Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

Addendum to “examples of semiperfect rings”

We fill a gap in [4], and provide a rigorous example of a local ringR whose Jacobson radical is locally nilpotent, butM ₂(R) is not strongly π-regular. The online version of the original article can be found at The work of the first author was partially supported by the DGICYT (Spain), through the grant PB92-0586, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya.     

A SCALAR IRRADIANCE FIBER-OPTIC MICROPROBE FOR THE MEASUREMENT OF ULTRAVIOLET RADIATION AT HIGH SPATIAL RESOLUTION

Abstract— The construction of a new type of microprobe for the measurement of scalar irradiance (integral dose rate) in the UV down to wavelengths of 250 nm is described. The microprobes were made from tapered standard optical fibers and a tip-diffuser of magnesia/silica vitroceramic. The sensing tips were ca 100 μm in diameter and had maximal deviations in the angular response of ± 15%. I present measurements of scalar irradiance at high spatial resolution within dry beach sand and suspensions of microorganisms. These two media are environments in which microorganisms are exposed to UV, either under natural (sand) or laboratory conditions (suspensions). In both cases, the space distribution of UV scalar irradiance, and thus the distribution of integral dose rates, departed significantly from that predicted by absorptive effects alone. The results underscore the importance of small-scale, in situ measurements of scalar irradiance for UV dosimetry in such scattering media.     

Liquid chromatographic/electrospray ionization tandem mass spectrometric study of the phenolic composition of cocoa (Theobroma cacao)

Liquid chromatography coupled with ionspray mass spectrometry in the tandem mode (LC/MS/MS) with negative ion detection was used for the identification of a variety of phenolic compounds in a cocoa sample. Gradient elution with water and acetonitrile, both containing 0.1% HCOOH, was used. Standard solutions of 31 phenolic compounds, including benzoic and cinnamic acids and flavonoid compounds, were studied in the negative ion mode using MS/MS product ion scans. At low collisional activation, the deprotonated molecule [M - H](-) was observed for all the compounds studied. For cinnamic and benzoic acids, losses of CO(2) or formation of [M - CH(3)](-*) in the case of methoxylated compounds were observed. However, for flavonol and flavone glycosides, the spectra present both the deprotonated molecule [M - H](-) of the glycoside and the ion corresponding to the deprotonated aglycone [A - H](-). The latter ion is formed by loss of the rhamnose, glucose, galactose or arabinose residue from the glycosides. Different fragmentation patterns were observed in MS/MS experiments for flavone-C-glycosides which showed fragmentation in the sugar part. Fragmentation of aglycones provided characteristic ions for each family of flavonoids. The optimum LC/MS/MS conditions were applied to the characterization of a cocoa sample that had been subjected to an extraction/clean-up procedure which involved chromatography on Sephadex LH20 and thin-layer chromatographic monitoring. In addition to compounds described in the literature, such as epicatechin and catechin, quercetin, isoquercitrin (quercetin-3-O-glucoside) and quercetin-3-O-arabinose, other compounds were identified for the first time in cocoa samples, such as hyperoside (quercetin-3-O-galactoside), naringenin, luteolin, apigenin and some O-glucosides and C-glucosides of these compounds.     

Aryl‐Copper(III)‐Acetylides as Key Intermediates in CCsp Model Couplings under Mild Conditions

The mechanism of copper‐mediated Sonogashira couplings (so‐called Stephens–Castro and Miura couplings) is not well understood and lacks clear comprehension. In this work, the reactivity of a well‐defined aryl‐Cu^III species ( 1 ) with p‐R‐phenylacetylenes (R=NO₂, CF₃, H) is reported and it is found that facile reductive elimination from a putative aryl‐Cu^III‐acetylide species occurs at room temperature to afford the C_aryl?C_sp coupling species ( I_R ), which in turn undergo an intramolecular reorganisation to afford final heterocyclic products containing 2H‐isoindole ( P , P , P_Ha ) or 1,2‐dihydroisoquinoline ( P_Hb ) substructures. Density Functional Theory (DFT) studies support the postulated reductive elimination pathway that leads to the formation of C?C_sp bonds and provide the clue to understand the divergent intramolecular reorganisation when p‐H‐phenylacetylene is used. Mechanistic insights and the very mild experimental conditions to effect C_aryl?C_sp coupling in these model systems provide important insights for developing milder copper‐catalysed C_aryl?C_sp coupling reactions with standard substrates in the future.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Understanding conjugation and hyperconjugation from electronic delocalization measures

The concepts of conjugation and hyperconjugation play an important role to provide an explanation for several fundamental phenomena observed in organic chemistry. Because these effects cannot be directly measured experimentally, their assessment became a primary concern for chemists from the very beginning. In general, the stabilization produced by both phenomena has been studied by means of isodesmic reactions and energy based analysis such as the energy decomposition analysis. In recent years, electronic delocalization measures have been successfully applied to elucidate the nature of chemical bonding and the aromatic character of all kind of molecules. Because conjugation and hyperconjugation stabilizations are strongly linked to the concept of electron delocalization, this paper will give an account of both effects from the point of view of electronic delocalization measures calculated within the framework of the quantum theory of atoms in molecules. In particular, we focus our attention in the controversial case of the stabilization by conjugation in 1,3-butadiyne and 1,3-butadiene. Unexpectedly, theoretical calculations based on the scheme proposed by Kistiakowsky to quantify the extent of stabilization due to conjugation predicted that the conjugation of 1,3-butadiyne was zero. Subsequent energetic analyses contradicted this observation. These studies pointed out the presence of hyperconjugation stabilization in the hydrogenated product of 1,3-butadiyne and 1,3-butadiene that were used as reference systems in the Kistiakowsky's scheme. Consequently, the extra stabilization of 1-butyne due to hyperconjugation hides the stabilization by conjugation of 1,3-butadiyne. Our results based on electron delocalization measures confirm both the presence of conjugation in 1,3-butadiene and 1,3-butadiyne and hyperconjugation stabilization in their respective hydrogenated products, 1-butene and 1-butyne.     

A non-adiabatic quantum-classical dynamics study of the intramolecular excited state hydrogen transfer in ortho-nitrobenzaldehyde

Ab initio surface-hopping dynamics calculations have been performed to simulate the intramolecular excited state hydrogen transfer dynamics of ortho-nitrobenzaldehyde (o-NBA) in the gas phase from the electronic S(1) excited state. Upon UV excitation, the hydrogen is transferred from the aldehyde substituent to the nitro group, generating o-nitrosobenzoic acid through a ketene intermediate. The semiclassical propagations show that the deactivation from the S(1) is ultrafast, in agreement with the experimental measurements, which detect the ketene in less than 400 fs. The trajectories show that the deactivation mechanism involves two different conical intersections. The first one, a planar configuration with the hydrogen partially transferred, is responsible for the branching between the formation of a biradical intermediate and the regeneration of the starting material. The conversion of the biradical to the ketene corresponds to the passage through a second intersection region in which the ketene group is formed.     

Synthesis of γ-lactones from easily and accessible reactants catalyzed by Cu–MnOx catalysts

The mechanism of the oxidative [3+2] cycloaddition of alkenes with anhydrides using oxygen as an oxidant to synthesize γ-lactones has been studied using a heterogeneous dual copper-manganese–based catalyst. The cyclization takes place through two coexisting reaction mechanisms, the involvement of different reaction intermediates and a clear synergistic effect between copper and manganese. In fact it appears that CuO clusters dispersed on the surface of a manganese-based oxide increase the redox capability of manganese ions and leads to an increase in the release of oxygen from the surface.