Only the first term of some series counts

Let X,X₁,X₂,… be i.i.d. random variables, and set S_n=X₁+?+X_n. We prove that for three important distributions of X, namely normal, exponential and geometric, series of the type ∑_n≥1a_nP(|S_n|≥xb_n) or ∑_n≥1a_nP(S_n≥xb_n) behave like their first term as x→∞.     

On the roles of solid-bound ligand scavengers in the removal of palladium residues and in the distinction between homogeneous and heterogeneous catalysis

We have studied the roles and behavior of typical resin- and silica-bound thiol scavengers in the removal of palladium (Pd) residues and in the determination of the true catalytic species in the Heck coupling of bromobenzene and styrene. The results of Pd scavenging and catalyst poisoning by elemental analysis (EA) and transmission electron microscopy (TEM) indicate that silica-bound thiols have an advantage over resin-bound thiols in residual Pd removal from a Heck reaction solution and that all of these scavengers poison effectively the catalytic species but hardly scavenge Pd clusters, even as small as 1 nm from solution presumably because of the steric barrier. Because of a smaller proportion of soluble Pd clusters, using a molecular Pd precatalyst results in a much higher Pd scavenging efficiency than using a supported Pd particle precatalyst. With the aid of catalyst poisoning by the scavengers, filtration testing and TEM studies further illustrate that Pd clusters are inactive for the Heck reaction over Pd(0)/SiO(2), with molecular Pd(0) being solely active. Studies through EA and thermogravimetric analysis suggest that the bound thiols are leached from the scavengers to a different extent at reaction temperatures of 90-135 °C, probably owing to base-catalyzed decomposition or based-promoted dissociation of functional groups from the surfaces, leading to interaction between leached thiols and a solid Pd precatalyst. Meanwhile, the effect of solid-bound thiol binding to soluble Pd on the efficiency of Pd scavenging and the impact of a scavenger on the Pd leaching from supported Pd particles are discussed.     

A versatile palladium catalyst system for Suzuki-Miyaura coupling of alkenyl tosylates and mesylates

A general and effective palladium system for Suzuki-Miyaura coupling of alkenyl electrophiles under mild reaction conditions is reported. With the Pd(OAc)(2)/CM-phos system, a variety of alkenyl tosylates are coupled well with ArB(OH)(2). Moreover, the first successful examples of using alkenyl mesylates in alkenylation are also described.     

TG–FTIR analysis applied to the study of thermal behaviour of some edible mushrooms

The article is devoted to the study on the thermal behaviour of three species of edible mushrooms: Boletus edulis (foot and cap), Pleurotus ostreatus (foot and cap), Lactarius deterrimus (cap) by the TG–FTIR-coupled technique, in air, over the 30–900 °C temperature range. The analysis of the TG–DTG–DTA curves reveals the thermal degradation mechanism to be complex and specific to every species under the recording conditions applied. A similar degradation mechanism is noticed for the foot and cap of Pleurotus ostreatus in comparison with the Boletus edulis and Lactarius deterrimus species where the mechanisms are different. The TG–FTIR analysis, combustion heats and IR spectra of the starting samples also support these results. The initial degradation temperatures from TG–DTG indicate the temperature range where these species are thermally stable and their nutrient features maintained making them proper for food. The TG–FTIR analysis gives information on the gaseous species evolved by the thermal degradation bringing thus a contribution to the elucidation of the changes developing by processing the edible mushrooms (industrialization, conservation, culinary preparations, etc.) at temperatures above the initial degradation temperature. At the same time, the environmental impact, when the mushroom failed cultures are burned, is also important.     

Emerging Issues in Nanoparticle Aerosol Science and Technology

Journal of Nanoparticle Research -     

Estimating functions of canonical correlation coefficients

Let ρ²₁,…,ρ²_p be the squares of the population canonical correlation coefficients from a normal distribution. This paper is concerned with the estimation of the parameters δ₁,…,δ_p, where $\text{δ}{}_{\mathrm{i}}\text{=}\text{ρ}{}^2{}_{\mathrm{i}}\text{(1 ? ρ}{}^2{}_{\mathrm{i}}\text{)}$, i = 1,…,p, in a decision theoretic way. The approach taken is to estimate a parameter matrix Δ whose eigenvalues are δ₁,…,δ_p, given a random matrix F whose eigenvalues have the same distribution as $\text{r}{}^2{}_{\mathrm{i}}\text{(1 ? r}{}^2{}_{\mathrm{i}}\text{)}$, i = 1,…,p, where r₁,…,r_p are the sample canonical correlation coefficients.     

On weyl's identity in the differential geometry of surfaces

Summary At the end of his classical paper on convex surfaces in thelarge,H. Weyl (1916) gave an identity connecting the first and second fundamental forms of a surface. The identity is, however, a purelylocal relation and it holds also when the Gaussian curvature, instead of being positive, is negative. The present paper centers around this identity. Various applications of it are considered and the conditions of validity are specified.