Asymptotic analysis of a second-order singular perturbation model for phase transitions

We study the asymptotic behavior, as ${\varepsilon}$ tends to zero, of the functionals ${F^k_\varepsilon}$ introduced by Coleman and Mizel in the theory of nonlinear second-order materials; i.e., $$F^k_\varepsilon(u):=\int\limits_{I} \left(\frac{W(u)}{\varepsilon}-k\,\varepsilon\,(u')^2+\varepsilon^3(u'')^2\right)\,dx,\quad u\in W^{2,2}(I),$$ where k?>?0 and ${W:\mathbb{R}\to[0,+\infty)}$ is a double-well potential with two potential wells of level zero at ${a,b\in\mathbb{R}}$ . By proving a new nonlinear interpolation inequality, we show that there exists a positive constant k ₀ such that, for k?<?k ₀, and for a class of potentials W, ${(F^k_\varepsilon)}$ ??(L ¹)-converges to $$F^k(u):={\bf m}_k \, \#(S(u)),\quad u\in BV(I;\{a,b\}),$$ where m _k is a constant depending on W and k. Moreover, in the special case of the classical potential ${W(s)=\frac{(s^2-1)^2}{2}}$ , we provide an upper bound on the values of k such that the minimizers of ${F_\varepsilon^k}$ cannot develop oscillations on some fine scale and a lower bound on the values for which oscillations occur, the latter improving a previous estimate by Mizel, Peletier and Troy.     

Tyrosine or Tryptophan? Modifying a Metalloradical Catalytic Site by Removal of the Cys–Tyr Cross-Link in the Galactose 6-Oxidase Homologue GlxA

The concerted redox action of a metal ion and an organic cofactor is a unique way to maximize the catalytic power of an enzyme. An example of such synergy is the fungal galactose 6-oxidase, which has inspired the creation of biomimetic copper oxidation catalysts. Galactose 6-oxidase and its bacterial homologue, GlxA, possess a metalloradical catalytic site that contains a free radical on a covalently linked Cys–Tyr and a copper atom. Such a catalytic site enables for the two-electron oxidation of alcohols to aldehydes. When the ability to form the Cys–Tyr in GlxA is disrupted, a radical can still be formed. Surprisingly, the radical species is not the Tyr residue but rather a copper second-coordination sphere Trp residue. This is demonstrated through the introduction of a new algorithm for Trp-radical EPR spectra simulation. Our findings suggest a new mechanism of free-radical transfer between aromatic residues and that the Cys–Tyr cross-link prevents radical migration away from the catalytic site.     

Synthesis and characterization of Si/Ga Eni Carbon Silicates

Phenylene-gallosilicates were prepared with the same crystalline structure as their aluminum ana-logues. The new Ga-Eni Carbon Silicates (Ga-ECS) phases were investigated by X-ray diffraction, scanning electron microscopy, nuclear magnetic resonance and thermogravimetric analysis, which demonstrated that gallium isomorphously replaced aluminum in the framework of the organ-ic-inorganic hybrids similar to the case of classical zeolites. Hybrid ECS materials were obtained with different types of bridged silsesquioxane precursors that maintained the aluminum-silicate nature of the inorganic moiety. This work confirms a new level of crystal chemistry versatility for this class of materials, and demonstrates the possibility to tailor also the inorganic part of the framework by changing the nature of the trivalent heteroatom.     

A Note on Closed Degrees of Difficulty of the Medvedev Lattice

We consider some nonprincipal filters of the Medvedev lattice. We prove that the filter generated by the nonzero closed degrees of difficulty is not principal and we compare this filter, with respect to inclusion, with some other filters of the lattice. All the filters considered in this paper are disjoint from the prime ideal generated by the dense degrees of difficulty. Mathematics Subject Classification: 03D30.     

On the fractional chromatic index of a graph and its complement

Jensen and Toft conjectured that for a graph with an even number of vertices, either the minimum number of colours in a proper edge colouring is equal to the maximum vertex degree, or this is true in its complement. We prove a fractional version of this conjecture.     

Solid‐State NMR of PEGylated Proteins

PEGylated proteins are widely used in biomedicine but, in spite of their importance, no atomic‐level information is available since they are generally resistant to structural characterization approaches. PEGylated proteins are shown here to yield highly resolved solid‐state NMR spectra, which allows assessment of the structural integrity of proteins when PEGylated for therapeutic or diagnostic use.     

Hovenia dulcis Thumberg: Phytochemistry,Pharmacology, Toxicology and Regulatory Framework for Its Use in the European Union

Hovenia dulcis Thunberg is an herbal plant, belonging to the Rhamnaceae family, widespread in west Asia, USA, Australia and New Zealand, but still almost unknown in Western countries. H. dulcis has been described to possess several pharmacological properties, such as antidiabetic, anticancer, antioxidant, anti-inflammatory and hepatoprotective, especially in the hangover treatment, validating its use as an herbal remedy in the Chinese Traditional Medicine. These biological properties are related to a variety of secondary metabolites synthesized by the different plant parts. Root, bark and leaves are rich of dammarane-type triterpene saponins; dihydrokaempferol, quercetin, 3,3′,5′,5,7-pentahydroflavone and dihydromyricetin are flavonoids isolated from the seeds; fruits contain mainly dihydroflavonols, such as dihydromyricetin (or ampelopsin) and hovenodulinol, and flavonols such as myricetin and gallocatechin; alkaloids were found in root, barks (frangulanin) and seeds (perlolyrin), and organic acids (vanillic and ferulic) in hot water extract from seeds. Finally, peduncles have plenty of polysaccharides which justify the use as a food supplement. The aim of this work is to review the whole scientific production, with special focus on the last decade, in order to update phytochemistry, biological activities, nutritional properties, toxicological aspect and regulatory classification of H. dulcis extracts for its use in the European Union.     

Enantioselective synthesis of sphingadienines and aromatic ceramide analogs

A new approach to the synthesis of sphingoid bases has been developed. The strategy is based on Sonogashira coupling of a chiral acetylenic carbamate that can be prepared in enantiomerically enriched form from 2,3-epoxy-4-pentyn-1-ol, which is readily accessible by Sharpless asymmetric epoxidation. Several N-Boc-sphingadienines and aromatic ceramide analogs have been synthesized.     

Regular Moebius transformations of the space of quaternions

Quaternionic Moebius transformations have been investigated for more than 100 years and their properties have been characterized in detail. In recent years G. Gentili and D. C. Struppa introduced a new notion of regular function of a quaternionic variable, which is developing into a quite rich theory. Several properties of regular quaternionic functions are analogous to those of holomorphic functions of one complex variable, although the diversity of the non-commutative setting introduces new phenomena. Unfortunately, the (classical) quaternionic Moebius transformations are not regular. However, in this paper we are able to construct a different class of Moebius-type transformations that are indeed regular. This construction requires several steps: we first find an analog to the Casorati-Weierstrass theorem and use it to prove that the group \({Aut(\mathbb{H})}\) of biregular functions on \({\mathbb{H}}\) coincides with the group of regular affine transformations. We then show that each regular injective function from \({\widehat{\mathbb{H}} = \mathbb{H}\cup \{\infty\}}\) to itself belongs to a special class of transformations, called regular fractional transformations. Among these, we focus on the ones which map the unit ball \({\mathbb{B} = \{q \in \mathbb{H} : |q| < 1 \}}\) onto itself, called regular Moebius transformations. We study their basic properties and we are able to characterize them as the only regular bijections from \({\mathbb{B}}\) to itself.