Processes governed by signed measures connected with third-order “heat-type” equations

Dipartamento di Statistica, Probabilita e Statistiche Applicate, University of Rome, La Sapienza, Italy. Published in Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 31, No. 2, pp. 323–336, April–June, 1991.     

Enantioselective organocatalyzed functionalization of benzothiophene and thiophenecarbaldehyde derivatives

Herein we report a study on the enantioselective organocatalyzed cross-aldol reaction of 1-benzothiophene and thiophenecarbaldehydes with different ketones. The reactions were conducted at 0 °C or room temperature to afford the corresponding adducts in high yields and good to excellent ee using different organocatalysts. Interestingly, using (S)-pyrrolidine tetrazole and acetoxyacetone an inversion of the aldol regiochemistry was observed.     

Lipase-Catalyzed Regio- and Stereoselective Acylation of Hydroxy Groups in Steroid Side Chains

 Lipase from Pseudomonas cepacia (PCL) catalyzes the regio- and stereoselective acylation of primary and secondary hydroxy groups in steroid side chains under irreversible transesterification conditions with vinyl acetate in organic solvents.     

Estimates for Functionals of Solutions to Higher-Order Heat-Type Equations with Random Initial Conditions

In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable \(\varphi \)-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.     

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N(t) Poisson events, there are N(t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.     

Ranking vertices or edges of a network by loops: a new approach

We introduce loop ranking, a new ranking measure based on the detection of closed paths, which can be computed in an efficient way. We analyze it with respect to several ranking measures which have been proposed in the past, and are widely used to capture the relative importance of the vertices in complex networks. We argue that loop ranking is a very appropriate measure to quantify the role of both vertices and edges in the network traffic.     

Two-point self-coordination of a dizinc(II) bispyridylporphyrin ruthenium complex leading selectively to a discrete molecular assembly: solution and solid-state characterization

The dizinc(II) bispyridylporphyrin ruthenium complex trans,cis,cis[RuCl2(CO)2(Zn.4'-cisDPyP)2] (1Zn, 4'-cisDPyP = 5,10-bis(4'-pyridyl)-15,20-diphenylporphyrin) features two donor (the uncoordinated 4'-N(py) atoms) and two acceptor (the Zn atoms) sites and is thus a building block suited for two-point coordination. 1H NMR spectroscopy indicates that 1Zn self-assembles in solution through Zn-4'-N(py) interactions to yield selectively a highly symmetrical discrete species, in which all donor and all acceptor sites of 1Zn are mutually saturated. Single-crystal X-ray analysis established that this adduct is a dimeric species, (1Zn)2, with a global S4 symmetry, in which the four porphyrins have a propeller-like arrangement. The dimeric species (1Zn)2 is a meso form derived from the combination of two 1Zn units with opposite helical chirality. The geometry of this highly symmetrical tetraporphyrin assembly in solution, as determined by NMR spectroscopy, is essentially the same as that found in the solid state. Thus 1Zn is an unprecedented example of metal-containing self-complementary building block that selectively recognizes itself through four Zn-N(py) interactions, and thus yields a very stable and symmetrical dimeric species, (1Zn)2, that features four porphyrins and six metal atoms (two Ru and four Zn).     

Solar cells based on a fullerene-azothiophene dyad

A power conversion efficiency of 0.37%, under white light of 80 mW cm-2 intensity, was obtained when a fullerene-azothiophene dyad was used as the active layer of a photovoltaic cell.     

Anisotropy of domain growth in nematic liquid crystals

We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field.