Extension of Bernstein Polynomials to Infinite Dimensional Case

The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting. The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space.Comment: 14 pages. to appear on Journal of Approximation Theor

The many-property problem is your problem, too

The many-property problem has traditionally been taken to show that the adverbial theory of perception is untenable. This paper first shows that several widely accepted views concerning the nature of perception---including both representational and non-representational views---likewise face the many-property problem. It then presents a solution to the many-property problem for these views, but goes on to show how this solution can be adapted to provide a novel, fully compositional solution to the many-property problem for adverbialism. Thus, with respect to the many-property problem, adverbialism and several widely accepted views in the philosophy of perception are on a par, and the problem is solved

Form factor in K+ --> pi+ pi0 gamma: interference versus direct emission

We analyze the effect of a form factor in the magnetic contribution to K+ --> pi+ pi0 gamma. We emphasize how this can show up experimentally: in particular we try to explore the difference between a possible interference contribution and a form factor in the magnetic part. The form factor used for K+ --> pi+ pi0 gamma is analogous to the one for KL --> pi+ pi- gamma, experimentally well established.Comment: 9 pages revtex, 10 eps figures; improved presentation of theoretical and experimental status; refs. adde

A new critical curve for a class of quasilinear elliptic systems

We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non parametric form. We prove that if the exponents lie under a certain curve, then the system has only the trivial solution. These results hold without any restriction provided the possible solutions are more regular. The underlying framework is the classical Euclidean case as well as the Carnot groups setting.Comment: 28 page

Long-distance contribution to the forward-backward asymmetry in decays K+ --> pi+ l+ l-

The long-distance contribution via the two-photon intermediate state to the forward-backward asymmetries in decays K+ --> pi+ l+ l- (l=e and mu) has been studied within the standard model. In order to evaluate the dispersive part of the K+ --> pi+ gamma* gamma* --> pi+ l+ l- amplitude, we employ a phenomenological form factor to soften the ultraviolet behavior of the transition. It is found that, this long-distance transition, although subject to some theoretical uncertainties, can lead to significant contributions to the forward-backward asymmetries, which could be tested in the future high-precise experiments.Comment: 13 pages, 5 figure

Kaon decays and the flavour problem

After a brief introduction to the so-called flavour problem, we discuss the role of rare K decays in probing the mechanism of quark-flavour mixing. Particular attention is devoted to the formulation of the Minimal Flavour Violation hypothesis, as a general and natural solution to the flavour problem, and to the fundamental role of K -> pi nu nu-bar decays in testing this scenario.Comment: 10 pages, 6 figures, contribution to TH 2002 (Paris, July 2002

K^+ -> pi^+pi^0e^+e^-: a novel short-distance probe

We study the decay K^+ -> pi^+ pi^0 e^+ e^-, currently under analysis by the NA62 Collaboration at CERN. In particular, we provide a detailed analysis of the Dalitz plot for the long-distance, gamma^*-mediated, contributions (Bremsstrahlung, direct emission and its interference). We also examine a set of asymmetries to isolate genuine short-distance effects. While we show that charge asymmetries are not required to test short distances, they provide the best environment for its detection. This constitutes by itself a strong motivation for NA62 to study K^- decays in the future. We therefore provide a detailed study of different charge asymmetries and the corresponding estimated signals. Whenever possible, we make contact with the related processes K^+ -> pi^+ pi^0 gamma and K_L -> pi^+ pi^- e^+ e^- and discuss the advantages of K^+ -> pi^+ pi^0 e^+ e^- over them.Comment: 25 pages, 6 figure

The use of non-selective beta-blockers in patients with cirrhosis: more doubts than certainties

In conclusion, prospective RCT would be needed on the use of NSBBs in decompensated cirrhotic patients with ascites however these trials are difficult to organize and will need a large sample size. A case control study could be useful if the two groups were patients matched for MELD, MELD Na, creatinine, mean arterial pressure, with the same type of ascites (refractory, recurrent, severe) taking or not taking NSBBs. The better and more relevant end pointshould probably be survival. In the meanwhile, the Baveno recommendations can be utilized in clinical practice to remind that severe hypotension is a well-known contraindication for NSBBs which may suggest dose reduction or even therapy discontinuation. Last but not least, NSBBs may have several beneficial effects in patients with cirrhosis beyond the reduction in portal hypertension. They reduce markers of intestinal permeability, bacterial translocation and systemic inflammation, and also the risk of SBP (15,16). The risk to enlarge the indication to stop NSBBs in cirrhotic patients without a real evidence could be as to “throw the baby out with the bath water

Poverty and Time

We examine the measurement of individual poverty in an intertemporal context. In contrast to earlier contributions, we assign importance to the persistence in a state of poverty and we characterize a class of individual intertemporal poverty measures reflecting this feature. In addition, we axiomatize an aggregation procedure to obtain intertemporal poverty measures for entire societies and we illustrate our new indices with an application to EU countries.Intertemporal Poverty Measurement, Equity