On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

Given a finite simple graph G with n vertices, we can construct the Cayley graph on the symmetric group S _n generated by the edges of G, interpreted as transpositions. We show that, if G is complete multipartite, the eigenvalues of the Laplacian of Cay (G) have a simple expression in terms of the irreducible characters of transpositions and of the Littlewood–Richardson coefficients. As a consequence, we can prove that the Laplacians of G and of Cay (G) have the same first nontrivial eigenvalue. This is equivalent to saying that Aldous’s conjecture, asserting that the random walk and the interchange process have the same spectral gap, holds for complete multipartite graphs.     

Classification of rotational special Weingarten surfaces of minimal type in {\mathbb{S}^2 \times \mathbb{R}} and {\mathbb{H}^2 \times \mathbb{R}}

In this paper we classify the complete rotational special Weingarten surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ ; i.e. rotational surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ whose mean curvature H and extrinsic curvature K _e satisfy H = f(H ² ? K _e ), for some function ${f \in \mathcal{C}^1([0,+\infty))}$ such that f(0) = 0 and 4x(f′(x))² < 1 for any x ≥ 0. Furthermore we show the existence of non-complete examples of such surfaces.     

On the cardinality of Urysohn spaces

Recently, in Cammaroto et al. (2013) [4] we obtained a generalization of the famous inequality established by A.V. Arhangel?ski? in 1969 for Hausdoff spaces. In this paper, following this line of research, we present a common variation of this inequality for Urysohn spaces by developing a Main Theorem for obtaining inequalities. In particular, we extend a 2006 inequality by Hodel for Urysohn spaces. Moreover, this extended inequality is used to analyze a result containing an increasing chain of spaces that satisfies the same cardinality inequality and this new result solves an open problem in Cammaroto et al. (2013) [4] for Urysohn spaces. This general theorem also provides a new cardinal inequality for Hausdorff spaces. The paper is concluded with some open problems.     

Sphaerococcus coronopifolius (Rhodophyta,Gigartinales): a Mediterranean red alga with potential and applications in restoration

Abstract

Experimental studies conducted on some species of Mediterranean red algae allowed to identify Sphaerococcus coronopifolius Stackhouse as a valid alternative to the Pacific alga Gloiopeltis furcata (Postels & Ruprecht) J. Agardh, for the extraction of a material usable as natural consolidant and adhesive in the field of restoration. Promising results have been observed by comparing the extracts obtained from these two algae after the same extraction procedure. Chemical analysis (FTIR) revealed that S. coronopifolius has qualities similar to G. furcata. Even more promising results for S. coronopifolius compared to G. furcata were observed after the analysis of pH and conductivity, and the adhesion tests carried out on both extracts.     

A modular approach to catalyst hydrophobicity for an asymmetric aldol reaction in a biphasic aqueous environment

Catalyst 5, an ion pair consisting of a hydrophilic cation and a lipophilic anion, fulfils the solubility requirements needed to couple efficiency (enantioselectivities and anti-diastereoselectivities up to > or = 99%) and catalyst recyclability in asymmetric aldol reactions under aqueous biphasic conditions.