Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids

The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach is the use of the BBGKY hierarchy for the time-dependent reduced density matrices. In contrast, our contribution is motivated by the kinetic theory of the weakly nonlinear Schrodinger equation. The main observation is that the results obtained in the latter context carry over directly to weakly interacting quantum fluids provided one does not insist on normal order in the Duhamel expansion. We discuss the term by term convergence of the expansion and the equilibrium time correlation .Comment: 43 pages, corrected typos, updated assumptions in sec.

Baseline psychosocial predictors of survival in localised breast cancer

Despite the large number of studies on the impact of psychosocial factors on breast cancer progression, there is no certainty about the contributing factors or processes involved. We investigated the relative impacts of socioeconomic, psychological, and psychosocial factors on survival in breast cancer. A consecutive sample of 102 patients (participation 82%) under 72 years of age with locoregional breast cancer completed validated questionnaires on coping with cancer, emotional expression (anger), perceived available support, noncancer life stresses, and quality of life 3−4 months after diagnosis. Survival times were measured from the date of diagnosis to the date of relapse and further to the date of death or date of last follow-up. Cumulative Cox regression analyses were carried out. After controlling for biological prognostic factors, age, and baseline treatment, longer survival was predicted by a long education and a minimising-related coping, while shorter survival was predicted by emotional defensiveness (antiemotionality), behavioural-escape coping, and a high level of perceived support. A shorter event-free time was also predicted by unemployment and depressive symptoms. Cancer survival is affected by a complex combination of psychosocial factors, among which minimising predicts a favourable prognosis and anger nonexpression and escape behaviour an unfavourable prognosis. Higher socioeconomic status is associated with longer survival. High scores in well-being scales may reflect emotional nonexpression

A new transportation distance between non-negative measures, with applications to gradients flows with Dirichlet boundary conditions

In this paper we introduce a new transportation distance between non-negative measures inside a domain $Omega$. This distance enjoys many nice properties, for instance it makes the space of non-negative measures inside $Omega$ a geodesic space, without any convexity assumption on $Omega$. Moreover, we will show that the gradient flow of the entropy functional w.r.t. this distance coincides with the heat equation, subject to the Dirichlet boundary condition equal to 1Dans ce papier, nous introduisons une nouvelle distance sur l\u2019espace des mesures positive dans un domaine $Omega$. Cette distance satisfait plusieurs proprietes interessantes : par exemple, elle fait de l\u2019espace des mesures positives dans $Omega$ un espace geodesique, sans aucune hypothese de convexite sur le domaine. De plus, on montre que le flot gradient de la fonctionnelle d\u2019entropie par rapport a cette distance donne lieu a l\u2019equation de la chaleur, avec condition de Dirichlet egale a 1 sur le bord

Existence of non-degenerate continua of singular radial solutions for several classes of semilinear elliptic problems

We establish the existence of countably many branches of uncountably many solutions to elliptic boundary value problems with subcritical, and subsuper critical growth. We also prove the existence of two branches of uncountably many solutions to a problem with jumping nonlinearities. This case is remarkable since, generically, this problem has only finitely many regular solutions