On the stereochemistry of photoaddition between α,β-unsaturated ketones and olefins—II

Some years ago an empirical rule, which allows the prediction of product stereochemistry in cis-photocycloaddition reactions of α,β-unsaturated ketones and olefins was tentatively proposed. Several additional examples, both selected from the literature and synthesized in our laboratory, seem to strengthen the validity of the rule.     

On solving the Lagrangian dual of integer programs via an incremental approach

The Lagrangian dual of an integer program can be formulated as a min-max problem where the objective function is convex, piecewise affine and, hence, nonsmooth. It is usually tackled by means of subgradient algorithms, or multiplier adjustment techniques, or even more sophisticated nonsmooth optimization methods such as bundle-type algorithms. Recently a new approach to solving unconstrained convex finite min-max problems has been proposed, which has the nice property of working almost independently of the exact evaluation of the objective function at every iterate-point.     

Elliptic systems with nonlinearity q greater or equal than two with controlled growth. Global Hölder continuity of solutions to the Dirichlet problem

Hölder regularity up to the boundary of the solutions to the Dirichlet problem for second order elliptic systems with nonlinearity q>2 and with controlled growth is proved when n?q+2.     

Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations

We introduce a proximal bundle method for the numerical minimization of a nonsmooth difference-of-convex (DC) function. Exploiting some classic ideas coming from cutting-plane approaches for the convex case, we iteratively build two separate piecewise-affine approximations of the component functions, grouping the corresponding information in two separate bundles. In the bundle of the first component, only information related to points close to the current iterate are maintained, while the second bundle only refers to a global model of the corresponding component function. We combine the two convex piecewise-affine approximations, and generate a DC piecewise-affine model, which can also be seen as the pointwise maximum of several concave piecewise-affine functions. Such a nonconvex model is locally approximated by means of an auxiliary quadratic program, whose solution is used to certify approximate criticality or to generate a descent search-direction, along with a predicted reduction, that is next explored in a line-search setting. To improve the approximation properties at points that are far from the current iterate a supplementary quadratic program is also introduced to generate an alternative more promising search-direction. We discuss the main convergence issues of the line-search based proximal bundle method, and provide computational results on a set of academic benchmark test problems.     

Laplace equations,Lefschetz properties and line arrangements

In this note we extend the main result in [6] on artinian ideals failing Lefschetz properties, varieties satisfying Laplace equations and existence of suitable singular hypersurfaces. Moreover we characterize the minimal generation of ideals generated by powers of linear forms by the configuration of their dual points in the projective plane and we use this result to improve some propositions on line arrangements and Strong Lefschetz Property at range 2 in [6]. The starting point was an example in [3]. Finally we show the equivalence among failing SLP, Laplace equations and some unexpected curves introduced in [3].     

Multiplicity of positive and nodal solutions for scalar field equations

In this paper the question of finding infinitely many solutions to the problem −Δu+a(x)u=|u|^p−2u$-\mathrm{\Delta }u+a(x)u={|u|}^{p-2}u$, in R^N${\mathbb{R}}^N$, u∈H¹(R^N)$u\in H^1({\mathbb{R}}^N)$, is considered when N≥2$N\ge 2$, p∈(2,2N/(N−2))$p\in (2,2N/(N-2))$, and the potential a(x)$a(x)$ is a positive function which is not required to enjoy symmetry properties. Assuming that a(x)$a(x)$ satisfies a suitable “slow decay at infinity” condition and, moreover, that its graph has some “dips”, we prove that the problem admits either infinitely many nodal solutions or infinitely many constant sign solutions. The proof method is purely variational and allows to describe the shape of the solutions.     

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.     

Oligothiophenes as fluorescent markers for biological applications

This paper summarizes some of our results on the application of oligothiophenes as fluorescent markers for biological studies. The oligomers of thiophene, widely known for their semiconductor properties in organic electronics, are also fluorescent compounds characterized by chemical and optical stability, high absorbance and quantum yield. Their fluorescent emission can be easily modulated via organic synthesis by changing the number of thiophene rings and the nature of side-chains. This review shows how oligothiophenes can be derivatized with active groups such as phosphoramidite, N-hydroxysuccinimidyl and 4-sulfotetrafluorophenyl esters, isothiocyanate and azide by which the (bio)molecules of interest can be covalently bound. This paper also describes how molecules such as oligonucleotides, proteins and even nanoparticles, tagged with oligothiophenes, can be used in experiments ranging from hybridization studies to imaging of fixed and living cells. Finally, a few multilabeling experiments are described.     

Quinolines in clothing textiles—a source of human exposure and wastewater pollution?

A production process in which the use of various types of chemicals seems to be ubiquitous makes the textile industry a growing problem regarding both public health as well as the environment. Among several substances used at each stage, the present study focuses on the quinolines, a class of compounds involved in the manufacture of dyes, some of which are skin irritants and/or classified as probable human carcinogens. A method was developed for the determination of quinoline derivatives in textile materials comprising ultrasound-assisted solvent extraction, solid phase extraction cleanup, and final analysis by gas chromatography/mass spectrometry. Quinoline and ten quinoline derivatives were determined in 31 textile samples. The clothing samples, diverse in color, material, brand, country of manufacture, and price, and intended for a broad market, were purchased from different shops in Stockholm, Sweden. Quinoline, a possible human carcinogen, was found to be the most abundant compound present in almost all of the samples investigated, reaching a level of 1.9 mg in a single garment, and it was found that quinoline and its derivatives were mainly correlated to polyester material. This study points out the importance of screening textiles with nontarget analysis to investigate the presence of chemicals in an unbiased manner. Focus should be primarily on clothing worn close to the body.