Inverting the Nakanishi Integral Relation for a Bound State Euclidean Bethe–Salpeter Amplitude

The extraction of the weight function g of the Nakanishi integral representation of the Bethe–Salpeter amplitude is investigated. We studied the numerical inversion of the discretized Nakanishi kernel in the case of an Euclidean bound state. The discretized kernel is regularized by adding the identity operator times a small regularisation parameter \({\varepsilon}\) to avoid numerically unstabilities. We have found that the weight function g as well as the associated light-front valence wave function are unstable against variation of \({\varepsilon}\). These results suggest that the extraction of the Nakanishi weight function from an Euclidean amplitude, is an ill-defined problem. Without further assumptions on the solution or/and without developing more elaborate methods, the Nakanishi weight function, as well as the corresponding light-front valence wave function, cannot be safely determined.     

An Alexandrov–Fenchel-Type Inequality in Hyperbolic Space with an Application to a Penrose Inequality

We prove a sharp Alexandrov–Fenchel-type inequality for star-shaped, strictly mean convex hypersurfaces in hyperbolic n-space, n ≥ 3. The argument uses two new monotone quantities along the inverse mean curvature flow. As an application we establish, in any dimension, an optimal Penrose inequality for asymptotically hyperbolic graphs carrying a minimal horizon, with the equality occurring if and only if the graph is an anti-de Sitter–Schwarzschild solution. This sharpens previous results by Dahl–Gicquaud–Sakovich and settles, for this class of initial data sets, the conjectured Penrose inequality for time-symmetric space–times with negative cosmological constant. We also explain how our methods can be easily adapted to derive an optimal Penrose inequality for asymptotically locally hyperbolic graphs in any dimension n ≥ 3. When the horizon has the topology of a compact surface of genus at least one, this provides an affirmative answer, for this class of initial data sets, to a question posed by Gibbons, Chru?ciel and Simon on the validity of a Penrose-type inequality for exotic black holes.     

On Kulikov’s problem

Kulikov has given an étale morphism of degree d > 1 which is surjective modulo codimension two with X simply connected, settling his generalized jacobian problem. His method reduces the problem to finding a hypersurface and a subgroup of index d generated by geometric generators. By contrast we show that if D has simple normal crossings away from a set of codimension three and meets the hyperplane at infinity transversely, then necessarily d = 1. Received: 21 November 2006     

Pharmacological and Therapeutic Potential of Myristicin: A Literature Review

Natural products have been used by humanity for many centuries to treat various illnesses and with the advancement of technology, it became possible to isolate the substances responsible for the beneficial effects of these products, as well as to understand their mechanisms. In this context, myristicin, a substance of natural origin, has shown several promising activities in a large number of in vitro and in vivo studies carried out. This molecule is found in plants such as nutmeg, parsley, carrots, peppers, and several species endemic to the Asian continent. The purpose of this review article is to discuss data published in the last 10 years at Pubmed, Lilacs and Scielo databases, reporting beneficial effects, toxicity and promising data of myristicin for its future use in medicine. From 94 articles found in the literature, 68 were included. Exclusion criteria took into account articles whose tested extracts did not have myristicin as one of the major compounds.     

Csp-tellurium copper cross-coupling: synthesis of alkynyl tellurides a novel class of antidepressive-like compounds

We present here the results on the synthesis of functionalized alkynyl tellurides using the reaction of vinyl, alkynyl, and aryl tellurides with several alkynyl iodides catalyzed by copper iodide. The reaction proceeded cleanly under mild reaction conditions, at room temperature, in the absence of base and ligand giving alkynyl tellurides in acceptable yields. The obtained compounds 3a-c and 3m-o were screened for antidepressive-like activity using the tail suspension test (TST) in mice. Compounds 3a-c and 3m-o administered at 10 mg/kg by oral route produced a significant antidepressant-like effect on the TST in mice.     

Structural Determination of a Photochemically Active Diplatinum Molecule by Time‐Resolved EXAFS Spectroscopy

Metallica : A large contraction of the Pt? Pt bond in the triplet excited state of the photoreactive [Pt₂(P₂O₅H₂)₄]^4? ion is determined by time‐resolved X‐ray absorption spectroscopy (see picture). The strengthening of the Pt? Pt interaction is accompanied by a weakening of the ligand coordination bonds, resulting in an elongation of the platinum–ligand bond that is determined for the first time.

     

Excitation of local magnetic moments by tunneling electrons

The advent of milli-kelvin scanning tunneling microscopes (STM) with inbuilt magnetic fields has opened access to the study of magnetic phenomena with atomic resolution at surfaces. In the case of single atoms adsorbed on a surface, the existence of different magnetic energy levels localized on the adsorbate is due to the breaking of the rotational invariance of the adsorbate spin by the interaction with its environment, leading to energy terms in the meV range. These structures were revealed by STM experiments in IBM Almaden in the early 2000s for atomic adsorbates on CuN surfaces. The experiments consisted in the study of the changes in conductance caused by inelastic tunneling of electrons (IETS, inelastic electron tunneling spectroscopy). Manganese and Iron adatoms were shown to have different magnetic anisotropies induced by the substrate. More experiments by other groups followed up, showing that magnetic excitations could be detected in a variety of systems: e.g. complex organic molecules showed that their magnetic anisotropy was dependent on the molecular environment, piles of magnetic molecules showed that they interact via intermolecular exchange interaction, spin waves were excited on ferromagnetic surfaces and in Mn chains, and magnetic impurities have been analyzed on semiconductors. These experiments brought up some intriguing questions: the efficiency of magnetic excitations was very high, the excitations could or could not involve spin flip of the exciting electron and singular-like behavior was sometimes found at the excitation thresholds. These facts called for extended theoretical analysis; perturbation theories, sudden-approximation approaches and a strong coupling scheme successfully explained most of the magnetic inelastic processes. In addition, many-body approaches were also used to decipher the interplay between inelastic processes and the Kondo effect. Spin torque transfer has been shown to be effective in changing spin orientations of an adsorbate in theoretical works, and soon after it was shown experimentally. More recently, the previously mentioned strong coupling approach was extended to treat the excitation of spin waves in atomic chains and the ubiquitous role of electron–hole pair creation in de-exciting spins on surfaces has been analyzed. This review article expounds these works, presenting the theoretical approach by the authors while trying to thoroughly review parallel theoretical and experimental works.     

Thermodynamic Signatures of Structural Transitions and Dissociation of Charged Colloidal Clusters: A Parallel Tempering Monte Carlo Study

Computational simulation of colloidal systems make use of empirical interaction potentials that are founded in well-established theory. In this work, we have performed parallel tempering Monte Carlo (PTMC) simulations to calculate heat capacity and to assess structural transitions, which may occur in charged colloidal clusters whose effective interactions are described by a sum of pair potentials with attractive short-range and repulsive long-range components. Previous studies on these systems have shown that the global minimum structure varies from spherical-type shapes for small-size clusters to Bernal spiral and “beaded-necklace” shapes at intermediate and larger sizes, respectively. In order to study both structural transitions and dissociation, we have organized the structures appearing in the PTMC calculations by three sets according to their energy: (i) low-energy structures, including the global minimum; (ii) intermediate-energy “beaded-necklace” motifs; (iii) high-energy linear and branched structures that characterize the dissociative clusters. We observe that, depending on the cluster, either peaks or shoulders on the heat–capacity curve constitute thermodynamics signatures of dissociation and structural transitions. The dissociation occurs at T=0.20 for all studied clusters and it is characterized by the appearance of a significant number of linear structures, while the structural transitions corresponding to unrolling the Bernal spiral are quite dependent on the size of the colloidal system.     

Synthesis of guaiane sesquiterpenoids by a ring-closing metathesis annulation sequence

A new route for the synthesis of guaiane and nor-guaiane sesquiterpenoids is described, using a ring-closing metathesis annulation reaction sequence on a chiral enantiopure cycloheptenone derived from (R)-(−)-carvone.