Asymptotic stability and stabilizability of special classes of discrete-time positive switched systems

In this paper we consider discrete-time positive switched systems, switching among autonomous subsystems, characterized either by monomial matrices or by circulant matrices. Necessary and sufficient conditions are provided guaranteeing either (global uniform) asymptotic stability or stabilizability (i.e. the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence). Such conditions lead to simple algorithms that allow to easily detect, under suitable conditions, whether a given positive switched system is not stabilizable.     

A statistical mechanics approach to Granovetter theory

In this paper we try to bridge breakthroughs in quantitative sociology/econometrics, pioneered during the last decades by Mac Fadden, Brock–Durlauf, Granovetter and Watts–Strogatz, by introducing a minimal model able to reproduce essentially all the features of social behavior highlighted by these authors.     

A Solid-State NMR Investigation of MQ Silicone Copolymers

The structure of MQ copolymers of the general chemical formula [(CH₃)₃SiO_0.5]_m [SiO₂]_n was characterized by means of solid-state magic angle spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy. The MQ copolymers are highly branched polycyclic compounds (densely cross-linked nanosized networks). MQ copolymers were prepared by hydrolytic polycondensation in active medium. ²⁹Si NMR spectra were obtained by single pulse excitation (or direct polarization, DP) and cross-polarization (CP) ²⁹Si{¹H} techniques in concert with MAS. It was shown that material consist of monofunctional M (≡SiO Si (CH₃)₃) and two types of tetrafunctional Q units: Q⁴ ((≡SiO)₄ Si) and Q³ ((≡SiO)₃ SiOH). Spin–lattice relaxation times T ₁ measurements of ²⁹Si nuclei and analysis of ²⁹Si{¹H} variable contact time signal intensities allowed us to obtain quantitative data on the relative content of different sites in copolymers. These investigations indicate that MQ copolymers represent dense structure with core and shell.     

Domino Michael/aza-Wittig reaction in the diastereoselective construction of spiro[azepane-4,3′-oxindoles]

A convenient synthetic strategy for the diastereoselective assembly of spiro[azepane-4,3′-oxindoles] was developed via a Staudinger/Michael/aza-Wittig/reduction/N-deprotection reaction sequence starting from PMB-protected oxindole-substituted ethylazides. The key step of the method is a domino self-catalytic Michael/aza-Wittig reaction wherein the phosphazene moiety acts first as the catalyst and then as the reactant, resulting in the formation of a seven-membered N-heterocycle.     

Multiperiod Location-Routing with Decoupled Time Scales

This paper focuses on a multiperiod discrete facility location problem where transportation costs are considered together with location costs to design the operating facility pattern along a time horizon. The problem captures the difference in the scope of the location and routing decisions by considering different scales within the time horizon. Thus, solutions to this problem reflect the stability of locational decisions along time. The high complexity of this problem makes it impossible to be solved in practice with commercial software. For this reason, an approximation based on replacing vehicle routes by spanning trees is proposed, and its capability for providing good quality solutions is assessed in a series of computational experiments.     

A transmission problem on a polygonal partition: regularity and shape differentiability

We consider a transmission problem on a polygonal partition for the two-dimensional conductivity equation. For suitable classes of partitions we establish the exact behaviour of the gradient of solutions in a neighbourhood of the vertexes of the partition. This allows to prove shape differentiability of solutions and to establish an explicit formula for the shape derivative.     

Extragradient-type method for optimal control problem with linear constraints and convex objective function

The paper presents a method for solving optimal control problem with free right end and linear differential equations constraints. The proposed iterative process of extragradient-type is formulated in the functional subspace of piecewise continuous controls of L ₂. The convergence of the method is proved.