The Gelfand–Kirillov dimension of the universal algebras of M a,b (E)⊗E in positive characteristic

In this paper we calculate the Gelfand–Kirillov dimension of the relatively free (also called universal) algebra of rank m, U _m (M _a,b (E)?E), in the variety generated by M _a,b (E)?E, in positive characteristic p>2.     

Influence of membrane surface properties on the growth of neuronal cells isolated from hippocampus

Membranes have become of great interest for tissue engineering application, since they offer the advantage of developing neuronal tissue that may be used in implantable or in vitro hybrid systems for the simulation of brain function. The behaviour of neurons isolated from the hippocampus on membranes with different surface properties was investigated.     

The 1:1 cocrystals of the proton‐transfer compound dilituric acid–phenyl­biguanide monohydrate

A proton‐transfer compound, 1‐phenyl­biguanidium 5‐nitro‐2,6‐dioxo‐1,2,3,6‐tetra­hydro­pyrimidin‐4‐olate monohydrate, C₈H₁₂N₅⁺·C₄H₂N₃O₅⁻·H₂O, has been synthesized by a reaction between dilituric acid (5‐nitro‐2,4,6‐trihydroxy­pyrimi­dine, Dilit) and phenyl­biguanide (N‐phenyl­imido­carbonimidic diamide, Big). This compound cocrystallized as a 1:1 adduct, and the asymmetric unit consists of two dilituric amino–oxo planar tautomeric anions (Dilit⁻), two monoprotonated phenyl­biguanidium cations (BigH⁺) and two water mol­ecules of crystallization (Z′ = 2). Protonation occurs at the N atom attached to the phenyl ring of Big as a result of the proton‐transfer process from the acidic hydr­oxy group of Dilit. In the crystal structure, the hydrated 1:1 adduct is stabilized by 25 two‐ and three‐center hydrogen bonds.     

Efficient and selective oxidation of methyl substituted cycloalkanes by heterogeneous methyltrioxorhenium–hydrogen peroxide systems

Polymer-supported methyltrioxorhenium (MTO) systems are efficient catalysts for the oxidative functionalisation of cyclohexane and cyclopentane derivatives with H₂O₂ as oxygen donor. Using poly(4-vinyl)pyridine and poly(4-vinyl)pyridine-N-oxide as MTO supports, cycloalkanol, cycloalkanediol, cycloalkanone and ω-hydroxy methyl ketone derivatives were obtained in different yields depending on the experimental conditions. Interestingly, cycloalkane dimers were selectively recovered in acceptable to good yields when the oxidation was performed with polystyrene-microencapsulated MTO catalyst. The EPR investigation suggests that the homolytic cleavage of the CH₃–Re bond with formation of CH₃ radicals occurs inside the polystyrene capsule, indicating a possible role of methyl radical in the cycloalkane dimerisation pathway.     

Piecewise rigidity

In this paper we provide a Liouville type theorem in the framework of fracture mechanics, and more precisely in the theory of SBV deformations for cracked bodies. We prove the following rigidity result: if u∈SBV(Ω,RN) is a deformation of Ω whose associated crack Ju has finite energy in the sense of Griffith's theory (i.e., HN−1(Ju)<∞), and whose approximate gradient ∇u is almost everywhere a rotation, then u is a collection of an at most countable family of rigid motions. In other words, the cracked body does not store elastic energy if and only if all its connected components are deformed through rigid motions. In particular, global rigidity can fail only if the crack disconnects the body.     

Vibro-acoustic characterization of railway wheels

For many years the problem of noise generated by trains has had an increasing importance; in this paper, attention is focused on the noise generated by the train wheels due to their vibration. Today there are many kinds of railway wheels which are affected by different noise generation mechanisms. If the traditional and well known solid wheel is considered, a lot of data is already present in the literature both concerning the vibration and the noise point of view. On the other hand, the widely used resilient wheels are not so well known in their vibratory and acoustic behaviour as in the case of solid ones. The extensive experimentation presented and commented in this paper looks for a confirmation of some literature data first, and then it gives new results. Particularly the vibro-acoustic characterization of different kinds of wheels (both solid and resilient ones) has been carried out, in order to have a comparison between the behaviour of the newly built wheels and the older ones, representing the state of the art. Besides it has been shown that a detailed modal analysis of the suspended wheel coupled to sound measurements can give useful information about the wheel noise emission in its normal operating conditions.     

A generalization of the Motzkin–Straus theorem to hypergraphs

In 1965, Motzkin and Straus established a remarkable connection between the global maxima of the Lagrangian of a graph G over the standard simplex and the clique number of G. In this paper, we provide a generalization of the Motzkin–Straus theorem to k-uniform hypergraphs (k-graphs). Specifically, given a k-graph G, we exhibit a family of (parameterized) homogeneous polynomials whose local (global) minimizers are shown to be in one-to-one correspondence with maximal (maximum) cliques of G.     

Some observations about the extreme points of the Generalized Cardinality-Constrained Shortest Path Problem polytope

The Generalized Cardinality-Constrained Shortest Path Problem (GCCSPP) consists in finding the minimum cost path in a digraph, using at most r arcs in a subset F of the arc set. We propose an algebraic characterization of the extreme points of the associated polytope, and then we show that it is equivalent to the geometric one, obtained extending to the GCCSPP some known results for the cardinality-constrained shortest path problem.