On Hilbert extensions of Weierstrass' theorem with weights

In this paper we study the set of functions \GG-valued which can be approximated by \GG-valued continuous functions in the norm L^\infty_{\GG}(I,w), where $I$ is a compact interval, \GG is a real and separable Hilbert space and $w$ is certain \GG-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.Comment: Corrected version, 14 page

Two-Higgs-Doublet Models and Enhanced Rates for a 125 GeV Higgs

We examine the level of enhancement that can be achieved in the ZZ and \gamma\gamma channels for a two-Higgs-doublet model Higgs boson (either the light h or the heavy H) with mass near 125 GeV after imposing all constraints from LEP data, B physics, precision electroweak data, vacuum stability, unitarity and perturbativity. The latter constraints restrict substantially the possibilities for enhancing the gg -> h -> \gamma\gamma or gg -> H -> \gamma\gamma signal relative to that for the SM Higgs, hSM. Further, we find that a significant enhancement of the gg -> h -> \gamma\gamma or gg -> H -> \gamma\gamma signal in Type II models is possible only if the gg -> h -> ZZ or gg -> H -> ZZ mode is even more enhanced, a situation disfavored by current data. In contrast, in the Type I model one can achieve enhanced rates in the \gamma\gamma final state for the h while having the ZZ mode at or below the SM rate - the largest [gg -> h -> \gamma\gamma]/[gg -> hSM -> \gamma\gamma] ratio found is of order ~1.3 when the two Higgs doublet vacuum expectation ratio is tan\beta = 4 or 20 and the charged Higgs boson has its minimal LEP-allowed value of m_{H^\pm} = 90 GeV.Comment: 15 pages, 9 figure

Characterization of Plum Procyanidins by Thiolytic Depolymerization

The phenolic compounds of ?Green Gage? (GG) plums (Prunus domestica L.), ?Rainha Cla?udia Verde?, from a ?protected designation of origin? (PDO), in Portugal, were quantified in both flesh and skin tissues of plums collected in two different orchards (GG-V and GG-C). Analyzes of phenolic compounds were also performed on another GG European plum obtained in France (GG-F) and two other French plums, ?Mirabelle? (M) and ?Golden Japan? (GJ). Thiolysis was used for the first time in the analysis of plum phenolic compounds. This methodology showed that the flesh and skin contain a large proportion of flavan-3-ols, which account, respectively, for 92 and 85% in GJ, 61 and 44% in GG-V, 62 and 48% in GG-C, 54 and 27% in M, and 45 and 37% in GG-F. Terminal units of procyanidins observed in plums are mainly (+)-catechin (54?77% of all terminal units in flesh and 57?81% in skin). The GJ plums showed a phenolic composition different from all of the others, with a lower content of chlorogenic acid isomers and the presence of A-type procyanidins as dimers and terminal residues of polymerized forms. The average degree of polymerization (DPn) of plum procyanidins was higher in the flesh (5?9 units) than in the skin (4?6 units). Procyanidin B7 was observed in the flesh of all GG plums and in the skin of the Portuguese ones. Principal component analysis of the phenolic composition of the flesh and skin of these plums obtained after thiolysis allowed their distinction according to the variety and origin, opening the possibility of the use of phenolic composition for variety/origin identification

Strong effect of weak diffusion on scalar turbulence at large scales

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$, injection scale, $l$, and diffusive scale, $r_d$. The scales are well separated if the diffusivity is small, $r_d\ll l,L$, and one normally says that effects of diffusion are confined to smaller scales, $r\ll r_d$. However, if the velocity is single scale one finds that a weak dependence of the scalar correlations on the molecular diffusivity persists to even larger scales, e.g. $l\gg r\gg r_d$ \cite{95BCKL}. We consider the case of $L\gg l$ and report a counter-intuitive result -- the emergence of a new range of large scales, $L\gg r\gg l^2/r_d$, where the diffusivity shows a strong effect on scalar correlations.Comment: 4 pages, 1 figure, submitted to Physics of Fluid