Synthesis of tetramic acids with a benzo[f]indolizine skeleton. Transannular rearrangements in pyrazino[1,2-b]isoquinolin-4-ones

Pyrazino[1,2-b]isoquinoline-1,4-diones (3) having a bulky activating group at the N(2)-position were rearranged to tetramic acids with a benzo[f]indolizine skeleton (8) in the presence of K^tBuO or LHMDS as bases. This rearrangement was diasteroselective for the 6,11a-trans-isomers of the starting compounds. 1-Hydroxy-pyrazino[1,2-b]isoquinolin-4-one (7) afforded a 1-trichloroacetamido derivative (14) after treatment with trichloroacetonitrile and a catalytic amount of sodium hydride as a base, through two subsequent base-promoted transannular rearrangements. In summary, the combination of functions in the piperazine ring of the starting tricyclic compounds conferred to them new reactivities that imply different base-promoted transannular rearrangements and led to unexpected transformations.     

Occupational and consumer risk estimates for nanoparticles emitted by laser printers

Several studies have reported laser printers as significant sources of nanosized particles (<0.1 μm). Laser printers are used occupationally in office environments and by consumers in their homes. The current work combines existing epidemiological and toxicological evidence on particle-related health effects, measuring doses as mass, particle number and surface area, to estimate and compare the potential risks in occupational and consumer exposure scenarios related to the use of laser printers. The daily uptake of laser printer particles was estimated based on measured particle size distributions and lung deposition modelling. The obtained daily uptakes (particle mass 0.15–0.44 μg d⁻¹; particle number 1.1–3.1 × 10⁹ d⁻¹) were estimated to correspond to 4–13 (mass) or 12–34 (number) deaths per million persons exposed on the basis of epidemiological risk estimates for ambient particles. These risks are higher than the generally used definition of acceptable risk of 1 × 10⁻⁶, but substantially lower than the estimated risks due to ambient particles. Toxicological studies on ambient particles revealed consistent values for lowest observed effect levels (LOELs) which were converted into equivalent daily uptakes using allometric scaling. These LOEL uptakes were by a factor of about 330–1,000 (mass) and 1,000–2,500 (particle surface area) higher than estimated uptakes from printers. This toxicological assessment would indicate no significant health risks due to printer particles. Finally, our study suggests that particle number (not mass) and mass (not surface area) are the most conservative risk metrics for the epidemiological and toxicological risks presented here, respectively.     

Hydrophobicity, shape, and pi-electron contributions during translesion DNA synthesis

Translesion DNA synthesis, the ability of a DNA polymerase to misinsert a nucleotide opposite a damaged DNA template, represents a common route toward mutagenesis and possibly disease development. To further define the mechanism of this promutagenic process, we synthesized and tested the enzymatic incorporation of two isosteric 5-substituted indolyl-2'deoxyriboside triphosphates opposite an abasic site. The catalytic efficiency for the incorporation of the 5-cyclohexene-indole derivative opposite an abasic site is 75-fold greater than that for the 5-cyclohexyl-indole derivative. The higher efficiency reflects a substantial increase in the k(pol) value (compare 25 versus 0.5 s(-1), respectively) as opposed to an influence on ground-state binding of either non-natural nucleotide. The faster k(pol) value for the 5-cyclohexene-indole derivative indicates that pi-electron density enhances the rate of the enzymatic conformational change step required for insertion opposite the abasic site. However, the kinetic dissociation constants for the non-natural nucleotides are identical and indicate that pi-electron density does not directly influence ground-state binding opposite the DNA lesion. Surprisingly, each non-natural nucleotide can be incorporated opposite natural templating bases, albeit with a greatly reduced catalytic efficiency. In this instance, the lower catalytic efficiency is caused by a substantial decrease in the k(pol) value rather than perturbations in ground-state binding. Collectively, these data indicate that the rate of the conformational change during translesion DNA synthesis depends on pi-electron density, while the enhancement in ground-state binding appears related to the size and shape of the non-natural nucleotide.     

Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof

In this paper, we propose an enriched and extended application of Harel and Sowder’s proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students’ emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14–15) secondary students. We capture these students’ first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students’ multi-faceted and evolving competence in, and appreciation for, proof and proving.     

Regularity results for an optimal design problem with quasiconvex bulk energies

Regularity results for equilibrium configurations of variational problems involving both bulk and surface energies are established. The bulk energy densities are uniformly strictly quasiconvex functions with quadratic growth, but are otherwise not subjected to any further structure conditions. For a minimal configuration (u, E), partial Hölder continuity of the gradient of the deformation u is proved, and partial regularity of the boundary of the minimal set E is obtained.     

State Independence for Tunnelling Processes Through Black Hole Horizons and Hawking Radiation

Tunnelling processes through black hole horizons have recently been investigated in the framework of WKB theory, discovering an interesting interplay with Hawking radiation. In this paper, we instead adopt the point of view proper of QFT in curved spacetime, namely, we use a suitable scaling limit towards a Killing horizon to obtain the leading order of the correlation function relevant for the tunnelling. The computation is done for a certain large class of reference quantum states for scalar fields, including Hadamard states. In the limit of sharp localization either on the external side or on opposite sides of the horizon, the quantum correlation functions appear to have thermal nature. In both cases the characteristic temperature is referred to the surface gravity associated with the Killing field and thus connected with the Hawking one. Our approach is valid for every stationary charged rotating non-extremal black hole. However, since the computation is completely local, it covers the case of a Killing horizon which just temporarily exists in some finite region, too. These results provide strong support to the idea that the Hawking radiation, which is detected at future null infinity and needs some global structures to be defined, is actually related to a local phenomenon taking place even for local geometric structures (local Killing horizons), existing just for a while.     

A characterization of hyperbolic potentials of rational maps

Consider a rational map f of degree at least 2 acting on its Julia set J(f), a H?lder continuous potential φ: J(f) → ℝ and the pressure P(f,φ). In the case where

Determination of natural pesticides in fresh fruits using liquid chromatography/mass spectrometry

An analytical procedure was developed for the determination of some natural pesticides (piperonyl butoxide, nicotine, rotenone, spinosad, and abamectin B1a) in fruit matrixes. The quick, easy, cheap, effective, rugged, and safe (QuEChERS) method was used for extraction. Analysis of the extract was performed by LC-electrospray ionization (ESI)-MS/MS. The ions prominent in the ESI spectra were [M+Na]+ for abamectin B1a, [M+NH4]+ for piperonyl butoxide, and [M+H]+ for the rest of the compounds. A Zorbax SB-C18 column was used with a programmed gradient mobile phase consisting of (A) water containing 0.1% formic acid and 5 mM ammonium formate, and (B) acetonitrile containing 2 mM sodium acetate. The method was linear within the investigated concentration range, displaying a calibration curve correlation factor of 0.99. The CVs obtained were below 20%, and recoveries were in the 70-110% range.     

Apolar carbohydrates as DNA capping agents

Mono- and disaccharides have been shown to stack on top of DNA duplexes stabilizing sequences with terminal C-G base pairs. Here we present an apolar version of glucose and cellobiose as new capping agents that stack on DNA increasing considerably its stability with respect to their natural polyhydroxylated mono- and disaccharide DNA conjugates.     

Erratum and addendum to “Two-point b.v.p. for multivalued equations with weakly regular r.h.s.”

In this paper, we define a topological index for compact multivalued maps in convex metrizable subsets of a locally convex topological vector space in order to correct the proofs of Theorems 4.1 and 4.2 in Benedetti et al. (2011) [1].