On Logarithmic Smoothing of the Maximum Function

We consider the maximum function f resulting from a finite number of smooth functions. The logarithmic barrier function of the epigraph of f gives rise to a smooth approximation g of f itself, where >0 denotes the approximation parameter. The one-parametric family g converges – relative to a compact subset – uniformly to the function f as tends to zero. Under nondegeneracy assumptions we show that the stationary points of g and f correspond to each other, and that their respective Morse indices coincide. The latter correspondence is obtained by establishing smooth curves x() of stationary points for g , where each x() converges to the corresponding stationary point of f as tends to zero. In case of a strongly unique local minimizer, we show that the nondegeneracy assumption may be relaxed in order to obtain a smooth curve x().     

New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations, and a Shannon-type sampling formula is also obtained.     

Electron scattering on two-neutron halo nuclei: The case of He

The formalism to describe electron scattering reactions on two-neutron halo nuclei is developed. The halo nucleus is described as a three-body system (core +n + n), and the wave function is obtained by solving the Faddeev equations in coordinate space. We discuss elastic and quasielastic scattering using the impulse approximation to describe the reaction mechanism. We apply the method to investigate the case of electron scattering on ⁶He. Spectral functions, response functions, and differential cross sections are calculated for both neutron knockout and knockout by the electron.     

Conic Set-Valued Maps in Vector Optimization

The paper deals with the properties of a conic set-valued function defined on the set of all ideal points of vector programming problems. The results here about the continuity and derivability of this conic set-valued map, can be used to get information about the sensitivity of the problem and the stability of the order associated to every ideal point. Furthermore, it is proved that certain contingent cones are determined by the ideal conic set-valued map.      

Crystallization and crystal structure of poly(ester amide)s derived from L‐tartaric acid

The crystal structure and crystallization behavior of a series of poly(ester amide)s derived from L ‐tartaric acid, 1,6‐hexanediamine, and 6‐amino‐1‐hexanol were examined. The study included aregic polymers containing 5, 10, and 20% of ester groups in addition to the syndioregic polymer containing equal amounts of amide and ester groups. X‐ray diffraction data revealed that all the aregic poly(ester amide)s adopt the same crystal structure as the parent polyamide made of L ‐tartaric acid, and 1,6‐hexanediamine. In this structure, chains are slightly compressed and arranged as in the α‐form of nylon 66. Solid‐state nuclear magnetic resonance (NMR) revealed that ester groups are excluded from the crystal phase except for the case of the syndioregic polymer. Isothermal crystallization kinetics was analyzed according to the Avrami theory. Crystallization rates were found to decrease regularly with increasing contents in ester groups and with increasing crystallization temperature. Avrami exponent values close to 2 were found whereas spherulitic morphologies were observed by optical microscopy. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 116–125, 2007     

Ab initio study on the thermolysis of β-hydroxyolefins in gas phase

Thermolysis studies of β-hydroxyolefins in gas phase were realized using ab initio MP2 and DFT methods at the 6-31G^* levels to explore the possibility of determining a possible concerted process with a six-membered cyclic transition state (TS). Vibrational frequency calculations were carried out in order to confirm the stationary states, including TS structures. IRC calculations have been performed in all cases in order to verify that localized TS structures connect with the corresponding minimum stationary points associated with the reactant and products. With the aim of corroborating the postulated mechanism in the experimental study, we present a theoretical study in order to calculate the rate constants and the activation parameters. The results obtained are in accordance with the experimental conclusions.     

Steric effects on alkyl cation affinities of maingroup-element hydrides

We have carried out an extensive exploration of gas‐phase alkyl cation affinities (ACA) of archetypal anionic and neutral bases across the periodic system using zeroth order regular approximation‐relativistic density functional theory at BP86/QZ4P//BP86/TZ2P. ACA values were computed for the methyl, ethyl, i‐propyl and t‐butyl cations and compared with the corresponding proton affinities (PA). One purpose of this work is to provide an intrinsically consistent set of values of the 298 K ACA of all anionic (XH) and neutral bases (XH_n) constituted by maingroup‐element hydrides of groups 14–17 and the noble gases (group 18) along the periods 1–6. Another purpose is to determine and rationalize the trend in affinity for a cation as the latter varies from proton to t‐butyl cation. This undertaking is supported by quantitative bond energy decomposition analyses. Correlations are established between PA and ACA values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Adunanza del 25 Dicembre 1904 [418a]

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Adunanze dal 12 giugno all’II dicember 1904

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Pharmacognostic and acute toxicological evaluation of Scaptotrigona aff. postica propolis extract in pre-clinical assays

The propolis of Scaptotrigona aff. postica is popularly used in Maranh?o State, Brazil, for treating wounds and respiratory illnesses. Nevertheless, little is known about the chemical composition of this propolis and the adverse effects of its use. Hence, this study is a pharmacognostic characterisation of the propolis hydroalcoholic extract (PHE) from S. aff. postica. The methodology consisted of an evaluation of the sensory and chemical parameters. Chemical analysis of PHE indicated high concentrations of phenolic and triterpens substances, and the absence of steroids. Additionally, we evaluated the acute toxicity of propolis using 48 Swiss male and female mice. The animals received single doses of PHE (1000, 2000 or 4000 mg kg?1) orally and were observed for 14 days. After this period, the mice were sacrificed and the blood was used for biochemical and haematological evaluation. PHE did not induce any death, and the acute treatment significantly reduced serum concentrations of alanine aminotransferase and alkaline phosphatase. The resultant data indicate that PHE from S. aff. postica has low toxicity when used orally, even in high doses.