Lie group symmetries as integral transforms of fundamental solutions

We obtain fundamental solutions for PDEs of the form ut = σ xγ ux x + f (x) ux - μ xr u by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform. © 2006 Elsevier Inc. All rights reserved

Some recent developments in the theory of Lie group symmetries for PDEs

Lie group symmetry methods provide a powerful tool for the analysis of PDEs. Over the last thirty years, considerable progress has been made in the development of this field. In this article, we provide a brief introduction to the method developed by Lie for the systematic computation of symmetries, then move on to a survey of some of the more recent developments. Our focus is on the use of Lie symmetry methods to construct fundamental solutions of partial differential equations of parabolic type. We will show how recent work has uncovered an intriguing connection between Lie symmetry analysis and the theory of integral transforms. Fundamental solutions of families of PDEs which arise in various applications, can be obtained by exploiting this connection. The major applications we give will be in financial mathematics. We will illustrate our results with the problem of pricing a so called zero coupon bond, as well as giving some applications to option pricing. We also discuss some results on group invariant solutions and show how an important PDE in nilpotent harmonic analysis can be studied via its group invariant solutions

Lie symmetry methods for multidimensional linear parabolic PDEs and diffusions

University of Technology, Sydney. Faculty of Science.No abstract available

Enhancement of CO2 Uptake and Selectivity in a Metal-Organic Framework by the Incorporation of Thiophene Functionality

The complex [Zn2(tdc)2dabco] (H2tdc = thiophene-2,5-dicarboxylic acid; dabco = 1,4-diazabicyclooctane) shows a remarkable increase in carbon dioxide (CO2) uptake and CO2/dinitrogen (N2) selectivity compared to the nonthiophene analogue [Zn2(bdc)2dabco] (H2bdc = benzene-1,4-dicarboxylic acid; terephthalic acid). CO2 adsorption at 1 bar for [Zn2(tdc)2dabco] is 67.4 cm3·g–1 (13.2 wt %) at 298 K and 153 cm3·g–1 (30.0 wt %) at 273 K. For [Zn2(bdc)2dabco], the equivalent values are 46 cm3·g–1 (9.0 wt %) and 122 cm3·g–1 (23.9 wt %), respectively. The isosteric heat of adsorption for CO2 in [Zn2(tdc)2dabco] at zero coverage is low (23.65 kJ·mol–1), ensuring facile regeneration of the porous material. Enhancement by the thiophene group on the separation of CO2/N2 gas mixtures has been confirmed by both ideal adsorbate solution theory calculations and dynamic breakthrough experiments. The preferred binding sites of adsorbed CO2 in [Zn2(tdc)2dabco] have been unambiguously determined by in situ single-crystal diffraction studies on CO2-loaded [Zn2(tdc)2dabco], coupled with quantum-chemical calculations. These studies unveil the role of the thiophene moieties in the specific CO2 binding via an induced dipole interaction between CO2 and the sulfur center, confirming that an enhanced CO2 capacity in [Zn2(tdc)2dabco] is achieved without the presence of open metal sites. The experimental data and theoretical insight suggest a viable strategy for improvement of the adsorption properties of already known materials through the incorporation of sulfur-based heterocycles within their porous structures

Extending basic principles of measurement models to the design and validation of Patient Reported Outcomes

A recently published article by the Scientific Advisory Committee of the Medical Outcomes Trust presents guidelines for selecting and evaluating health status and health-related quality of life measures used in health outcomes research. In their article, they propose a number of validation and performance criteria with which to evaluate such self-report measures. We provide an alternate, yet complementary, perspective by extending the types of measurement models which are available to the instrument designer. During psychometric development or selection of a Patient Reported Outcome measure it is necessary to determine which, of the five types of measurement models, the measure is based on; 1) a Multiple Effect Indicator model, 2) a Multiple Cause Indicator model, 3) a Single Item Effect Indicator model, 4) a Single Item Cause Indicator model, or 5) a Mixed Multiple Indicator model. Specification of the measurement model has a major influence on decisions about item and scale design, the appropriate application of statistical validation methods, and the suitability of the resulting measure for a particular use in clinical and population-based outcomes research activities

Understanding the Interplay Among Regulatory Self-Efficacy, Moral Disengagement, and Academic Cheating Behaviour During Vocational Education: A Three-Wave Study

The literature has suggested that to understand the diffusion of unethical conduct in the workplace, it is important to investigate the underlying processes sustaining engagement in misbehaviour and to study what occurs during vocational education. Drawing on social-cognitive theory, in this study, we longitudinally examined the role of two opposite dimensions of the self-regulatory moral system, regulatory self-efficacy and moral disengagement, in influencing academic cheating behaviour. In addition, in line with the theories highlighting the bidirectional relationship between cognitive processes and behaviour, we aimed to also examine the reciprocal influence of behaviour on these dimensions over time. Overall, no previous studies have examined the longitudinal interplay between these variables. The sample included 866 (62.8% female) nursing students who were assessed three times annually from the beginning of their vocational education. The findings from a cross-lagged model confirmed that regulatory self-efficacy and moral disengagement have opposite influences on cheating behaviour, that regulatory self-efficacy negatively influences not only the engagement in misconduct but also the justification mechanisms that allow the divorce between moral standards and action, and that moral disengagement and cheating behaviour reciprocally support each other over time. Specifically, not only did moral disengagement influence cheating behaviour even when controlling for its prior levels, but also cheating behaviour affected moral disengagement one year later, controlling for its prior levels. These findings suggest that recourse to wrongdoing could gradually lead to further normalising this kind of behaviour and morally desensitising individuals to misconduct

Female Audit Partners and Extended Audit Reporting: UK Evidence

This study investigates whether audit partner gender is associated with the extent of auditor disclosure and the communication style regarding risks of material misstatements that are classified as key audit matters (KAMs). Using a sample of UK firms during the 2013–2017 period, our results suggest that female audit partners are more likely than male audit partners to disclose more KAMs with more details after controlling for both client and audit firm attributes. Furthermore, female audit partners are found to use a less optimistic tone and provide less readable audit reports, compared to their male counterparts, suggesting that behavioural variances between female and male audit partners may have significant implications on their writing style. Therefore, this study offers new insights on the role of audit partner gender in extended audit reporting. Our findings have important implications for audit firms, investors, policymakers and governments in relation to the development, implementation and enforcement of gender diversity