Vanishing of charge renormalization and anomalies in a supersymmetric gauge theory

We have determined the charge renormalization function β(g) for the supersymmetric nonabelian gauge model of Gliozzi, Scherk and Olive. We find that its one-and two-loop coefficients are zero. The model is thus anomaly-free at the level of our calculation.     

New aspects of the reactivity of tyrosinase

Tyrosinase was found to be active in the sulfoxidation of thioanisol, producing the (R)-sulfoxide with high enantiomeric excess. The activity of the enzyme with phenolic and diphenolic substrates in a mixed aqueous Hepes buffer pH 6.8-methanol-glycerol solvent was also investigated over a range of temperatures. These experiments enabled us to deduce the thermodynamic parameters associated with substrate binding to the enzyme and the activation parameters associated with the rate determining step of the enzymatic reaction.     

3D Electron Diffraction Structure Determination of Terrylene,a Promising Candidate for Intermolecular Singlet Fission

Herein we demonstrate the prowess of the 3D electron diffraction approach by unveiling the structure of terrylene, the third member in the series of peri-condensed naphthalene analogues, which has eluded structure determination for 65 years. The structure was determined by direct methods using electron diffraction data and corroborated by dispersion-inclusive density functional theory optimizations. Terrylene crystalizes in the monoclinic space group P2₁/a, arranging in a sandwich-herringbone packing motif, similar to analogous compounds. Having solved the crystal structure, we use many-body perturbation theory to evaluate the excited-state properties of terrylene in the solid-state. We find that terrylene is a promising candidate for intermolecular singlet fission, comparable to tetracene and rubrene.     

Structural Characterisation of Complex Layered Double Hydroxides and TGA‐GC‐MS Study on Thermal Response and Carbonate Contamination in Nitrate‐ and Organic‐Exchanged Hydrotalcites

Layered double hydroxides (LDHs) are versatile materials used for intercalating bioactive molecules in the fields of pharmaceuticals, nutraceuticals and cosmetics, with the purpose of protecting them from degradation, enhancing their water solubility to increase bioavailability and improving their pharmacokinetic properties and formulation stability. Moreover, LDHs are used in various technological applications to improve stability and processability. The crystal chemistry of hydrotalcite‐like compounds was investigated by X‐ray powder diffraction (XRPD), automated electron diffraction tomography (ADT) and thermogravimetric analysis (TGA)‐GC‐MS to shed light on the mechanisms involved in ion exchange and absorption of contaminants, mainly carbonate anions. For the first time, ADT allowed a structural model of LDH_NO₃ to be obtained from experiment, shedding light on the conformation of nitrate inside LDH and on the loss of crystallinity due to the layer morphology. The ADT analysis of a hybrid LDH sample (LDH_EUS) clearly revealed an increase in defectivity in this material. XRPD demonstrated that the presence of carbonate can influence the intercalation of organic molecules into LDH, since CO₃‐contaminated samples tend to adopt d spacings that are approximate multiples of the d spacing of LDH_CO₃. TGA‐GC‐MS allowed intercalated and surface‐ adsorbed organic molecules to be distinguished and quantified, the presence and amount of carbonate to be confirmed, especially at low concentrations (<2 wt %), and the different types and strengths of adsorption to be classified with respect to the temperature of elimination.     

Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems

We consider a family of nonlocal capillarity models, where surface tension is modeled by exploiting the family of fractional interaction kernels \(|z|^{-n-s}\), with \(s\in (0,1)\) and n the dimension of the ambient space. The fractional Young’s law (contact angle condition) predicted by these models coincides, in the limit as \(s\rightarrow 1^-\), with the classical Young’s law determined by the Gauss free energy. Here we refine this asymptotics by showing that, for s close to 1, the fractional contact angle is always smaller than its classical counterpart when the relative adhesion coefficient \(\sigma \) is negative, and larger if \(\sigma \) is positive. In addition, we address the asymptotics of the fractional Young’s law in the limit case \(s\rightarrow 0^+\) of interaction kernels with heavy tails. Interestingly, near \(s=0\), the dependence of the contact angle from the relative adhesion coefficient becomes linear.     

The distortion dimension of $$\mathbb $$-rank 1 lattices

Let \(X=G/K\) be a symmetric space of noncompact type and rank \(k\ge 2\). We prove that horospheres in X are Lipschitz \((k-2)\)-connected if their centers are not contained in a proper join factor of the spherical building of X at infinity. As a consequence, the distortion dimension of an irreducible \(\mathbb {Q}\)-rank-1 lattice \(\Gamma \) in a linear, semisimple Lie group G of \(\mathbb R\)-rank k is \(k-1\). That is, given \(m< k-1\), a Lipschitz m-sphere S in (a polyhedral complex quasi-isometric to) \(\Gamma \), and a \((m+1)\)-ball B in X (or G) filling S, there is a \((m+1)\)-ball \(B'\) in \(\Gamma \) filling S such that \({{\mathrm{vol}}}B'\sim {{\mathrm{vol}}}B\). In particular, such arithmetic lattices satisfy Euclidean isoperimetric inequalities up to dimension \(k-1\).     

On the real rank of monomials

In this paper we study the real rank of monomials and we give an upper bound for it. We show that the real and the complex ranks of a monomial coincide if and only if the least exponent is equal to one.