of non-exclusive information), then interim egalitarian equivalence and interim incentive efficiency remain compatible, as they were under complete information. When incentive constraints are more restrictive, on the other hand, the two criteria may become incompatible.

On Borel equivalence relations in generalized Baire space

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