On general infinite dimensional complementarity problems

The aim of this paper is to present a way to study directly generalized complementarity problems in normed spaces. By means of new results on infinite dimensional Lagrange theory we show some optimality conditions which reduce the study of the problems to the one of suitable systems of equalities and inequalities.     

The social diversification of fashion

We propose a model to investigate the dynamics of fashion traits purely driven by social interactions. We assume that people adapt their style to maximize social success, and we describe the interaction as a repeated group game in which the payoffs reflect the social norms dictated by fashion. On one hand, the tendency to imitate the trendy stereotypes opposed to the tendency to diverge from them to proclaim identity; on the other hand, the exploitation of sex appeal for dating success opposed to the moral principles of the society. These opposing forces promote diversity in fashion traits, as predicted by the modeling framework of adaptive dynamics. Our results link the so-called horizontal dynamics—the primary driver of fashion evolution, compared with the vertical dynamics accounting for interclass and economic drivers—to style variety.     

Gevrey local solvability in locally integrable structures

We consider a locally integrable real-analytic structure, and we investigate the local solvability in the category of Gevrey functions and ultradistributions of the complex \(\mathrm{d}^{\prime }\) naturally induced by the de Rham complex. We prove that the so-called condition \(Y(q)\) on the signature of the Levi form, for local solvability of \(\mathrm{d}^{\prime }u=f\) , is still necessary even if we take \(f\) in the classes of Gevrey functions and look for solutions \(u\) in the corresponding spaces of ultradistributions.     

Porous medium equations on manifolds with critical negative curvature: unbounded initial data

We investigate existence and uniqueness of solutions of the Cauchy problem for the porous medium equation on a class of Cartan–Hadamard manifolds. We suppose that the radial Ricci curvature, which is everywhere nonpositive as well as sectional curvatures, can diverge negatively at infinity with an at most quadratic rate: in this sense it is referred to as critical. The main novelty with respect to previous results is that, under such hypotheses, we are able to deal with unbounded initial data and solutions. Moreover, by requiring a matching bound from above on sectional curvatures, we can also prove a blow-up theorem in a suitable weighted space, for initial data that grow sufficiently fast at infinity.     

Uniqueness of solutions to degenerate parabolic and elliptic equations in weighted Lebesgue spaces

We investigate uniqueness for degenerate parabolic and elliptic equations in the class of solutions belonging to weighted Lebesgue spaces and not satisfying any boundary condition. The uniqueness result that we provide relies on the existence of suitable positive supersolutions of the adjoint equations. Under proper assumptions on the behavior at the boundary of the coefficients of the operator, such supersolutions are constructed, mainly using the distance function from the boundary.     

Betti numbers in multidimensional persistent homology are stable functions

Multidimensional persistence mostly studies topological features of shapes by analyzing the lower level sets of vector‐valued functions, called filtering functions. As is well known, in the case of scalar‐valued filtering functions, persistent homology groups can be studied through their persistent Betti numbers, that is, the dimensions of the images of the homomorphisms induced by the inclusions of lower level sets into each other. Whenever such inclusions exist for lower level sets of vector‐valued filtering functions, we can consider the multidimensional analog of persistent Betti numbers. Varying the lower level sets, we obtain that persistent Betti numbers can be seen as functions taking pairs of vectors to the set of non‐negative integers. In this paper, we prove stability of multidimensional persistent Betti numbers. More precisely, we prove that small changes of the vector‐valued filtering functions imply only small changes of persistent Betti numbers functions. This result can be obtained by assuming the filtering functions to be just continuous. Multidimensional stability opens the way to a stable shape comparison methodology based on multidimensional persistence. In order to obtain our stability theorem, some other new results are proved for continuous filtering functions. They concern the finiteness of persistent Betti numbers for vector‐valued filtering functions and the representation via persistence diagrams of persistent Betti numbers, as well as their stability, in the case of scalar‐valued filtering functions. Finally, from the stability of multidimensional persistent Betti numbers, we obtain a lower bound for the natural pseudo‐distance. Copyright © 2013 John Wiley & Sons, Ltd.     

Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics

We study an optimal control problem for a hybrid system exhibiting several internal switching variables whose discrete evolutions are governed by some delayed thermostatic laws. By the dynamic programming technique we prove that the value function is the unique viscosity solution of a system of several Hamilton-Jacobi equations, suitably coupled. The method involves a contraction principle and some suitably adapted results for exit-time problems with discontinuous exit cost.     

Methane Direct Conversion on Mo/ZSM-5 Catalysts Modified by Pd and Ru

The effect of addition of Ru and Pd to Mo/HZSM-5 catalysts used in the dehydroaromatiza-tion of methane was investigated. Catalytic tests and temperature-programmed oxidation results showed that Pd-based catalysts were more selective to naphthalene and suffered strong deactivation. The presence of Ru improved the activity and stability, with a decrease in the carbonaceous deposit probably because of a mechanism of protection of the Mo2C surface.     

Efficient synthesis and environmentally friendly reactions of PEG-supported 1,2-diaza-1,3-butadiene

[reaction: see text] Here, we report the protocol for the preparation of new poly(ethylene glycol)-supported 1,2-diaza-1,3-butadiene. In addition, we discuss an application of this supported reagent in an efficient and environmentally friendly one-pot synthesis of 2-thiazol-4-one derivatives by reaction with thioamides.     

Using ring strain to inhibit a decomposition path: first synthesis of an Alkyl-BIAN ligand (Alkyl-BIAN = bis(alkyl)acenaphthenequinonediimine)

N-Alkyl imines of acenaphthenequinone are not stable because an isomerization occurs that releases part of the ring strain of the initially formed imine by changing the hybridization of one of the ring carbon atoms from sp(2) to sp(3); however, if an even more strained ring is present in the alkyl group, the isomerization becomes unfavorable and the compound is stable.