New degree bounds for polynomial threshold functions

A real multivariate polynomial p(x ₁, …, x _n ) is said to sign-represent a Boolean function f: {0,1} ⁿ →{−1,1} if the sign of p(x) equals f(x) for all inputs x∈{0,1} ⁿ . We give new upper and lower bounds on the degree of polynomials which sign-represent Boolean functions. Our upper bounds for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs.     

Wave propagation in anisotropic turbulent superfluids

In this work, a hydrodynamical model of Superfluid Turbulence previously formulated is applied to study how the presence of a non-isotropic turbulent vortex tangle modifies the propagation of waves. Two cases are considered: wave front parallel and orthogonal to the heat flux. Using a perturbation method, the first-order corrections due to the presence of the vortex tangle to the speeds and to the amplitudes of the first and second sound are determined. It is seen that the presence of the quantized vortices couples first and second sound, and the attenuation of second sound is proportional to the line density L if the wave propagates orthogonal to the heat flux, while it is proportional to the square root of L if the wave propagates parallel with the heat flux.     

Synthesis of optically active leukotriene (SRS-A) intermediates

In an approach to SRS-A and analogues thereof, the key (5$\text{S}$, 6$\text{S}$)-epoxy alcohol $\text{9}$ and its 6-epimer $\text{18}$ were prepared starting from $\text{D}$-araboascorbic acid and $\text{L}$-diethyl tartrate, respectively.     

A comparison of results obtained using liquid injection and headspace solid-phase microextraction for crude oil analysis by GC with mass spectrometer detection

Gas chromatographic (GC) analysis in solution and head space solid-phase microextraction (SPME)-GC analysis of a sample of crude oil gave different results. The SPME technique allowed the identification of a larger number of components than by using usual GC-mass spectrometry (MS). The method failed within the range of C14-C25 where GC-MS in solution allowed to obtain more representative results; on the contrary, SPME allowed to obtain data on the presence of volatile compounds that can not be identified in GC-MS analysis in solution. Furthermore, in the range C8-C12, SPME allowed to identify approximately 30 compounds not shown in the GC-MS analysis in solution. SPME analysis showed the presence of some alkenes not identified in GC-MS analysis in solution. SPME-GC-MS can be used in the analysis of crude oil in contaminated soil.     

Self-assembled monolayers of an oligo(ethylene oxide) disulfide and its corresponding thiol assembled from water: characterization and protein resistance

Self-assembled monolayers (SAMs) of the disulfide [S(CH2CH2O)6CH3]2 ([S(EO)6]2) on Au from 95% ethanol and from 100% water are described. Spectroscopic ellipsometry and reflection-absorption infrared spectroscopy indicate that the [S(EO)6]2 films are similar to the disordered films of HS(CH2CH2O)6CH3 ((EO)6) and HS(CH2)3O(CH2CH2O)5CH3 (C3EO5) at their protein adsorption minima. The [S(EO)6]2 SAMs exhibit constant film thickness (d) of 1.2 +/- 0.2 nm over long immersion times (up to 20 days) and do not attain the highly ordered, 7/2 helical structure of the (EO)6 and C3EO5 SAMs (d = 2.0 nm). Exposure of these self-limiting [S(EO)6]2 SAMs to bovine serum albumin show high resistance to protein adsorption.     

Enantioselective hydrogenation with self-assembling rhodium phosphane catalysts: influence of ligand structure and solvent

Three sets of new and related chiral phospholane and phosphepine ligands have been prepared for Rh-catalyzed enantioselective hydrogenation. The size and substitution pattern of the cyclic monophosphanes were varied. More importantly, the ligands differ in the nature of the heterocyclic group linked to the trivalent phosphorus atom: 2-pyridone or 2-alkoxypyridine. In the corresponding Rh complexes, the pyridone units of two monodentate P ligands can assemble by hydrogen bonding and form chelates. In contrast, synthetic precursors bearing alkoxypyridine appendages are not able to aggregate via intramolecular hydrogen bonds. The nature of self-assembly is dependent on the nature of the P ligand and the solvent used for the hydrogenation (CH2Cl2 vs. MeOH). These features affect the rate of the reaction as well as the enantioselectivity, which varied in the range of 0-99 % ee Complexation studies and DFT calculations were performed to explain these differences.     

Genetic and phytochemical difference between some Indian and Italian plants of Withania somnifera (L.) Dunal

The geographical distribution of Withania somnifera (L.) Dunal is quite wide. However, in Italy, this species is very rare and grows spontaneously only in Sicily and in Sardinia. The PCR-RAPD technique has been utilized in this work to determine the genetic relationship among Sicilian, Sardinian and Indian samples and the HPLC analysis of whitaferin A was used as a marker to evaluate the phytochemical differences. The genetic difference between Indian and Sicilian plants of W. somnifera turned out to be smaller than that between Indian and Sardinian plants of this species. The phytochemical analysis as well showed that the Sardinian specimen strongly differed from the Indian and Sicilian ones in its contents of withaferin A. Our results seem to confirm the hypothesis that the Italian populations of this species may not be indigenous but naturalised. Due to the high withaferin A content of the Sardinian samples, these plants could be used as a source for pharmaceutical purposes.     

Effects in B–doped KDP crystals irradiated with neutrons of large spectra energy

The results obtained for the r₆₃ electro‐optic coefficient of B‐doped and undoped KDP (KH₂PO₄) crystals irradiated with neutrons (including thermalized neutrons) produced by scattering of 30 Mev cyclotron protons on a target of Ta²⁰¹, are presented and compared to those obtained for non‐irradiated doped and undoped crystals. The B‐doped (H₃BO₃, Na₂B₄O₇ and Li₂B₄O₇) crystals were obtained by the conventional growth method by temperature decrease with 1 wt % dopant concentration in solution. The thermal neutron flux was around ϕ = 1. 10¹⁰ n/cm² s. Pulses of ∼15 μs long, in damped oscillatory mode (V= 8 kV, τ=1.95 μs) were used for the electro‐optic measurements. A Pockels cell, a photomultiplier, a He‐Ne laser (λ=632.8 nm, 5 mW, linearly polarized) and a Tk 720 A oscilloscope complete the experimental setup. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lifetimes and transition probabilities of Xe II: Experimental measurements and theoretical calculations

In this work we make an experimental and theoretical investigation of transition probabilities (A) and lifetimes of Xe II. Eighteen A_ij's corresponding to the 6p-6d array were measured using a Laser Produced Plasma (LPP) as the spectroscopic source. The ab initio (AI) and Least Square Fitting (LSF) approaches were used to calculate the atomic parameters. Relativistic corrections and Configuration Interaction (CI) effects have been taken into account using the HFR approach described by Cowan. Whereas the AI parameters corresponding to 6p levels are not very affected by CI effects, several of the 6d levels with J=1/2, 3/2and 5/2 making transitions to the fundamental levels 5p⁵ are affected by CI effects due to both, discrete nd and continuum states, modifying their lifetimes values. An extensive comparison with other measurements and calculations are made. In particular, concerned with branching ratio and forbidden transitions. Received 15 July 1999