Some properties of the solutions of obstacle problems with measure data

We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity.Comment: 18 page

Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Neuroendocrine responses in neonatal mother-deprived rabbits

To study both short- and long-term adaptation mechanisms activated by rabbits which were separated from their mothers (DLS) for 48 h between postnatal days 9 and 11, we examined plasma corticosterone concentrations before, during, and after DLS as well as the expression of glucocorticoid receptor (GR) in the hippocampus and the adrenal axis responses to a mild stress stimuli or exogenous ACTH injection. At postnatal day 10, plasma corticosterone concentration of DLS rabbits was similar to that of controls, but rose two-fold at day 11 (17.7 ± 1.3 vs. 9.3 ± 1.2 μg/dl, P < 0.01) and then decreased at day 12, when suckling was allowed again, to match those of controls with no difference thereafter. At postnatal day 14, both control and DLS rabbits had similar basal corticosterone concentrations (2.2 ± 0.4 vs. 2.3 ± 1.1 μg/dl, respectively) as well as at day 120 (8.8 ± 3.2 vs. 9.7 ± 2.8 μg/dl, respectively). After the standardized stress stimulus, plasma corticosterone concentrations were lower in DLS rabbits than controls at postnatal days 14 (P < 0.01) and 120 (P < 0.05). At day 120, corticosterone levels rose similarly seven-fold (P < 0.01) within 30 min after ACTH administration and remained sustained thereafter in both control and DLS rabbits. Positive immunoreactivity for GR was detected in the hippocampus and in the dorsal medial hypothalamic region at postnatal day 14. The present data suggest that 48 h DLS from postnatal days 9 to 11 results in a modified hypothalamic–pituitary–adrenal axis reactivity later in life

Pasta consumption and connected dietary habits: Associations with glucose control, adiposity measures, and cardiovascular risk factors in people with type 2 diabetes—TOSCA.IT study

Background: Pasta is a refined carbohydrate with a low glycemic index. Whether pasta shares the metabolic advantages of other low glycemic index foods has not really been investigated. The aim of this study is to document, in people with type-2 diabetes, the consumption of pasta, the connected dietary habits, and the association with glucose control, measures of adiposity, and major cardiovascular risk factors. Methods: We studied 2562 participants. The dietary habits were assessed with the European Prospective Investigation into Cancer and Nutrition (EPIC) questionnaire. Sex-specific quartiles of pasta consumption were created in order to explore the study aims. Results: A higher pasta consumption was associated with a lower intake of proteins, total and saturated fat, cholesterol, added sugar, and fiber. Glucose control, body mass index, prevalence of obesity, and visceral obesity were not significantly different across the quartiles of pasta intake. No relation was found with LDL cholesterol and triglycerides, but there was an inverse relation with HDL-cholesterol. Systolic blood pressure increased with pasta consumption; but this relation was not confirmed after correction for confounders. Conclusions: In people with type-2 diabetes, the consumption of pasta, within the limits recommended for total carbohydrates intake, is not associated with worsening of glucose control, measures of adiposity, and major cardiovascular risk factors

Leptin receptor expression and in vitro leptin actions on prostaglandin release and nitric oxide synthase activity in the rabbit oviduct

In this study, we have examined the presence and the distribution of receptors for leptin (Ob-R) in the oviduct of rabbits, and the effects of leptin on the release of prostaglandin (PG) F2alpha and PGE2 and on the activity of nitric oxide (NO) synthase (NOS) by oviducts cultured in vitro. Rabbits were killed during the follicular phase and the oviducts were incubated in vitro with leptin, PGF2alpha, PGE2, NO donor and inhibitors of NOS and cyclo-oxigenase (COX). Using immunohistochemistry, Ob-R-like positive reaction was observed only in the cytoplasm of secretory cells, having stronger intensity in the infundibulum and ampulla tracts than in the isthmus. Both leptin and NO donor inhibited PGE2 release, whereas they enhanced PGF2alpha release; NOS inhibitor alone or with leptin increased PGE2 and decreased PGF2alpha production; NOS activity was enhanced by leptin, while PGs did not affect this enzyme. This study suggests that the oviduct could be a potential target for endocrine regulation by leptin, whose circulating levels may act as a metabolic signal modulating oviductal PG release through mediation of the NOS/NO system

Statistical Consequences of Devroye Inequality for Processes. Applications to a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functions, then it holds uniformly in the function spaces. In the last appendix we prove that for the subclass of one-dimensional systems studied in \cite{young} the density of the absolutely continuous invariant measure belongs to a Besov space.Comment: 33 pages; companion of the paper math.DS/0412166; corrected version; to appear in Nonlinearit

A Wasserstein approach to the one-dimensional sticky particle system

We present a simple approach to study the one-dimensional pressureless Euler system via adhesion dynamics in the Wasserstein space of probability measures with finite quadratic moments. Starting from a discrete system of a finite number of "sticky" particles, we obtain new explicit estimates of the solution in terms of the initial mass and momentum and we are able to construct an evolution semigroup in a measure-theoretic phase space, allowing mass distributions with finite quadratic moment and corresponding L^2-velocity fields. We investigate various interesting properties of this semigroup, in particular its link with the gradient flow of the (opposite) squared Wasserstein distance. Our arguments rely on an equivalent formulation of the evolution as a gradient flow in the convex cone of nondecreasing functions in the Hilbert space L^2(0,1), which corresponds to the Lagrangian system of coordinates given by the canonical monotone rearrangement of the measures.Comment: Added reference

Effects of Dietary Zn/Se and α-Tocopherol Supplementation on Metabolic Milieu, Haemogram and Semen Traits of Breeding Stallions

Trace element status and metabolic milieu are sometimes overlooked in common veterinary clinical practice across animal species. The evaluation of requirements of trace elements, in fact, may be useful to prevent the perturbation of tissue-specific metabolic impair. In particular, essential trace elements in the diet play key roles within sub-cellular metabolic patterns with macro effects at the systemic level, like blood cell stability and semen quality. This effect was studied in breeding stallions, in which semen quality and haemogram are important for reproduction. A case-control feeding trial involved 40 stallions (age: 8–21&nbsp;years; body weight, BW: 510–531&nbsp;kg) of one stud centre, allotted to two experimental groups (n = 20 control, CON vs. n&nbsp;= 20 supplemented, SUPPL100), following a matched-pairs approach based on age. Supplemented stallions (SUPPL100) received a mixed mineral and vitamin supplement of Zn/Se and α-tocopherol (α-TOH) (100&nbsp;g/day stallion) to compound feed, fed as control diet to horses of the control group (CON). Horses resulted deficient in circulating α-TOH and Zn at the start, though clinically healthy. After supplementation, different plasmatic levels of α-TOH, Zn and Se were found between groups. Circulating basophils (BASO) and mean cell haemoglobin concentration (MCHC) were affected by the dietary treatment (p &lt; 0.05). Plasmatic Se affected monocyte count, haematocrit, mean cell volume and mean cell haemoglobin concentration. Semen traits were not affected by the dietary treatment per se, except for mobile/progressive sperm cells (%) of stallions aged &gt; 13&nbsp;years marginal circulating levels of α-TOH (p = 0.04). Ameliorating the micromineral status showed to improve the haemogram of stallions in view of circulating levels of Cu. Semen quality appeared to be strongly dependent on animal effects