Infinite dimensional duality and applications

The usual duality theory cannot be applied to infinite dimensional problems because the underlying constraint set mostly has an empty interior and the constraints are possibly nonlinear. In this paper we present an infinite dimensional nonlinear duality theory obtained by using new separation theorems based on the notion of quasi-relative interior, which, in all the concrete problems considered, is nonempty. We apply this theory to solve the until now unsolved problem of finding, in the infinite dimensional case, the Lagrange multipliers associated to optimization problems or to variational inequalities. As an example, we find the Lagrange multiplier associated to a general elastic–plastic torsion problem.     

A new class of chiral organogermanes derived from C2-symmetric dithiols: synthesis,characterization and stereoselective free radical reactions

A new class of dithiostannanes and dithiogermanes have been prepared from 1,1'-binaphthyl-2,2'-dithiol and 3,3'-bis(trimethylsilyl)-1,1'-binaphtho-2,2'-dithiol. While reduction of 4-butyl-4-chloro-3,5-dithia-4-stanna-cyclohepta[2,1-a;3,4-a']dinaphthalene to the corresponding tin hydride was unsuccessful, 4-tert-butyl-3,5-dithia-4-germa-cyclohepta[2,1-a;3,4-a']dinaphthalene and 4-tert-butyl-2,6-bis(trimethylsilyl)-3,5-dithia-4-germa-cyclohepta[2,1-a;3,4-a']dinaphthalene were obtained by reduction of the parent germanium chlorides with NaBH(4) and LiBH(4), respectively. Kinetic constants for hydrogen transfer to a primary alkyl radical were measured for both germanium hydrides. Reduction of alpha-halo carbonyl compounds by these germanium hydrides occurs with moderate ee values (up to 42%), while hydrogermylation of methyl methacrylate occurs with low selectivity (<3/1) for the former hydride but high selectivity (>10/1) for the latter.     

Chemical fingerprinting of Equisetum arvense L. using HPTLC densitometry and HPLC

Equisetum arvense L. is a herbaceous medicinal plant, commonly known as horsetail, whose extracts have been reported to possess diuretic and haemostatic properties. The aim of this study was to evaluate the use of fingerprint chromatographic methods on commercially available raw materials or preparations of E. arvense L. in order to ascertain their quality and identify possible adulterants using HPLC and HPTLC densitometry. Two chromatographic methods were used to determine the chemical fingerprints of E. arvense and other allied species. The first was based on HPTLC identification followed by densitometric measurement at 350?nm. The second was based on HPLC separation. The ease of sample preparation and the possibility of simultaneous analysis of several samples in a short time make HPTLC a method of choice for the comprehensive quality evaluation of herbal products.     

On the convergence of sequences of stationary jump Markov processes

This paper presents two main results: first, a Liapunov type criterion for the existence of a stationary probability distribution for a jump Markov process; second, a Liapunov type criterion for existence and tightness of stationary probability distributions for a sequence of jump Markov processes. If the corresponding semigroups T_N(t) converge, under suitable hypotheses on the limit semigroup, this last result yields the weak convergence of the sequence of stationary processes (T_N(t), π_N) to the stationary limit one.     

Positive solutions for some Schrödinger equations having partially periodic potentials

This paper is concerned with the problem of finding positive solutions of the equation −Δu+(a_∞+a(x))u=|u|^q−2u, where q is subcritical, Ω is either RN or an unbounded domain which is periodic in the first p coordinates and whose complement is contained in a cylinder , a_∞>0, a∈C(RN,R) is periodic in the first p coordinates, infx∈RN(a_∞+a(x))>0 and a(x^′,x^″)→0 as |x^″|→∞ uniformly in x^′. The cases a?0 and a?0 are considered and it is shown that, under appropriate assumptions on a, the problem has one solution in the first case and p+1 solutions in the second case when p?N−2.     

On some abstract variable domain hyperbolic differential equations

The Cauchy problem is studied for a class of linear abstract differential equations of hyperbolic type with variable domain. Existence and uniqueness results are proved for (suitably defined) weak solutions. Some applications to P.D.E. are also given: they concern linear hyperbolic equations either in non-cylindrical regions or with mixed variable lateral conditions.This work was supported in part by the M.U.R.S.T. (Italy), through 60% and 40% research funds, and by the «G.N.AF.A. of the C.N.R.» (Italy).     

Territorial origin of olive oil: representing georeferenced maps of olive oils by NMR profiling

ABSTRACT Proton NMR profiling is nowadays a consolidated technique for the identification of geographical origin of food samples. The common approach consists in correlating NMR spectra of food samples to their territorial origin by multivariate classification statistical algorithms. In the present work, we illustrate an alternative perspective to exploit territorial information, contained in the NMR spectra, which is based on the implementation of a geographic information system (GIS). Nuclear magnetic resonance spectra are used to build a GIS map permitting the identification of territorial regions having strong similarities in the chemical content of the produced food (terroir units). These terroir units can, in turn, be used as input for labeling samples to be analyzed by traditional classification methods. In this work, we describe the methods and the algorithms that permit to produce GIS maps from NMR profiles and apply the described method to the analysis of the geographical distribution of olive oils in an Italian region. In particular, we analyzed by ¹H NMR up to 98 georeferenced olive oil samples produced in the Abruzzo Italian region. By using the first principal component of the NMR variables selected according to the Moran test, we produced a GIS map, in which we identified two regions incidentally corresponding to the provinces of Teramo and Pescara. We then labeled the samples according to the province of provenience and built an LDA model that provides a classification ability up to 99% . A comparison between the variables selected in the geostatistics and classification steps is finally performed. Copyright © 2016 John Wiley & Sons, Ltd.     

A model of imperfect interface with damage

In this paper two models of damaged materials are presented. The first one describes a structure composed by two adherents and an adhesive which is micro-cracked and subject to two different regimes, one in traction and one in compression. The second model is a model of interface derived from the first one through an asymptotic analysis, and it can be interpreted as a model for contact with adhesion and unilateral constraint. Simple numerical examples are presented.     

Studies on crude oil‐water biphasic mixtures by low‐field NMR

Low‐field ¹H NMR was used in this work for the analysis of mixtures involving crude oils and water. CPMG experiments were performed to determine the transverse relaxation time (T₂) distribution curves, which were computed by the inverse Laplace transform of the echo decay data. The instrument's ability of quantifying water and petroleum in biphasic mixtures following different methodologies was tested. For mixtures between deionized water and petroleum, one achieved excellent results, with root mean squared error of cross‐validation (RMSECV) of 0.8% for a regression between the water content (wt %) and the relative area of the water peak in the T₂ distribution curve, or a standard deviation of 0.9% for the relationship between the water content and the relative water peak area, corrected by the relative hydrogen index of the crude. In the case of biphasic mixtures of Mn²⁺‐doped water and crude oils, the best result of RMSECV = 1.6% was achieved by using the raw magnetization decay data for a partial least squares regression. Copyright © 2012 John Wiley & Sons, Ltd.     

Doubly diastereoselective conjugate addition of enantiopure lithium amides to enantiopure N-enoyl oxazolidin-2-ones: a mechanistic probe

The doubly diastereoselective conjugate addition of the antipodes of lithium N-benzyl-N-(α-methylbenzyl)amide to a range of enantiopure N-enoyl oxazolidin-2-ones has been used as a mechanistic probe to determine that the reactive conformation is the anti-s-cis form. The β-amino carbonyl products resulting from these conjugate addition reactions are useful templates for further elaboration into an α,β,α-pseudotripeptide.