Generalization of the BTK Theory to the Case of Finite Quasiparticle Lifetimes

A generalization to the BTK theory is developed based on the fact that the quasiparticle lifetime is finite as a result of the damping caused by the interactions. For this purpose, appropriate self-energy expressions and wave functions are inserted into the strong coupling version of the Bogoliubov equations and subsequently, the coherence factors are computed. By applying the suitable boundary conditions to the case of a normal-superconducting interface, the probability current densities for the Andreev reflection, the normal reflection, the transmission without branch crossing and the transmission with branch crossing are determined. Accordingly the electric current and the differential conductance curves are calculated numerically for Nb, Pb, and Pb0.9Bi0.1 alloy. The generalization of the BTK theory by including the phenomenological damping parameter is critically examined. The observed differences between our approach and the phenomenological approach are investigated by the numerical analysis.

Using stimulus equivalence to teach monetary skills to school-age children with autism

The present study evaluated the use of stimulus equivalence in teaching monetary skills to school aged children with autism. An AB within-subject design with periodic probes was used. At pretest, three participants demonstrated relation DA, an auditory-visual relation (matching dictated coin values to printed coin prices). Using a three-choice match-to-sample procedure, with a multi-component intervention package, these participants were taught two trained relations, BA (matching coins to printed prices) and CA (matching coin combinations to printed prices). Two participants achieved positive tests of equivalence, and the third participant demonstrated emergent performances with a symmetric and transitive relation. In addition, two participants were able to show generalization of learned skills with a parent, in a second naturalistic setting. The present research replicates and extends the results of previous studies by demonstrating that stimulus equivalence can be used to teach an adaptive skill to children with autism.

The effects of computer assisted interactive fiction on the development of reading comprehension in grade five students

This study was undertaken in order to determine the effects of playing computer based text adventure games on the reading comprehension gains of students. Forty-five grade five students from one elementary school were randomly assigned to experimental and control groups, and were tested with regard to ability, achievement and reading skills. An experimental treatment, consisting of playing computer based interactive fiction games of the student's choice for fifteen minutes each day over an eight-week period, was administered. A comparison treatment engaged the control group in sustained silent reading of materials of the student's choice for an equal period of time. Following the experimental period all students were post-tested with an alternate form of the pre-test in reading skills, and gain scores were analysed. It was found that there were no significant differences in the gain scores of the experimental and control groups for overall reading comprehenSion, but the experimental group showed greater gains than the control group in the structural analysis reading sub-skill. Extreme variance in the data made generalization very difficult, but the findings indicated a potential for computer based interactive fiction as a useful tool for developing reading sl

A sequential analysis of therapist scaffolding and child concept formation in narrative therapy

Narrative therapy is a postmodern therapy that takes the position that people create self-narratives to make sense of their experiences. To date, narrative therapy has compiled virtually no quantitative and very little qualitative research, leaving gaps in almost all areas of process and outcome. White (2006a), one of the therapy's founders, has recently utilized Vygotsky's (1934/1987) theories of the zone of proximal development (ZPD) and concept formation to describe the process of change in narrative therapy with children. In collaboration with the child client, the narrative therapist formalizes therapeutic concepts and submits them to increasing levels of generalization to create a ZPD. This study sought to determine whether the child's development proceeds through the stages of concept formation over the course of a session, and whether therapists' utterances scaffold this movement. A sequential analysis was used due to its unique ability to measure dynamic processes in social interactions. Stages of concept formation and scaffolding were coded over time. A hierarchical log-linear analysis was performed on the sequential data to develop a model of therapist scaffolding and child concept development. This was intended to determine what patterns occur and whether the stated intent of narrative therapy matches its actual process. In accordance with narrative therapy theory, the log-linear analysis produced a final model with interactions between therapist and child utterances, and between both therapist and child utterances and time. Specifically, the child and youth participants in therapy tended to respond to therapist scaffolding at the corresponding level of concept formation. Both children and youth and therapists also tended to move away from earlier and toward later stages of White's scaffolding conversations map as the therapy session advanced. These findings provide support for White's contention that narrative therapists promote child development by scaffolding child concept formation in therapy.

Detectives and Superheroes: A Pilot Study Teaching Flexible Thinking in Social Situations to a Child with High Functioning Autism

Complex social-cognitive deficits are common in individuals diagnosed with high functioning autism and Asperger syndrome. Research on effective and evidence-based social interventions is needed for this population. This study focused specifically on the challenges these individuals face with respect to flexible thinking and related flexible behaviour in social situations. Madrigal and Winner's (2008) Superflex curriculum - targets social flexibility, however at the time of this study no published research had been conducted to determine the effectiveness of this approach. This study was a pilot study, which sought to examine the impact of the Superflex curriculum within a 10-week training program in teaching one individual with high functioning autism how to think and behave flexibly in social situations. Multiple measurement tools were utilized, and analyses within and across the measures revealed inconsistencies, especially with respect to generalization. Although preliminary, this study provided valuable information for subsequent research.

The Family Game: A Parent Education Intervention to Increase Positive Parent-Child Interactions in Parents with Learning Difficulties

Children of parents with learning difficulties (LD) are at risk for a variety of developmental problems including behavioural and psychiatric disorders. However, there are no empirically supported programs to prevent behavioural and psychiatric problems in these children. The purpose of the study was to test the effectiveness of a parenting intervention designed to teach parents with learning difficulties positive child behaviour management strategies. A multiple baseline across skills design was used with two parents, who were taught three skills: 1) clear instructions, 2) recognition of compliance and 3) correction of noncompliance. Training scores improved on each skill and maintained at a 1-month follow-up. Scores on generalization cards were high and showed maintenance, but improvements in parenting skills in the naturalistic environment were low at posttest and follow-up. Increases were seen in child compliance at posttest and 1-month follow-up. Results of pre-post social validity measures were also generally positive.

Prime Rational Functions and Integral Polynomials

Let f(x) be a complex rational function. In this work, we study conditions under which f(x) cannot be written as the composition of two rational functions which are not units under the operation of function composition. In this case, we say that f(x) is prime. We give sufficient conditions for complex rational functions to be prime in terms of their degrees and their critical values, and we derive some conditions for the case of complex polynomials. We consider also the divisibility of integral polynomials, and we present a generalization of a theorem of Nieto. We show that if f(x) and g(x) are integral polynomials such that the content of g divides the content of f and g(n) divides f(n) for an integer n whose absolute value is larger than a certain bound, then g(x) divides f(x) in Z[x]. In addition, given an integral polynomial f(x), we provide a method to determine if f is irreducible over Z, and if not, find one of its divisors in Z[x].

An Abstract Algebraic Theory of L-Fuzzy Relations for Relational Databases

Classical relational databases lack proper ways to manage certain real-world situations including imprecise or uncertain data. Fuzzy databases overcome this limitation by allowing each entry in the table to be a fuzzy set where each element of the corresponding domain is assigned a membership degree from the real interval [0…1]. But this fuzzy mechanism becomes inappropriate in modelling scenarios where data might be incomparable. Therefore, we become interested in further generalization of fuzzy database into L-fuzzy database. In such a database, the characteristic function for a fuzzy set maps to an arbitrary complete Brouwerian lattice L. From the query language perspectives, the language of fuzzy database, FSQL extends the regular Structured Query Language (SQL) by adding fuzzy specific constructions. In addition to that, L-fuzzy query language LFSQL introduces appropriate linguistic operations to define and manipulate inexact data in an L-fuzzy database. This research mainly focuses on defining the semantics of LFSQL. However, it requires an abstract algebraic theory which can be used to prove all the properties of, and operations on, L-fuzzy relations. In our study, we show that the theory of arrow categories forms a suitable framework for that. Therefore, we define the semantics of LFSQL in the abstract notion of an arrow category. In addition, we implement the operations of L-fuzzy relations in Haskell and develop a parser that translates algebraic expressions into our implementation.