A treatment of atomic mean square displacement in higher order perturbation theory

A general derivation of the anharmonic coefficients for a periodic lattice invoking the special case of the central force interaction is presented. All of the contributions to mean square displacement (MSD) to order 14 perturbation theory are enumerated. A direct correspondance is found between the high temperature limit MSD and high temperature limit free energy contributions up to and including 0(14). This correspondance follows from the detailed derivation of some of the contributions to MSD. Numerical results are obtained for all the MSD contributions to 0(14) using the Lennard-Jones potential for the lattice constants and temperatures for which the Monte Carlo results were calculated by Heiser, Shukla and Cowley. The Peierls approximation is also employed in order to simplify the numerical evaluation of the MSD contributions. The numerical results indicate the convergence of the perturbation expansion up to 75% of the melting temperature of the solid (TM) for the exact calculation; however, a better agreement with the Monte Carlo results is not obtained when the total of all 14 contributions is added to the 12 perturbation theory results. Using Peierls approximation the expansion converges up to 45% of TM• The MSD contributions arising in the Green's function method of Shukla and Hubschle are derived and enumerated up to and including 0(18). The total MSD from these selected contributions is in excellent agreement with their results at all temperatures. Theoretical values of the recoilless fraction for krypton are calculated from the MSD contributions for both the Lennard-Jones and Aziz potentials. The agreement with experimental values is quite good.

Organizational commitment and perceived relatedness as correlates of the intention to continue officiating in track and field

The objectives of the present study were to explore three components of organizational commitment (affective [AC], normative [NC] and continuance [CC] commitment; Allen & Meyer, 1991), perceived relatedness (Oeci & Ryan, 1985; 2002), and behavioural intention (Ajzen, 2002) within the context of volunteer track and field officiating. The objectives were examined in a 2-phase study. Ouring phase 1, experts (N = 10) with domain familiarity assessed the item content relevance and representation of modified organizational commitment (OC; Meyer, Allen & Smith, 1993) and perceived relatedness (La Guardia, Oeci, Ryan & Couchman, 2000) items. Fourteen of 26 (p < .05) items were relevant (Aiken's coefficient V) and NC (M = 3.88, SO = .64), CC (M = 3.63, SD = .52), and relatedness (M = 4.00, SD = .93) items had mean item content-representation ratings of either "good" or "very good" while AC (M = 2.50, SD = 0.58) was rated "fair". Participants in phase 2 (N = 80) responded to items measuring demographic variables, perceptions of OC to Athletics Canada, perceived relatedness to other track and field officials, and a measure of intention (yiu, Au & Tang, 2001) to continue officiating. Internal consistency reliability estimates (Cronbach's (1951) coefficient alpha) were as follows: (a) AC = .78, (b) CC = .85, (c) NC = .80 (d) perceived relatedness = .70 and, (e) intention = .92 in the present sample. Results suggest that the track and field officials felt only minimally committed to Athletics Canada (AC M = 3.90, SD = 1.23; NC M = 2.47, SD = 1.25; CC M = 3.32; SD = 1.34) and that their relationships with other track and field officials were strongly endorsed (M = 5.86, SD = 0.74). Bivariate correlations (Pearson r) indicated that perceived relatedness to other track and field officials demonstrated the strongest relationship with intention to continue officiating (r = .346, p < .05), while dimensions of OC were not significantly related to intention (all p's > .05). Together perceived relatedness (j3 = .339, p = .004), affective commitment (j3 = -.1 53, p = .308), normative commitment (j3 = -.024, p = .864) and continuance commitment (j3 = .186, P = .287) contribute to the prediction of intention to continued officiating (K = .139). These relationships remained unaffected by the inclusion of demographic (j3age = -.02; P years with Athletics Canada = -.13; bothp's > .05) or alternative commitment (j3sport = -.19; P role = .15; Pathletes = .20; all p' s > .05) considerations. Three open-ended questions elicited qualitative responses regarding participants' reasons for officiating. Responses reflecting initial reasons for officiating formed these higher order themes: convenience, helping reasons, extension of role, and intrinsic reasons. Responses reflecting reasons for continuing to officiate formed these higher order themes: track and field, to help, and personal benefits. Responses reflecting changes that would influence continued involvement were: political, organizational/structural, and personal. These results corroborate the findings of previous investigations which state that the reasons underpinning volunteer motivations change over time (Cuskelly et al., 2002). Overall, the results of this study suggest that track and field officials feel minimal commitment to the organization of Athletics Canada but a stronger bond with their fellow officials. Moreover, the degree to which track and field officials feel meaningfully connected to one another appears to exert a positive influence on their intentions to continue officiating. As such, it is suggested that in order to promote continued involvement, Athletics Canada increases its focus on fostering environments promoting positive interactions among officials.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Dinocyst biochronology and palynofacies : inferred systems tract character of Miocene sequences from New Jersey mid-Atlantic transect (ODP legs 174A and 174AX) /

One of the main objectives of the mid-Atlantic transect is to improve dating resolution of sequences and unconfonnity surfaces. Dinoflagellate cysts from two Ocean Drilling Program boreholes, the onshore Leg 174AX Ocean View Site and Leg 174A continental shelf Site 1071, are used to provide age estimates for sequences and unconfonnities fonned on the New Jersey continental margin during the Miocene epoch. Despite the occasional lack of dinocysts in barren and oxidized sections, dinocyst biochronology still offers greater age control than that provided by other microfossils in marginal marine environments. An early Miocene to late Miocene chronology based on ages detennined for the two study sites is presented. In addition, .palynofacies are used to unravel the systems tract character of the Miocene sequences and provide insight into the effects of taphonomy and preservation of palynomorphs in marginal marine and shelf environments under different ~ea level conditions. More precise placement of maximum flooding surfaces is possible through the identification of condensed sections and palynofacies shifts can also reveal subaerially exposed sections and surfaces not apparent in seismic or lithological analyses. The problems with the application of the pollen record in the interpretation of Miocene climate are also discussed. Palynomorphs provide evidence for a second-order lowering of sea level during the Miocene, onto which higher order sea level fluctuations are super-imposed. Correlation of sequences and unconfonnities is attempted between onshore boreholes and from the onshore Ocean View borehole to offshore Site 1071.

A five factor model of grief : a q-methodological study /

Q-methodology permitted 41 people to communicate their perspective of grief. In an attempt to clarify the research to date and to allow those who have experienced this human journey to direct the scientists, 80 statements were chosen to present to the participants based on the research from academic and counselling sources. Five different perspectives emerged from the Q-sorts and factor analysis. Each perspective was valuable for the understanding of different groups of mourners. They were interpreted using questionnaire data and interview information. They are as follows: Factor 1- Growth Optimism; Factor 2 - Schema Destruction and Negative Affect; Factor 3- Identification with the Deceased Person; Factor 4- Intact World view with High Clarity and High Social Support; Factor 5- Schema Destruction with High Preoccupation and Attention to Emotion. Some people grow in the face of grief, others hold on to essentially the same schemas and others are devastated by their loss. The different perspectives reported herein supply clues to the sources of these differing outcomes. From examination of Factor 1, it appears that a healthy living relationship helps substantially in the event of loss. An orientation toward emotions that encourages clarity, exemplified by Factor 4, without hyper-vigilance to emotion may be helpful as well. Strategies for maintaining schematic representations of the world with little alteration include: identification with the values of the deceased person, as in Factor 3 and reliance on social support and/or God as demonstrated by Factor 4. When the relationship had painful periods, social support may be accessed to benefit some mourners. When the person's frame of reference or higher order schemas are assaulted by the events of loss, the people most at risk for traumatic grief seem to be those with difficult relationships as indicated by Factor 5 individuals. When low social support, high attention to emotion with low clarity and little belief that feelings can be altered for the better are also attributes of the mourner devastating grief can result. In the end, there are groups of people who are forced to endure the entire process of schema destruction and devastation. Some appear to recover in part and others appear to stay in a form of purgatory for many years. The results of this study suggest that, those who experience devastating grief may be in the minority. In the future interventions could be more specifically addressed if these perspectives are replicated in a larger, more detailed study.

Winâ Foy : functional object-oriented programming language

This thesis will introduce a new strongly typed programming language utilizing Self types, named Win--*Foy, along with a suitable user interface designed specifically to highlight language features. The need for such a programming language is based on deficiencies found in programming languages that support both Self types and subtyping. Subtyping is a concept that is taken for granted by most software engineers programming in object-oriented languages. Subtyping supports subsumption but it does not support the inheritance of binary methods. Binary methods contain an argument of type Self, the same type as the object itself, in a contravariant position, i.e. as a parameter. There are several arguments in favour of introducing Self types into a programming language (11. This rationale led to the development of a relation that has become known as matching [4, 5). The matching relation does not support subsumption, however, it does support the inheritance of binary methods. Two forms of matching have been proposed (lJ. Specifically, these relations are known as higher-order matching and I-bound matching. Previous research on these relations indicates that the higher-order matching relation is both reflexive and transitive whereas the f-bound matching is reflexive but not transitive (7]. The higher-order matching relation provides significant flexibility regarding inheritance of methods that utilize or return values of the same type. This flexibility, in certain situations, can restrict the programmer from defining specific classes and methods which are based on constant values [21J. For this reason, the type This is used as a second reference to the type of the object that cannot, contrary to Self, be specialized in subclasses. F-bound matching allows a programmer to define a function that will work for all types of A', a subtype of an upper bound function of type A, with the result type being dependent on A'. The use of parametric polymorphism in f-bound matching provides a connection to subtyping in object-oriented languages. This thesis will contain two main sections. Firstly, significant details concerning deficiencies of the subtype relation and the need to introduce higher-order and f-bound matching relations into programming languages will be explored. Secondly, a new programming language named Win--*Foy Functional Object-Oriented Programming Language has been created, along with a suitable user interface, in order to facilitate experimentation by programmers regarding the matching relation. The construction of the programming language and the user interface will be explained in detail.

Equational Reasoning about Object-Oriented Programs

Formal verification of software can be an enormous task. This fact brought some software engineers to claim that formal verification is not feasible in practice. One possible method of supporting the verification process is a programming language that provides powerful abstraction mechanisms combined with intensive reuse of code. In this thesis we present a strongly typed functional object-oriented programming language. This language features type operators of arbitrary kind corresponding to so-called type protocols. Sub classing and inheritance is based on higher-order matching, i.e., utilizes type protocols as basic tool for reuse of code. We define the operational and axiomatic semantics of this language formally. The latter is the basis of the interactive proof assistant VOOP (Verified Object-Oriented Programs) that allows the user to prove equational properties of programs interactively.

I Believe in me, not OCB: Evaluation of Group Function-Based CBT as a Treatment for Obsessive Compulsive Behaviour in Four Children with HFA

Researchers have conceptualized repetitive behaviours in individuals with Autism Spectrum Disorder (ASD) on a continuum oflower-Ievel, motoric, repetitive behaviours and higher-order, repetitive behaviours that include symptoms ofOCD (Hollander, Wang, Braun, & Marsh, 2009). Although obsessional, ritualistic, and stereotyped behaviours are a core feature of ASD, individuals with ASD frequently experience obsessions and compulsions that meet DSM-IV-TR (American Psychiatric Association, 2000) criteria for Obsessive-Compulsive Disorder (OCD). Given the acknowledged difficulty in differentiating between OCD and Autism-related obsessive-compulsive phenomena, the present study uses the term Obsessive Compulsive Behaviour (OCB) to represent both phenomena. This study used a multiple baseline design across behaviours and ABC designs (Cooper, Heron, & Heward, 2007) to investigate if a 9-week Group Function-Based Cognitive Behavioural Therapy (CBT) decreased OCB in four children (ages 7 - 11 years) with High Functioning Autism (HFA). Key treatment components included traditional CBT components (awareness training, cognitive-behavioural skills training, exposure and response prevention) as well as function-based assessment and intervention. Time series data indicated significant decreases in OCBs. Standardized assessments showed decreases in symptom severity, and increases in quality of life for the participants and their families. Issues regarding symptom presentation, assessment, and treatment of a dually diagnosed child are discussed.

L-Fuzzy Relations in Coq

Heyting categories, a variant of Dedekind categories, and Arrow categories provide a convenient framework for expressing and reasoning about fuzzy relations and programs based on those methods. In this thesis we present an implementation of Heyting and arrow categories suitable for reasoning and program execution using Coq, an interactive theorem prover based on Higher-Order Logic (HOL) with dependent types. This implementation can be used to specify and develop correct software based on L-fuzzy relations such as fuzzy controllers. We give an overview of lattices, L-fuzzy relations, category theory and dependent type theory before describing our implementation. In addition, we provide examples of program executions based on our framework.