A model for the quasi-static growth of brittle fractures based on local minimization

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the $L^2$-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Francfort and Marigo and in our previous paper, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith's criterion holds at the crack tips. We prove also that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.Comment: 20 page

On weak convergence of locally periodic functions

We prove a generalization of the fact that periodic functions converge weakly to the mean value as the oscillation increases. Some convergence questions connected to locally periodic nonlinear boundary value problems are also considered.Comment: arxiv version is already officia

Power calculation for gravitational radiation: oversimplification and the importance of time scale

A simplified formula for gravitational-radiation power is examined. It is shown to give completely erroneous answers in three situations, making it useless even for rough estimates. It is emphasized that short timescales, as well as fast speeds, make classical approximations to relativistic calculations untenable.Comment: Three pages, no figures, accepted for publication in Astronomische Nachrichte

Diffeomorphism-invariant properties for quasi-linear elliptic operators

For quasi-linear elliptic equations we detect relevant properties which remain invariant under the action of a suitable class of diffeomorphisms. This yields a connection between existence theories for equations with degenerate and non-degenerate coerciveness.Comment: 16 page

A second order minimality condition for the Mumford-Shah functional

A new necessary minimality condition for the Mumford-Shah functional is derived by means of second order variations. It is expressed in terms of a sign condition for a nonlocal quadratic form on $H^1_0(\Gamma)$, $\Gamma$ being a submanifold of the regular part of the discontinuity set of the critical point. Two equivalent formulations are provided: one in terms of the first eigenvalue of a suitable compact operator, the other involving a sort of nonlocal capacity of $\Gamma$. A sufficient condition for minimality is also deduced. Finally, an explicit example is discussed, where a complete characterization of the domains where the second variation is nonnegative can be given.Comment: 30 page

Hepatitis C virus and non-Hodgkin's lymphomas: Meta-analysis of epidemiology data and therapy options.

Hepatitis C virus (HCV) is a global health problem affecting a large fraction of the world\u2019s population: This virus is able to determine both hepatic and extrahepatic diseases. Mixed cryoglobulinemia, a B-cell \u201cbenign\u201d lymphoproliferative disorders, represents the most closely related as well as the most investigated HCV-related extrahepatic disorder. Since this virus is able to determine extrahepatic [non-Hodgkin\u2019s lymphoma (NHL)] as well as hepatic malignancies (hepatocellular carcinoma), HCV has been included among human cancer viruses. The most common histological types of HCV-associated NHL are the marginal zone, the lymphoplasmacytic and diffuse large cell lymphomas. The role of the HCV in the pathogenesis of the B-cell lymphoproliferative disorders is confirmed also by the responsiveness of the NHL to antiviral therapy. The purpose of this review is to provide an overview of the recent literature and a meta analysis of the epidemiology data, to explain the role of HCV in the development of NHL\u2019s lymphoma. Furthermore, the possibility to treat these HCV-related NHL with the antiviral therapy or with other therapeutic options, like chemotherapy, is also discussed

Classic Kaposi's sarcoma in Italy, 1985–1998

To evaluate incidence rates (IRs) of classic Kaposi's sarcoma (CKS) in Italy after the spread of AIDS, we distinguished CKS from AIDS-related KS (AKS) using an ‘ad hoc' record linkage procedure between 15 Cancer Registries (CRs) (21% of the Italian population) and the national AIDS Registry. Between 1985 and 1998, 874 cases of CKS and 634 cases of AKS were diagnosed in the study areas. CKS accounted for 16 and 27% of KS cases below 55 years of age in men and women, respectively, but for 91 and 100% of those above age 55. The IRs for CKS were 1.0/ in men and 0.4/100 000 in women, but they varied between 0.3 in Umbria and 4.7 in Sassari in men, and between 0.1 in Parma and 1.7 in Sassari in women. IRs of CKS in both genders were stable between 1985–1987 and 1993–1998. In Northern and Central CRs the IR (adjusted for age and gender) for CKS was 0.5 in individuals born in the same area, but 1.6 in individuals born in Southern Italy or in the Islands (rate ratio=3.2) suggesting that KS-associated herpesvirus, the cause of KS, is acquired early in life

Towards Critical Occidentalism Studies: Re-inventing the 'West' and 'Japan' in Mangaesque Popular Cultures

This paper investigates the reproduction of the imagined geography of the ‘West’ in contemporary Japan by employing a relational, intersectional and positional approach in order to examine Occidentalism and its hegemonic identification and othering process. Particular attention will be paid to emerging Japanese subcultures enacting a parodic and sexualised re-invention of Westernness and Japaneseness within a globalising mangaesque media mix