Fermat-linked relations for the Boubaker polynomial sequences via Riordan matrices analysis

The Boubaker polynomials are investigated in this paper. Using Riordan matrices analysis, a sequence of relations outlining the relations with Chebyshev and Fermat polynomials have been obtained. The obtained expressions are a meaningful supply to recent applied physics studies using the Boubaker polynomials expansion scheme (BPES).Comment: 12 pages, LaTe

Point sets on the sphere S2\mathbb{S}^2 with small spherical cap discrepancy

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order $N^{-1/2}$. Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given

Quasi-Monte Carlo rules for numerical integration over the unit sphere S2\mathbb{S}^2

We study numerical integration on the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ using equal weight quadrature rules, where the weights are such that constant functions are integrated exactly. The quadrature points are constructed by lifting a $(0,m,2)$-net given in the unit square $[0,1]^2$ to the sphere $\mathbb{S}^2$ by means of an area preserving map. A similar approach has previously been suggested by Cui and Freeden [SIAM J. Sci. Comput. 18 (1997), no. 2]. We prove three results. The first one is that the construction is (almost) optimal with respect to discrepancies based on spherical rectangles. Further we prove that the point set is asymptotically uniformly distributed on $\mathbb{S}^2$. And finally, we prove an upper bound on the spherical cap $L_2$-discrepancy of order $N^{-1/2} (\log N)^{1/2}$ (where $N$ denotes the number of points). This slightly improves upon the bound on the spherical cap $L_2$-discrepancy of the construction by Lubotzky, Phillips and Sarnak [Comm. Pure Appl. Math. 39 (1986), 149--186]. Numerical results suggest that the $(0,m,2)$-nets lifted to the sphere $\mathbb{S}^2$ have spherical cap $L_2$-discrepancy converging with the optimal order of $N^{-3/4}$

Jet production in ep collisions at high Q(2) and determination of alpha(s)

The production of jets is studied in deep-inelastic e(+/-) p scattering at large negative four momentum transfer squared 150 LT Q(2) LT 15000 GeV2 using HERA data taken in 1999-2007, corresponding to an integrated luminosity of 395 pb(-1). Inclusive jet, 2-jet and 3-jet cross sections, normalised to the neutral current deep-inelastic scattering cross sections, are measured as functions of Q(2), jet transverse momentum and proton momentum fraction. The measurements are well described by perturbative QCD calculations at next-to-leading order corrected for hadronisation effects. The strong coupling as determined from these measurement

A prodrug approach to increasing the oral potency of a phenolic drug. 1. Synthesis, characterization, and stability of an O-(imidomethyl) derivative of 17β-estradiol

An O‐(saccharinylmethyl) prodrug was synthesized to improve the poor oral potency of the phenolic drug 17β‐estradiol. This O‐(imidomethyl) type of prodrug was designed to undergo chemical hydrolysis and to be a poor substrate for enzymatic hydrolysis. At 37 °C, it was found to exhibit half‐lives of about 13 min in 50% methanol:pH 7.0 (v/v) phosphate buffer, about 3 min in rat plasma, about 15 min in human plasma, and about 50 min in 20% rat liver homogenate. Introduction of the enzyme poison tetraethyl pyrophosphate or the protein denaturant sodium fluoride into rat plasma had no significant effect on the half‐life. Thus, the observed increased rate of hydrolysis in biological media is not due to enzymatic catalysis but to a nonspecific solventlike effect. The fact that the rate of hydrolysis in the methanol:buffer exhibited a first‐order dependence on the hydroxide ion concentration and that the rate of hydrolysis increased with increasing methanol concentrations up to 70% supported an S2 mechanism of hydrolysis for the prodrug. These results suggest that an O‐(imidomethyl) type prodrug is insensitive to enzymatic catalysis of hydrolysis yet may hydrolyze quickly enough to release 17β‐estradiol faster than 17β‐estradiol is conjugated and excreted. Copyrigh

Mechanism of Hydrolysis of O-Imidomethyl Derivatives of Phenols

Three series of O-imidomethyl derivatives of para-substituted phenolic compounds were synthesized and their rates of hydrolysis were studied. Saccharin, phthalimide, and succinimide served as the imide portions of the derivatives. Their rates of hydrolysis were found to be first order with respect to hydroxide from pH 7.0 to 10 or 11 and dependent on the acidity (leaving group potential) of both the imide and the phenol portions. The more acidic the imide or the phenol, the faster the rate of hydrolysis. However, the rates of hydrolysis were more sensitive to the acidity of the phenol. Trapping experiments with cyanide also suggested that the phenol anion was functioning as the leaving group in what is apparently an S2 reaction. An amide derivative was found to hydrolyze more slowly than predicted from the analogous imide series and the pK of the amide. This result is apparently due partially to stereoelectronic constraints in the imide series that cause the CH−O bond to be oriented more nearly perpendicular to the plane of the C(═O)N group and hence more accessible to nucleophilic attack

Effect of price on pleasantness ratings and use intentions of a functional chocolate bar in the presence and absence of a health claim

The effect of price information on hedonic and use intention responses to a chocolate bar was investigated in the absence and presence of a health claim related to energy, satiety value and cholesterol content. First, Finnish students (n = 79) tasted and rated blind three chocolate bars (one regular, two containing functional ingredients). Second, one group (“Informed,” n = 40) evaluated the samples with the health claim and price information, the other group (“Control,” n = 39) as a regular bar with price information only. A separate focus group (n = 6) interview was conducted to obtain further views of the claim and samples. Neither the health claim nor the price affected pleasantness ratings, while the increasing price significantly reduced the likelihood of buying and preferred frequency of eating the chocolate bar in both groups. Price affected the likelihood of buying more strongly among females than among males, and involvement with chocolate bars affected the likelihood of buying in the control, but not in the informed group. The focus group interview indicated that healthfulness might be irrelevant for chocolate products. Overall, price heavily affected the likelihood of buying the target product, but price and the health claim were incapable of altering hedonic responses to it