The Fueter mapping theorem in integral form and the ℱ‐functional calculus

In this paper we show a version of the Fueter mapping theorem that can be stated in integral form based on the Cauchy formulas for slice monogenic (or slice regular) functions. More precisely, given a holomorphic function f of a paravector variable, we generate a monogenic function by an integral transform whose kernel is particularly simple. This procedure allows us to define a functional calculus for n‐tuples of commuting operators (called ?‐functional calculus) based on a new notion of spectrum, called ?‐spectrum, for the n‐tuples of operators. Analogous results are shown for the quaternionic version of the theory and for the related ?‐functional calculus. Copyright © 2010 John Wiley & Sons, Ltd.     

A Gas‐Phase CanMn4−nO4+ Cluster Model for the Oxygen‐Evolving Complex of Photosystem II

One of the fundamental processes in nature, the oxidation of water, is catalyzed by a small CaMn₃O₄?MnO cluster located in photosystem II (PS II). Now, the first successful preparation of a series of isolated ligand‐free tetrameric Ca_nMn_4?nO₄⁺ (n=0–4) cluster ions is reported, which are employed as structural models for the catalytically active site of PS II. Gas‐phase reactivity experiments with D₂O and H₂¹⁸O in an ion trap reveal the facile deprotonation of multiple water molecules via hydroxylation of the cluster oxo bridges for all investigated clusters. However, only the mono‐calcium cluster CaMn₃O₄⁺ is observed to oxidize water via elimination of hydrogen peroxide. First‐principles density functional theory (DFT) calculations elucidate mechanistic details of the deprotonation and oxidation reactions mediated by CaMn₃O₄⁺ as well as the role of calcium.     

Cutaneous Photoprotective Activity of a Short‐term Ingestion of High‐Flavanol Cocoa: A Nutritional Intervention Study

In vivo and in vitro studies have shown that prolonged oral administration of flavanol‐rich cocoas extracts have photoprotective effects. The aim of the present study was to assess the photoprotective activity of short‐time administration of a new variety of naturally selected cocoa extract rich in bioactive compounds. We selected a cocoa powder particularly rich in polyphenols, flavanols, caffeine, theobromine and theophylline. We then investigated, in 10 healthy subjects, the photoprotective effects of one week of daily oral administration of two doses of such powder. Phototesting with solar simulated radiation was performed at baseline and after cocoa supplementation. Visual assessment of the minimal erythema dose and spectrophotometric measurement of the “a” parameter were done after 24 h from the irradiation. Oral daily supplementation of 1 g of high‐flavanol cocoa was not effective but a one‐week administration of 4–6 g of cocoa induced a statistically significant increase in the visual erythema threshold and a significant reduction in the “a” parameter. We demonstrated that a new variety of naturally selected cocoa extract, even when administered for a short time, retains a dose‐dependent photoprotective effect. These results are also indicative of the fact that topical sunscreens could be supplemented by a specific diet.     

Entanglement in Finite Quantum Systems Under Twisted Boundary Conditions

In a recent publication, we have discussed the effects of boundary conditions in finite quantum systems and their connection with symmetries. Focusing on the one-dimensional Hubbard Hamiltonian under twisted boundary conditions, we have shown that properties, such as the ground-state and gap energies, converge faster to the thermodynamical limit (\(L \rightarrow \infty \)) if a special torsion Θ^? is adjusted to ensure particle-hole symmetry. Complementary to the previous research, the present paper extends our analysis to a key quantity for understanding correlations in many-body systems: the entanglement. Specifically, we investigate the average single-site entanglement 〈S_j〉 as a function of the coupling U/t in Hubbard chains with up to L =?8 sites and further examine the dependence of the per-site ground-state ??₀ on the torsion Θ in different coupling regimes. We discuss the scaling of ??₀ and 〈S_j〉 under Θ^? and analyze their convergence to Bethe Ansatz solution of the infinite Hubbard Hamiltonian. Additionally, we describe the exact diagonalization procedure used in our numerical calculations and show analytical calculations for the case study of a trimer.     

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.     

C−H Functionalization of Commodity Polymers

Synthetic manipulation of polymer substrates is one of the oldest and most reliable methods to increase the functional diversity of soft materials. Modifying the chemical structure of polymers that are already produced on a commodity scale leverages the current high‐volume and low‐cost production of commodity plastics for the discovery of modern materials. A myriad of polymer C?H functionalization methods have been developed which enable the modification of material properties on both a laboratory and industrial scale. More recently, driven by advances in C?H activation, photoredox catalysis, and radical chemistry, chemoselective approaches have emerged as a means to impart precise functionality onto commodity polymer substrates. This Review discusses the historical significance of and contemporary advances in the C?H functionalization of commodity polymers. The conceptual approach outlined herein presents exciting new directions for the field, including increasing the value of otherwise pervasive materials, uncovering entirely new material properties, and a viable path to upcycle post‐consumer plastic waste.     

Stereospecific synthesis of optically active phenylpropylene oxides

The stereospecific lithiation of diastereomeric phenylpropylene oxides has been studied as well as the trapping reaction with electrophiles. The reduction of the cis-alpha-benzoylpropylene oxide to give prevalently the anti-epoxy alcohol has been investigated as well.     

Regulatory and compliance activities to protect food-allergic consumers in Canada: research in support of standard setting and consumer protection

An overview is presented of the activities of Health Canada and the Canadian Food Inspection Agency (CFIA) in the area of food allergens. Since the 1990s, changes were made in the Food and Drug Regulations in order to better protect allergic consumers by imposing labeling requirements to clearly identify sources of priority food allergens in prepackaged foods. Policies of application as well as risk management strategies are discussed with some statistics on allergen-related food recalls in Canada for the years 1997--2001. Health Canada's allergen method development program is a pioneering research initiative that was developed in the early 1990s in support of the changing Canadian regulatory environment. The objectives and some of the accomplishments of this program are presented. The development of the Canadian Compendium of Allergen Methodologies under a Web-based application to compile data on evaluated allergen detection methods will provide further support to compliance activities nationally, as well as to the international analytical community in both government and the food industry. Some emerging techniques for the confirmation of results generated by enzyme-linked immunosorbent assays are also discussed.