Continuous dependence estimates for nonlinear fractional convection-diffusion equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.Comment: In this version we have corrected Example 3.4 explaining the link with the results in [51,59

Kaon Weak Decays in Chiral Theories

The ten nonleptonic weak decays $K \to 2\pi$, $K \to 3\pi$, $K_L \to 2\gamma$, $K_S \to 2\gamma$, $K_L \to \pi^\circ 2\gamma$, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a $K_L \to \pi^\circ \gamma\gamma$ rate which is 60% shy of the experimental value. This suggests that ChPT is an unsatisfactory approach towards predicting kaon weak decays.Comment: 12 pages, 8 eps figure

The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Introducing creativity techniques and software apps to the care of people with dementia

This poster reports research to introduce creative problem solving techniques and software to the care for people with dementia in residential homes

Factors perceived to influence exercise adherence in women with breast cancer participating in an exercise programme during adjuvant chemotherapy: a focus group study

Aims and objectives. To explore factors influencing exercise adherence among women with breast cancer while following an exercise programme. Background. Earlier research shows that women with breast cancer decrease physical activity following the cancer diagnosis and that adhering to exercise interventions can be a challenge. Research is needed to identify motivational factors and barriers for exercise adherence among women during treatment for breast cancer. Design. This was a qualitative study to explore patient’s perceptions of the challenges to exercise adherence during a randomised, controlled trial. Methods. Twenty-seven women with early-stage breast cancer were purposively sampled for focus group interviews during 2011–2012 from their participation in the exercise intervention group during 2010–2012. Five focus groups were performed, and data analysis was completed using the systematic text condensation method. Results. During the focus group study, five main themes were identified, which described factors participants perceived to influence their adherence to exercise during chemotherapy: ‘side effects of breast cancer treatment as a barrier to exercise’, ‘restoring and maintaining normality in daily life motivates exercise’, ‘other valued activities compete with exercise’, ‘constructive support enhances exercise’ and ‘positive beliefs about efficacy and outcomes motivate exercise’. Conclusion. Adherence to exercise in women with breast cancer is challenged by internal and external conditions and may be improved by attention to the impact of treatment side effects and by supporting patient self-efficacy towards changing health behaviour. Relevance to clinical practice. Nurses should be aware that exercise adherence could be a challenge among women with breast cancer. They should help identify obstacles to exercise for women and ways to overcome them, as well as support them in their beliefs that they are capable of changing their health behaviou

Exercise: a path to wellness during adjuvant chemotherapy for breast cancer?

Background: Breast cancer treatment can represent a threat to a patient’s wellness. The role of exercise in perceived wellness in women with breast cancer merits further study. Objective: The objective of this study was to describe how exercise is perceived by women to influence their physical and psychosocial wellness at the time they were receiving chemotherapy. Methods: Five focus group interviews with a total of 27 women with early-stage breast cancer were conducted. Prior to the focus groups, the women had participated in an exercise intervention during chemotherapy treatment. Results: Three themes emerged from the analysis: exercise shapes feelings of psychological wellness; exercise stimulates feelings of physical wellness; and exercise influences social wellness. The women reported feeling stronger in a psychological sense after exercising, that the strength exercise improved their upper-limb functioning, and that engaging in exercise triggered social support and interactions. Conclusions: Exercise during breast cancer treatment is perceived to enhance the patients’ wellness on several dimensions and in particular psychological wellness. Exercise might support the patients’ efforts to restore their sense of wellness and enhance their level of daily life functioning. Implications for Practice: Cancer nurses should promote exercise as a wellness-fostering intervention during chemotherapy treatment. Focusing on how exercise can contribute to feelings of wellness may help women with breast cancer choose exercise as a health-promoting activity that contributes to their recovery

On Nonlinear Stochastic Balance Laws

We are concerned with multidimensional stochastic balance laws. We identify a class of nonlinear balance laws for which uniform spatial $BV$ bounds for vanishing viscosity approximations can be achieved. Moreover, we establish temporal equicontinuity in $L^1$ of the approximations, uniformly in the viscosity coefficient. Using these estimates, we supply a multidimensional existence theory of stochastic entropy solutions. In addition, we establish an error estimate for the stochastic viscosity method, as well as an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux and random source functions. Various further generalizations of the results are discussed

Consistently computing the K -> pi long distance weak transition

First we extract the long-distance (LD) weak matrix element from certain data and give compatible theoretical estimates. We also link this LD scale to the single-quark-line (SQL) transition scale and then test the latter SQL scale against the decuplet weak decay amplitude ratio. Finally, we study LD decay. All of these experimental and theoretical values are in good agreement. We deduce an average value from eleven experimental determinations compared to the theoretical SQL values average.Comment: 19 pages, 9 figures minor change to the Conclusions and abstract sectio

Polynomial Cointegration among Stationary Processes with Long Memory

n this paper we consider polynomial cointegrating relationships among stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and we consider a form of spectral regression around frequency zero. For these estimates, we establish consistency by means of a more general result on continuously averaged estimates of the spectral density matrix at frequency zeroComment: 25 pages, 7 figures. Submitted in August 200