Rumor Processes in Random Environment on \mathbb{N} and on Galton–Watson Trees

The aim of this paper is to study rumor processes in random environment. In a rumor process a signal starts from the stations of a fixed vertex (the root) and travels on a graph from vertex to vertex. We consider two rumor processes. In the firework process each station, when reached by the signal, transmits it up to a random distance. In the reverse firework process, on the other hand, stations do not send any signal but they “listen” for it up to a random distance. The first random environment that we consider is the deterministic 1-dimensional tree $\mathbb{N}$ with a random number of stations on each vertex; in this case the root is the origin of $\mathbb{N}$ . We give conditions for the survival/extinction on almost every realization of the sequence of stations. Later on, we study the processes on Galton–Watson trees with random number of stations on each vertex. We show that if the probability of survival is positive, then there is survival on almost every realization of the infinite tree such that there is at least one station at the root. We characterize the survival of the process in some cases and we give sufficient conditions for survival/extinction.     

Nonlinear dynamics of mechanical systems with friction contacts: Coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions

Real applications in structural mechanics where the dynamic behavior is linear are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of excitation, joints can dramatically change the dynamic behavior of the whole system, and the modeling of this type of constraint is therefore crucial for a correct prediction of the amount of vibration.     

Effect of 5-Me substituent(s) on the catalytic activity of palladium(II) 2,2-bipyridine complexes in CO/4-tert-butylstyrene copolymerization

The coordination of two 5-substituted-2,2^′-bipyridines L (L¹=5-methyl-2,2^′-bipyridine, L²=5,5^′-dimethyl-2,2^′-bipyridine) to palladium was studied. The neutral complexes [Pd(L)Cl₂] and [Pd(L)(Me)Cl], and the cationic complexes obtained after chlorine abstraction [Pd(L)₂][BAr^′₄]₂ and [Pd(L)(Me)(NCMe)][BAr^′₄] (Ar^′=3,5-(CF₃)₂-C₆H₃), respectively, were isolated and characterized by NMR and FAB mass spectroscopy. The complex [Pd(L²)(L³)][BAr^′₄]₂ (L³=2,2^′-bipyridine) bearing different ligands, was prepared for comparison purposes. The activity of the monocationic and dicationic complexes as catalytic precursors in the CO/4-tert-butylstyrene copolymerization was compared with that of related well-known catalysts containing the unsubstituted 2,2^′-bipyridine as nitrogen ligand, to evaluate the influence of the substituents in 5- and 5,5^′-position. The presence of one or two substituents on the nitrogen ligand has a positive effect on productivity using both types of precursors. No influence was observed on the polymer properties in terms of molecular weight and tacticity. Analysis of the reactivity of the methyl-palladium complexes towards carbon monoxide shows further differences depending on the nitrogen ligand.     

Giant Enhancement of Second Harmonic Generation Accompanied by the Structural Transformation of 7-Fold to 8-Fold Interpenetrated Metal–Organic Frameworks (MOFs)

Interpenetration in metal–organic frameworks (MOFs) is an intriguing phenomenon with significant impacts on their properties, and functional applications. Herein, we show that a 7-fold interpenetrated MOF ( 1 ) is transformed into an 8-fold interpenetrated MOF by the loss of DMF in a single-crystal-to-single-crystal manner. This is accompanied by a giant enhancement of the second harmonic generation (SHG ca. 125 times) and two-photon photoluminescence (ca. 14 times). The strengthened π–π interaction between the individual diamondoid networks and intensified oscillator strength of the molecules aid the augment of dipole moments and boost the nonlinear optical conversion efficiency. Large positive and negative thermal expansions of 1 occur at 30–150 °C before the loss of DMF. These results offer an avenue to manipulate the NLO properties of MOFs using interpenetration and provide access to tunable single-crystal NLO devices.     

Heavy metals and nutrients in coastal, surface seawaters (Gulf of Trieste, Northern Adriatic Sea): an environmental study by factor analysis

Trace metals and nutrients were monitored voltammetrically and spectrophotometrically during a one-year period (1992/93) in the filtered fraction of coastal surface seawaters sampled with a monthly frequency at 6 different sites in the Gulf of Trieste (Northern Adriatic Sea), to evaluate the degree of pollution in an area receiving industrial, agricultural and urban wastes. The sites devoted to hatcheries of edible mussels are of particular interest. A multivariate statistical analysis of the collected concentration data by the principal component method allows to identify the sources and typology of pollution, and to discriminate between the quality of waters at the different sampling sites. The coastal waters in the Gulf of Trieste seem to be comparable to, or better than, waters of analogous areas in the Mediterranean Sea.     

Simultaneous determination of new thioamphetamine designer drugs in plasma by capillary electrophoresis coupled with mass spectrometry

A simple method for the simultaneous identification and quantification of four 2,5-methylenedioxy derivatives of 4-thioamphetamine (ALEPH series) in plasma samples was developed. The method consists of solid-phase extraction (SPE) using a Bond Elut C(18) cartridge and capillary electrophoresis coupled with electrospray ionisation mass spectrometry (CE/ESI-MS). The SPE method used required only simple steps and provided a clean extract from which identification of each drug was feasible, even at low concentrations. The method was validated according to international guidelines. The calibration curves were linear over the concentration range of 50 to 1000 ng/mL for all drugs with correlation coefficients that exceeded 0.998. The lower limits of detection of the drugs were 23-43 ng/mL. The absolute recoveries for the drugs were 64-92% and 75-96% at concentrations of 100 and 500 ng/mL, respectively. The validation data (precision, accuracy, and recovery) show the reproducibility and selectivity of the method. This clean and simple method allows the routine detection of designer drugs such as thioamphetamines which may become a serious problem in the control of illegal drugs.     

Iron,copper and their proteins in substantia nigra of human brain during aging

Liquid-liquid extraction of zirconium(IV) was investigated from dilute hydrochloric acid medium by salicyaldoxime (HA) in dichloromethane. The metal was spiked with ⁹⁵Zr and analyzed by its radioactivity. The effects of different donors, like trioctyl phosphine oxide (TOPO), triphenyl phosphine oxide (TPPO), tributyl phosphine oxide (TBPO), tributyl phosphate (TBP), trioctyl amine (TOA) and Amberlite LA-2 were studied. The adduct formation constants for both binary species (metal-ligand) and ternary species (metal-ligand-donor) were also calculated form the distribution data.One of the authors (S.B.) thanks The University of Burdwan for providing senior research fellowship to her. She also wishes to thank Dr. D. Mukherjee and Dr. S. Bhattacharya, B.U. for their valuable suggestions.