Theory and applications of fuzzy Volterra integral equations

Formulations of fuzzy integral equations in terms of the Aumann integral do not reflect the behavior of corresponding crisp models. Consequently, they are ill-adapted to describe physical phenomena, even when vagueness and uncertainty are present. A similar situation for fuzzy ODEs has been obviated by interpretation in terms of families of differential inclusions. The paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations. The investigation is restricted to Volterra type equations with mildly restrictive conditions, but the methods are capable of extensive generalization to other types and more general assumptions. The results are illustrated by integral equations relating to control models with fuzzy uncertainties.

The future role of government in knowledge-based economies

In this article, we draw together aspects of contemporary theories of knowledge (particularly organisational knowledge) and complexity theory to demonstrate how appropriate conceptual rigor enables both the role of government and the directions of policy development in knowledge-based economies to be identified. Specifically we ask, what is the role of government in helping shape the knowledge society of the future? We argue that knowledge policy regimes must go beyond the modes of policy analysis currently used in innovation, information and technology policy because they are based in an industrial rather than post-industrial analytical framework. We also argue that if we are to develop knowledge-based economies, more encompassing images of the future than currently obtain in policy discourse are required. We therefore seek to stimulate and provoke an array of lines of thought about government and policy for such economies. Our objective is to focus on ideas more than argument and persuasion.

Resolving the puzzle of productive and destructive conflict in culturally heterogeneous workgroups: A communication accommodation theory approach

This study presents an investigation of the communicative behaviors and strategies employed in the stimulation and management of productive and destructive conflict in culturally heterogeneous workgroups. Using communication accommodation theory (CAT), we argue that the type and course of conflict in culturally heterogeneous workgroups is impacted by the communicative behaviors and strategies employed by group members during interactions. Analysis of data from participant observations, non-participant observations, semi-structured interviews, and self-report questionnaires support CA T-based predictions and provide fresh insights into the triggers and management strategies associated with conflict in culturally heterogeneous workgroups. In particular, results indicated that the more groups used discourse management Strategies, the more they experienced productive conflict. In addition, the use of explanation and checking of own and others' understanding was a major feature of productive conflict, while speech interruptions emerged as a strategy leading to potential destructive conflict. Groups where leaders emerged and assisted in reversing communication breakdowns were better able to manage their discourse, and achieved consensus On task processes. Contributions to the understanding of the triggers and the management of productive conflict in culturally heterogeneous workgroups are discussed.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Growth of a Bose-Einstein condensate: a detailed comparison of theory and experiment

We extend the earlier model of condensate growth of Davis et at (Davis M J, Gardiner C W and Ballagh R J 2000 Phys. Rev. A 62 063608) to include the effect of gravity in a magnetic trap. We carry out calculations to model the experiment reported by Kohl et al (Kohl M, Davis M J, Gardiner C W, Hansch T and Esslinger T 2001 Preprint cond-mat/0106642) who study the formation of a rubidium Bose-Einstein condensate for a range of evaporative cooling parameters. We find that, in the regime where our model is valid, the theoretical curves agree with all the experimental data with no fitting parameters. However, for the slowest cooling of the gas the theoretical curve deviates significantly from the experimental curves. It is possible that this discrepancy may be related to the formation of a quasicondensate.

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Microevolution in island forms: the roles of drift and directional selection in morphological divergence of a passerine bird

Theory predicts that in small isolated populations random genetic drift can lead to phenotypic divergence; however this prediction has rarely been tested quantitatively in natural populations. Here we utilize natural repeated island colonization events by members of the avian species complex, Zosterops lateralis, to assess whether or not genetic drift alone is an adequate explanation for the observed patterns of microevolutionary divergence in morphology. Morphological and molecular genetic characteristics of island and mainland populations are compared to test three predictions of drift theory: (1) that the pattern of morphological change is idiosyncratic to each island; (2) that there is concordance between morphological and neutral genetic shifts across island populations; and (3) for populations whose time of colonization is known, that the rate of morphological change is sufficiently slow to be accounted for solely by genetic drift. Our results are not consistent with these predictions. First, the direction of size shifts was consistently towards larger size, suggesting the action of a nonrandom process. Second, patterns of morphological divergence among recently colonized populations showed little concordance with divergence in neutral genetic characters. Third, rate tests of morphological change showed that effective population sizes were not small enough for random processes alone to account for the magnitude of microevolutionary change. Altogether, these three lines of evidence suggest that drift alone is not an adequate explanation of morphological differentiation in recently colonized island Zosterops and therefore we suggest that the observed microevolutionary changes are largely a result of directional natural selection.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

Testing insect movement theory: empirical analysis of pest data routinely collected from agricultural crops

Observations of an insect's movement lead to theory on the insect's flight behaviour and the role of movement in the species' population dynamics. This theory leads to predictions of the way the population changes in time under different conditions. If a hypothesis on movement predicts a specific change in the population, then the hypothesis can be tested against observations of population change. Routine pest monitoring of agricultural crops provides a convenient source of data for studying movement into a region and among fields within a region. Examples of the use of statistical and computational methods for testing hypotheses with such data are presented. The types of questions that can be addressed with these methods and the limitations of pest monitoring data when used for this purpose are discussed. (C) 2002 Elsevier Science B.V. All rights reserved.

Corporate stadium sponsorships, signaling theory, agency conflicts, and shareholder wealth

Contrary to the plethora of critical articles recently appearing in both the popular and business press, this carefully controlled investigation of 49 stadium- and arena-naming-rights agreement announcements provides striking evidence that such sponsorships can significantly enhance the stock prices of sponsoring companies. Indeed, the results of the study show that the average stadium sponsor's stock prices increased by 1.65 percent at the time of announcement of the programs-a result considerably in excess of the returns associated with other major marketing programs such as the signing of Olympic sponsorships and celebrity endorsers. A multiple regression analysis employing firm-specific changes in stock prices as the dependent variable and quantifiable corporate and sponsorship-related attributes as independent variables is also presented. Variables positively and significantly correlated with perceived sponsorship success include team-winning percentages, contract length, and high technology and locally based companies. Overall, the findings of the study are consistent with the novel hypothesis that, for some firms, the real value-added of a stadium sponsorship may lie in its ability to serve as an effective or honest signal of managerial confidence in the future of the company.

Child welfare workers' use of theory in working with physical child abuse: Implications for professional supervision

This article examines child welfare workers' understanding of physical child abuse and the Implications for those supervising these workers. The article Is based on the results of a study that involved In-depth Interviews and focus groups with statutory child welfare workers. Analysis revealed that workers' understanding of physical child abuse embodied a wide range of ideas that were generally consistent with existing literature. The study highlights the value and utility of a reflective approach In stimulating and making explicit the theoretical underpinnings of child welfare workers practice. Specific Implications for professional supervision are addressed.

Exact theory of sedimentation equilibrium made useful

The exact description of the thermodynamics of solutions has been used to describe, without approximation, the distribution of all the components of an incompressible solution in a centrifuge cell at sedimentation equilibrium. Thermodynamic parameters describing the interactions between solute components of known molar mass can be obtained by direct analysis of the experimental data. Interpretation of the measured thermodynamic parameters in terms of molecular interactions requires that an arbitrary distinction be made between nonassociative forces, like hard-sphere volume-exclusion and mean-field electrostatic repulsion or attraction, and specific short-range forces of association that give rise to the formation of molecular aggregates. Provided the former can be accounted for adequately, the effects of the latter can be elucidated in the form of good estimates of the equilibrium constants for the reactions of aggregation.