Analytic dependence of a periodic analog of a fundamental solution upon the periodicity paramaters

We prove an analyticity result in Sobolev-Bessel potential spaces for the periodic analog of the fundamental solution of a general elliptic partial differential operator upon the parameters which determine the periodicity cell. Then we show concrete applications to the Helmholtz and the Laplace operators. In particular, we show that the periodic analogs of the fundamental solution of the Helmholtz and of the Laplace operator are jointly analytic in the spatial variable and in the parameters which determine the size of the periodicity cell. The analysis of the present paper is motivated by the application of the potential theoretic method to periodic anisotropic boundary value problems in which the `degree of anisotropy' is a parameter of the problem

Existence results for a nonlinear nonautonomous transmission problem via domain perturbation

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism. First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter

Shape analyticity and singular perturbations for layer potential operators

We study the effect of regular and singular domain perturbations on layer potential operators for the Laplace equation. First, we consider layer potentials supported on a diffeomorphic image (Ω) of a reference set Ω and we present some real analyticity results for the dependence upon the map. Then we introduce a perforated domain Ω(ϵ) with a small hole of size ϵ and we compute power series expansions that describe the layer potentials on Ω(ϵ) when the parameter ϵ approximates the degenerate value ϵ = 0

Developing shared understandings of recovery and care: a qualitative study of women with eating disorders who resist therapeutic care

Background: This paper explores the differing perspectives of recovery and care of people with disordered eating. We consider the views of those who have not sought help for their disordered eating, or who have been given a diagnosis but have not engaged with health care services. Our aim is to demonstrate the importance of the cultural context of care and how this might shape people’s perspectives of recovery and openness to receiving professional care. Method: This study utilised a mixed methods approach of ethnographic fieldwork and psychological evaluation with 28 women from Adelaide, South Australia. Semi-structured interviews, observations, field notes and the Eating Disorder Examination were the primary forms of data collection. Data was analysed using thematic analysis. Results & Discussion: Participants in our study described how their disordered eating afforded them safety and were consistent with cultural values concerning healthy eating and gendered bodies. Disordered eating was viewed as a form of self-care, in which people protect and ‘take care’ of themselves. These subjectively experienced understandings of care underlie eating disorder behaviours and provide an obstacle in seeking any form of treatment that might lead to recovery. Conclusion: A shared understanding between patients and health professionals about the function of the eating disorder may avoid conflict and provide a pathway to treatment. These results suggest the construction of care by patients should not be taken for granted in therapeutic guidelines. A discussion considering how disordered eating practices are embedded in a matrix of care, health, eating and body practices may enhance the therapeutic relationship.Connie Musolino, Megan Warin, Tracey Wade and Peter Gilchris

Mapping properties of weakly singular periodic volume potentials in Roumieu classes

The analysis of the dependence of integral operators on perturbations plays an important role in the study of inverse problems and of perturbed boundary value problems. In this paper, we focus on the mapping properties of the volume potentials with weakly singular periodic kernels. Our main result is to prove that the map which takes a density function and a periodic kernel to a (suitable restriction of the) volume potential is bilinear and continuous with values in a Roumieu class of analytic functions. This result extends to the periodic case of some previous results obtained by the authors for nonperiodic potentials, and it is motivated by the study of perturbation problems for the solutions of boundary value problems for elliptic differential equations in periodic domains

Lymphocyte Subsets and Inflammatory Cytokines of Monoclonal Gammopathy of Undetermined Significance and Multiple Myeloma

Almost all multiple myeloma (MM) cases have been demonstrated to be linked to earlier monoclonal gammopathy of undetermined significance (MGUS). Nevertheless, there are no identified characteristics in the diagnosis of MGUS that have been helpful in differentiating subjects whose cancer may progress to a malignant situation. Regarding malignancy, the role of lymphocyte subsets and cytokines at the beginning of neoplastic diseases is now incontestable. In this review, we have concentrated our attention on the equilibrium between the diverse lymphocyte subsets and the cytokine system and summarized the current state of knowledge, providing an overview of the condition of the entire system in MGUS and MM. In an age where the therapy of neoplastic monoclonal gammopathies largely relies on drugs capable of acting on the immune system (immunomodulants, immunological checkpoint inhibitors, CAR-T), detailed knowledge of the the differences existing in benign and neoplastic forms of gammopathy is the main foundation for the adequate and optimal use of new drugs

Dependence of effective properties upon regular perturbations

In this survey, we present some results on the behavior of effective properties in presence of perturbations of the geometric and physical parameters. We first consider the case of a Newtonian fluid flowing at low Reynolds numbers around a periodic array of cylinders. We show the results of [43], where it is proven that the average longitudinal flow depends real analytically upon perturbations of the periodicity structure and the cross section of the cylinders. Next, we turn to the effective conductivity of a periodic two-phase composite with ideal contact at the interface. The composite is obtained by introducing a periodic set of inclusions into an infinite homogeneous matrix made of a different material. We show a result of [41] on the real analytic dependence of the effective conductivity upon perturbations of the shape of the inclusions, the periodicity structure, and the conductivity of each material. In the last part of the chapter, we extend the result of [41] to the case of a periodic two-phase composite with imperfect contact at the interface