Sharply 1-transitive subsets of certain permutation groups

In this paper we give a method for constructing sharply 1-transitive permutation sets inside a finite permutation group with certain properties and we apply this method to obtain a family of sharply 1-transitive permutation subsets of the sharply 3-transitive permutation group M(p ^2f ) on PG(1, p ^2f ) for p ^f 1 (mod 4).Work supported by G.N.S.A.G.A. and M.P.I.     

Mixed Partitions of Projective Geometries

Starting from a linear collineation of PG(2n–1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n–1,q) consisting of two (n–1)-subspaces and caps, all having size (qⁿ–1)/(q–1) or (qⁿ–1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety of PG(8,q) into caps of size q²+q+1 which are Veronese surfaces.     

On two-transitive ovals in projective planes of even order

In memoria di Paola Biscarini     

Passive effects of rare-earth permanent magnets on flexible conductive structures

The paper presents a theoretical and experimental study of vibrating structures where paramagnetic or diamagnetic systems interact with rare-earth passive magnets.The theoretical model of the system is focused on the damping properties of permanent magnets and on their interactions with the dynamic behaviour of an Euler–Bernoulli beam. In particular, the magnetic model is based on the analogy of the equivalent currents method in a quasi-static open-circuit-type configuration and it is used to determine the influence of eddy currents on the dynamic behaviour of conducting material structures. The magnetic effects are characterised by a viscous-type damping and by a stiffening dynamic effect of the structure, called “phantom effect”.The authors present the experimental outcomes for uniform cantilever clamped-free beams of different kinds of paramagnetic or diamagnetic conducting materials. It appears that the system frequency response can be modified by the presence of a pair of concordant or discordant permanent magnets of high residual induction settled at the free end.Through the comparison between theoretical and experimental results, the paper demonstrates the validity of the model, that is able to describe both the above mentioned effect of dynamic stiffening of the structure and the considerable localised damping properties in paramagnetic or diamagnetic materials having low electric resistivity.     

Hyperbranched anatase TiO2 nanocrystals: nonaqueous synthesis, growth mechanism, and exploitation in dye-sensitized solar cells

A colloidal crystal-splitting growth regime has been accessed, in which TiO(2) nanocrystals, selectively trapped in the metastable anatase phase, can evolve to anisotropic shapes with tunable hyperbranched topologies over a broad size interval. The synthetic strategy relies on a nonaqueous sol-gel route involving programmed activation of aminolysis and pyrolysis of titanium carboxylate complexes in hot surfactant media via a simple multi-injection reactant delivery technique. Detailed investigations indicate that the branched objects initially formed upon the aminolysis reaction possess a strained monocrystalline skeleton, while their corresponding larger derivatives grown in the subsequent pyrolysis stage accommodate additional arms crystallographically decoupled from the lattice underneath. The complex evolution of the nanoarchitectures is rationalized within the frame of complementary mechanistic arguments. Thermodynamic pathways, determined by the shape-directing effect of the anatase structure and free-energy changes accompanying branching and anisotropic development, are considered to interplay with kinetic processes, related to diffusion-limited, spatially inhomogeneous monomer fluxes, lattice symmetry breaking at transient Ti(5)O(5) domains, and surfactant-induced stabilization. Finally, as a proof of functionality, the fabrication of dye-sensitized solar cells based on thin-film photoelectrodes that incorporate networked branched nanocrystals with intact crystal structure and geometric features is demonstrated. An energy conversion efficiency of 6.2% has been achieved with standard device configuration, which significantly overcomes the best performance ever approached with previously documented prototypes of split TiO(2) nanostructures. Analysis of the relevant photovoltaic parameters reveals that the utilized branched building blocks indeed offer light-harvesting and charge-collecting properties that can overwhelm detrimental electron losses due to recombination and trapping events.     

A Limited-Memory Multipoint Symmetric Secant Method for Bound Constrained Optimization

A new algorithm for solving smooth large-scale minimization problems with bound constraints is introduced. The way of dealing with active constraints is similar to the one used in some recently introduced quadratic solvers. A limited-memory multipoint symmetric secant method for approximating the Hessian is presented. Positive-definiteness of the Hessian approximation is not enforced. A combination of trust-region and conjugate-gradient approaches is used to explore useful information. Global convergence is proved for a general model algorithm. Results of numerical experiments are presented.     

On the sharply 1-transitive subsets of PGL(2,pm)

If p is an odd prime and R is a sharply 1-transitive subset of PGL(2,p^m) which contains the identity but is not a group, then the subgroup generated by R is either PSL(2,p^m) or PGL(2,p^m).work done within the activity of G.N.S.A.G.A. and supported by the Italian Ministry of Public EducationDedicated to Professor Helmut Karzel on his 60^th birthday     

Preparation and Characterization of Niobium Oxide Coated Cellulose Fiber

The Nb₂O₅/cellulose composite was prepared by reacting α-cellulose with NbCl_5-n(OC₂H₅)_n, in nonaqueous solvent, under nitrogen atmosphere and submitting the obtained material to hydrolysis. An increase in the crystallinity degree is observed in the composite material because the precursor reagent reacts with the amorphous phase of the cellulose fibers. Loadings between 4.5 and 16.0% of the oxide were achieved and in every case the oxide particles uniformly cover the fiber surface. Lewis and Brønsted acid sites were determined by using pyridine as the basic molecular probe.     

Quaternionic Starters

Let m be an integer, m 2 and set n = 2^m. Let G be a non-cyclic group of order 2n admitting a cyclic subgroup of order n. We prove that G always admits a starter and so there exists a one–factorization of K_2n admitting G as an automorphism group acting sharply transitively on vertices. For an arbitrary even n > 2 we also show the existence of a starter in the dicyclic group of order 2n.Research performed within the activity of INdAM–GNSAGA with the financial support of the Italian Ministry MIUR, project Strutture Geometriche, Combinatoria e loro Applicazioni