A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.

Design and analysis of ripple-based controls based on the discrete modeling and Floquet theory

Ripple-based controls can strongly reduce the required output capacitance in PowerSoC converter thanks to a very fast dynamic response. Unfortunately, these controls are prone to sub-harmonic oscillations and several parameters affect the stability of these systems. This paper derives and validates a simulation-based modeling and stability analysis of a closed-loop V 2Ic control applied to a 5 MHz Buck converter using discrete modeling and Floquet theory to predict stability. This allows the derivation of sensitivity analysis to design robust systems. The work is extended to different V 2 architectures using the same methodology.

A test of a stochastic theory of choice,

Mode of access: Internet.

Henselian Discrete Valued Fields Admitting One-Dimensional Local Class Field Theory

2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20.

Encouraging the intellectual craft of living research:tattoos, theory and time

This chapter contributes to the anthology on learning to research - researching to learn because it emphases a need to design curricula that enables living research, and on-going researcher development, rather than one that restricts student and staff activities, within a marketised approach towards time. In recent decades higher education (HE) has come to be valued for its contribution to the global economy. Referred to as the neo-liberal university, a strong prioritisation has been placed on meeting the needs of industry by providing a better workforce. This perspective emphasises the role of a degree in HE to secure future material affluence, rather than to study as an on-going investment in the self (Molesworth , Nixon & Scullion, 2009: 280). Students are treated primarily as consumers in this model, where through their tuition fees they purchase a product, rather than benefit from the transformative potential university education offers for the whole of life.Given that HE is now measured by the numbers of students it attracts, and later places into well-paid jobs, there is an intense pressure on time, which has led to a method where the learning experiences of students are broken down into discrete modules. Whilst this provides consistency, students can come to view research processes in a fragmented way within the modular system. Topics are presented chronologically, week-by-week and students simply complete a set of tasks to ‘have a degree’, rather than to ‘be learners’ (Molesworth , Nixon & Scullion, 2009: 277) who are living their research, in relation to their own past, present and future. The idea of living research in this context is my own adaptation of an approach suggested by C. Wright Mills (1959) in The Sociological Imagination. Mills advises that successful scholars do not split their work from the rest of their lives, but treat scholarship as a choice of how to live, as well as a choice of career. The marketised slant in HE thus creates a tension firstly, for students who are learning to research. Mills would encourage them to be creative, not instrumental, in their use of time, yet they are journeying through a system that is structured for a swift progression towards a high paid job, rather than crafted for reflexive inquiry, that transforms their understanding throughout life. Many universities are placing a strong focus on discrete skills for student employability, but I suggest that embedding the transformative skills emphasised by Mills empowers students and builds their confidence to help them make connections that aid their employability. Secondly, the marketised approach creates a problem for staff designing the curriculum, if students do not easily make links across time over their years of study and whole programmes. By researching to learn, staff can discover new methods to apply in their design of the curriculum, to help students make important and creative connections across their programmes of study.

Investigating a career choice for nursing based on social cognitive career theory

Nursing shortages still exist in the U.S. so it is important to determine factors that influence decisions to pursue nursing as a career. This comparative, correlational research study revealed factors that may contribute to, or deter students from choosing nursing as a career. The purpose of this study was to determine factors that contribute to a career choice for nursing based on the concepts of social cognitive career theory (SCCT), self efficacy, outcome expectations, and personal goals, among senior high school students, final year nursing students, and first year nursing students. Based on the results strategies may be developed to recruit a younger pool of students to the nursing profession and to boost retention efforts among those who already made a career choice in nursing. Data were collected using a three part questionnaire developed by the researcher to obtain demographic information and data about the respondents' self efficacy, outcome expectations, and personal goals with regards to nursing as a career. Point bi-serial correlations were used to determine relationships between the variables. ANOVAs and ANCOVAs were computed to determine differences in self efficacy and outcome expectations, among the three groups. Additional descriptive data determined reasons for and against a choice for nursing as a career. Self efficacy and outcome expectations were significantly correlated to career choice among all three groups. The nursing students had higher self efficacy perceptions than the high school students. There were no significant differences in outcome expectations between the three groups. The main categories identified as reasons for choosing nursing as a career were; (a) caring, (b) career and educational advancement, (c) personal accomplishment, (d) proficiency and love of the medical field. Common categories identified for not choosing nursing as a career were; (a) responsibility, (b) liability, (c) lack of respect, and (d) low salary. Other categories regarding not choosing nursing as a career included; (a) the nursing program and (b) professional (c) alternate career choice options and (d) fear of sickness and death. Findings from this study support the tenets of SCCT and may be used to recruit and retain nurses and develop curricula.

Queer Theory or Queer Choice of Identification?

The definition and nomenclature used in queer theory have become distorted from their initial meanings and intents.

H(infinity) filtering for rectangular discrete-time descriptor systems

This paper deals with the H(infinity) recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified gamma-level if the resulting cost is positive. In order to present some computational alternatives to the H(infinity) filters developed, they are rewritten in information form along with the respective array algorithms. (C) 2009 Elsevier Ltd. All rights reserved.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

The pareto-stability concept is a natural solution concept for discrete matching markets with indifferences

In a decentralized setting the game-theoretical predictions are that only strong blockings are allowed to rupture the structure of a matching. This paper argues that, under indifferences, also weak blockings should be considered when these blockings come from the grand coalition. This solution concept requires stability plus Pareto optimality. A characterization of the set of Pareto-stable matchings for the roommate and the marriage models is provided in terms of individually rational matchings whose blocking pairs, if any, are formed with unmatched agents. These matchings always exist and give an economic intuition on how blocking can be done by non-trading agents, so that the transactions need not be undone as agents reach the set of stable matchings. Some properties of the Pareto-stable matchings shared by the Marriage and Roommate models are obtained.