Analytic perturbation theory for bound states in the transfer matrix spectrum of weakly correlated lattice ferromagnetic spin systems

We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region ('beta' << 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter 'alfa' = ('S POT.4') - 3 '(S POT.2') POT.2' > 0, i.e. in the region which we call Gaussian subjugation, where ('S POT.K') denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass -ln 'beta' and a bound state below the two-particle threshold. We develop a 'beta' analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in 'beta'.

Analytic function theory.

Includes bibliographies.

On the application of a new analytic method to the theory of curves and curved surfaces.

Mode of access: Internet.

Does the theory of planned behaviour explain condom use behaviour among men who have sex with men? A meta-analytic review of the literature

The aim of this meta-analysis was to explore whether the constructs in the theory of planned behaviour (TPB; i.e., attitude, subjective norm, perceived behavioural control, intention) explain condom use behaviour among men who have sex with men (MSM). Electronic databases were searched for studies that measured TPB variables and MSM condom use. Correlations were meta-analysed using a random effects model and path analyses. Moderation analyses were conducted for the time frame of the behavioural measure used (retrospective versus prospective). Attitude, subjective norm and perceived behavioural control accounted for 24.0 % of the variance in condom use intention and were all significant correlates. Intention and PBC accounted for 12.4 % of the variance in condom use behaviour. However, after taking intention into account, PBC was no longer significantly associated with condom use. The strength of construct relationships did not differ between retrospective and prospective behavioural assessments. The medium to large effect sizes of the relationships between the constructs in the TPB, which are consistent with previous meta-analyses with different behaviours or target groups, suggest that the TPB is also a useful model for explaining condom use behaviour among MSM. However, the research in this area is rather small, and greater clarity over moderating factors can only be achieved when the literature expands.

Educating the Other: Standpoint and Theory on the 'Internationalisation' of Higher Education

How adequate are current theoretical standpoints, tools and categories for explaining the flows of international students to Anglo/American/European universities? This essay takes a different analytic tact and historical standpoint to the study of them and us, insiders and outsiders (cf. Foley, Levinson & Hurtig, 2001), in the internationalisation of education.

User-web interactions : how wholistic/analytic web users search the web?

User-Web interactions have emerged as an important research in the field of information science. In this study, we examine extensively the Web searching performed by general users. Our goal is to investigate the effects of users’ cognitive styles on their Web search behavior in relation to two broad components: Information Searching and Information Processing Approaches. We use questionnaires, a measure of cognitive style, Web session logs and think-aloud as the data collection instruments. Our study findings show wholistic Web users tend to adopt a top-down approach to Web searching, where the users searched for a generic topic, and then reformulate their queries to search for specific information. They tend to prefer reading to process information. Analytic users tend to prefer a bottom-up approach to information searching and they process information by scanning search result pages.

A rebirth of physical activity in parents : applying a theory-based approach

Physical inactivity is a serious concern both nationally and internationally. Despite the numerous benefits of performing regular physical activity, many individuals lead sedentary lifestyles. Of concern, though, is research showing that some population sub-groups are less likely to be active, such as parents of young children. Although there is a vast amount of research dedicated to understanding people.s physical activity-related behaviours, there is a paucity of research examining those factors that influence parental physical activity. More importantly, research applying theoretical models to understand physical activity decision-making among this at-risk population is limited. Given the current obesity epidemic, the decline in physical activity with parenthood, and the many social and health benefits associated with regular physical activity, it is important that adults with young children are sufficiently active. In light of the dearth of research examining parental physical activity and the scant research applying a theory-based approach to gain this understanding, the overarching aim of the current program of research was to adopt a mixed methods approach as well as use sound theoretical frameworks to understand the regular physical activity behaviour of mothers and fathers with young children. This program of research comprised of three distinct stages: a qualitative stage exploring individual, social, and psychological factors that influence parental regular physical activity (Stage 1); a quantitative stage identifying the important predictors of parental regular physical activity intentions and behaviour using sound theoretical frameworks and testing a single-item measure for assessing parental physical activity behaviour (Stage 2); and a qualitative stage exploring strategies for an intervention program aimed at increasing parental regular physical activity (Stage 3). As a thesis by publication, eight papers report the findings of this program of research; these papers are presented according to the distinct stages of investigation that guided this program of research. Stage One of the research program comprised a qualitative investigation using a focus group/interview methodology with parents of children younger than 5 years of age (N = 40; n = 21 mothers, n = 19 fathers) (Papers 1, 2, and 3). Drawing broadly on a social constructionist approach (Paper 1), thematic analytic methods revealed parents. understandings of physical activity (e.g., requires effort), patterns of physical activity-related behaviours (e.g., grab it when you can, declining physical activity habits), and how constructions of social role expectations might influence parents. physical activity decision making (e.g., creating an active family culture, guilt and selfishness). Drawing on the belief-based framework of the TPB (Paper 2), thematic content analytic methods revealed parents. commonly held beliefs about the advantages (e.g., improves parenting practices), disadvantages (e.g., interferes with commitments), barriers (e.g., time), and facilitators (e.g., social support) to performing regular physical activity. Parents. normative beliefs about social approval from important others or groups (e.g., spouse/partner) were also identified. Guided by theories of social support, Paper Three identified parents. perceptions about the specific social support dimensions that influence their physical activity decision making. Thematic content analysis identified instrumental (e.g., providing childcare, taking over chores), emotional (e.g., encouragement, companionship), and informational support (e.g., ideas and advice) as being important to the decision-making of parents in relation to their regular physical activity behaviour. The results revealed also that having support for being active is not straightforward (e.g., guilt-related issues inhibited the facilitative nature of social support for physical activity). Stage Two of the research program comprised a quantitative examination of parents. physical activity intentions and behaviour (Papers 4, 5, 6, and 7). Parents completed an extended TPB questionnaire at Time 1 (N = 580; n = 288 mothers, n = 292 fathers) and self-reported their physical activity at Time 2, 1 week later (N = 458; n = 252 mothers, n = 206 fathers). Paper Four revealed key behavioural (e.g., improving parenting practices), normative (e.g., people I exercise with), and control (e.g., lack of time) beliefs as significant independent predictors of parental physical activity. A test of the TPB augmented to include the constructs of self-determined motivation and planning was assessed in Paper Five. The findings revealed that the effect of self-determined motivation on intention was fully mediated by the TPB variables and the impact of intention on behaviour was partially mediated by the planning variables. Slight differences in the model.s motivational sequence between the sexes were also noted. Paper Six investigated, within a TPB framework, a range of social influences on parents. intentions to be active. For both sexes, attitude, perceived behavioural control, group norms, friend general support, and an active parent identity predicted intentions, with subjective norms and family support further predicting mothers. intentions and descriptive norms further predicting fathers. intentions. Finally, the measurement of parental physical activity was investigated in Paper Seven of Stage Two. The results showed that parents are at risk of low levels of physical activity, with the findings also revealing validation support for a brief single-item physical activity measure. Stage Three of the research program comprised a qualitative examination of parents. (N = 12; n = 6 mothers, n = 6 fathers) ideas for strategies that may be useful for developing and delivering an intervention program aimed at increasing parental physical activity (Paper 8). Parents revealed a range of strategies for what to include in a physical activity intervention designed for parents of young children. For example, parents identified persuasion and information type messages, problem-solving strategies that engage parents in generating a priority list of their lifestyle commitments, and behavioural modification techniques such as goal setting and incentives. Social intervention strategies (e.g., social comparison, counselling) and environmental approaches (e.g., community-based integrative parent/child programs) were also identified as was a skill-based strategy in helping parents generate a flexible life/family plan. Additionally, a range of strategies for how to best deliver a parental physical activity intervention was discussed. Taken as a whole, Paper Eight found that adopting a multifaceted approach in both the design and implementation of a resultant physical activity intervention may be useful in helping to increase parental physical activity. Overall, this program of research found support for parents as a unique group who hold both similar and distinctive perceptions about regular physical activity to the general adult population. Thus, these findings highlight the importance of targeting intervention strategies for parents of young children. Additionally, the findings suggest that it might also be useful to tailor some messages specifically to each sex. Effective promotion of physical activity in parents of young children is essential given the low rate of activity in this population. Results from this program of research highlight parents as an at-risk group for inactivity and provide an important first step in identifying the factors that influence both mothers. and fathers. physical activity decision making. These findings, in turn, provide a foundation on which to build effective intervention programs aimed at increasing parents. regular physical activity which is essential for ensuring the health and well-being of parents with young children.

Qualitative analysis and eating disorders : Discourse analytic research on anorexia nervosa

The absence of qualitative analysis in mainstream research on eating disorders is discussed in the following article as being a weakness in developing theory and clinical practice. This article includes an analysis of interviews with British healthcare workers who manage anorexic patients. This analysis presents an example of qualitative methodology in the form of discourse analysis, which is argued to provide a systematic, yet flexible approach to research on eating disorders. The overwhelming prevalence of anorexia nervosa in women is specifically examined within the context of the identification of the "discourse of femininity. " The research findings are discussed in relation to the use of discursive practices that contribute to the maintenance and reproduction of clinical processes and their relative efficacy.

Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Renormalization methods in KAM theory

It is well known that an integrable (in the sense of Arnold-Jost) Hamiltonian system gives rise to quasi-periodic motion with trajectories running on invariant tori. These tori foliate the whole phase space. If we perturb an integrable system, the Kolmogorow-Arnold-Moser (KAM) theorem states that, provided some non-degeneracy condition and that the perturbation is sufficiently small, most of the invariant tori carrying quasi-periodic motion persist, getting only slightly deformed. The measure of the persisting invariant tori is large together with the inverse of the size of the perturbation. In the first part of the thesis we shall use a Renormalization Group (RG) scheme in order to prove the classical KAM result in the case of a non analytic perturbation (the latter will only be assumed to have continuous derivatives up to a sufficiently large order). We shall proceed by solving a sequence of problems in which theperturbations are analytic approximations of the original one. We will finally show that the approximate solutions will converge to a differentiable solution of our original problem. In the second part we will use an RG scheme using continuous scales, so that instead of solving an iterative equation as in the classical RG KAM, we will end up solving a partial differential equation. This will allow us to reduce the complications of treating a sequence of iterative equations to the use of the Banach fixed point theorem in a suitable Banach space.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Self-consistent theory of localization in weakly disordered systems

An analytic treatment of localization in a weakly disordered system is presented for the case where the real lattice is approximated by a Cayley tree. Contrary to a recent assertion we find that the mobility edge moves inwards into the band as disorder increases from zero.

A molecular theory of collective orientational relaxation in pure and binary dipolar liquids

A molecular theory of collective orientational relaxation of dipolar molecules in a dense liquid is presented. Our work is based on a generalized, nonlinear, Smoluchowski equation (GSE) that includes the effects of intermolecular interactions through a mean‐field force term. The effects of translational motion of the liquid molecules on the orientational relaxation is also included self‐consistently in the GSE. Analytic expressions for the wave‐vector‐dependent orientational correlation functions are obtained for one component, pure liquid and also for binary mixtures. We find that for a dipolar liquid of spherical molecules, the correlation function ϕ(k,t) for l=1, where l is the rank of the spherical harmonics, is biexponential. At zero wave‐vector, one time constant becomes identical with the dielectric relaxation time of the polar liquid. The second time constant is the longitudinal relaxation time, but the contribution of this second component is small. We find that polar forces do not affect the higher order correlation functions (l>1) of spherical dipolar molecules in a linearized theory. The expression of ϕ(k,t) for a binary liquid is a sum of four exponential terms. We also find that the wave‐vector‐dependent relaxation times depend strongly on the microscopic structure of the dense liquid. At intermediate wave vectors, the translational diffusion greatly accelerates the rate of orientational relaxation. The present study indicates that one must pay proper attention to the microscopic structure of the liquid while treating the translational effects. An analysis of the nonlinear terms of the GSE is also presented. An interesting coupling between the number density fluctuation and the orientational fluctuation is uncovered.

Molecular theory of dielectric relaxation in a dense binary dipolar liquid

A molecular theory of dielectric relaxation in a dense binary dipolar liquid is presented. The theory takes into account the effects of intra- and interspecies intermolecular interactions. It is shown that the relaxation is, in general, nonexponential. In certain limits, we recover the biexponential form traditionally used to analyze the experimental data of dielectric relaxation in a binary mixture. However, the relaxation times are widely different from the prediction of the noninteracting rotational diffusion model of Debye for a binary system. Detailed numerical evaluation of the frequency-dependent dielectric function epsilon-(omega) is carried out by using the known analytic solution of the mean spherical approximation (MSA) model for the two-particle direct correlation function for a polar mixture. A microscopic expression for both wave vector (k) and frequency (omega) dependent dielectric function, epsilon-(k,omega), of a binary mixture is also presented. The theoretical predictions on epsilon-(omega) (= epsilon-(k = 0, omega)) have been compared with the available experimental results. In particular, the present theory offers a molecular explanation of the phenomenon of fusing of the two relaxation channels of the neat liquids, observed by Schallamach many years ago.