Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis

We present a new method for construction of high-order parametrizations of surfaces: starting from point clouds, the method we propose can be used to produce full surface parametrizations (by sets of local charts, each one representing a large surface patch – which, typically, contains thousands of the points in the original point-cloud) for complex surfaces of scientific and engineering relevance. The proposed approach accurately renders both smooth and non-smooth portions of a surface: it yields super-algebraically convergent Fourier series approximations to a given surface up to and including all points of geometric singularity, such as corners, edges, conical points, etc. In view of their C^∞ smoothness (except at true geometric singularities) and their properties of high-order approximation, the surfaces produced by this method are suitable for use in conjunction with high-order numerical methods for boundary value problems in domains with complex boundaries, including PDE solvers, integral equation solvers, etc. Our approach is based on a very simple concept: use of Fourier analysis to continue smooth portions of a piecewise smooth function into new functions which, defined on larger domains, are both smooth and periodic. The “continuation functions” arising from a function f converge super-algebraically to f in its domain of definition as discretizations are refined. We demonstrate the capabilities of the proposed approach for a number of surfaces of engineering relevance.     

Green Synthesis of Gold and Silver Nanoparticles Using Leaf Extract of Capsicum chinense Plant

So far, several studies have focused on the synthesis of metallic nanoparticles making use of extracts from the fruit of the plants from the genus Capsicum. However, as the fruit is the edible, and highly commercial, part of the plant, in this work we focused on the leaves, a part of the plant that is considered agro-industrial waste. The biological synthesis of gold (AuNPs) and silver (AgNPs) nanoparticles using aqueous extracts of root, stem and leaf of Capsicum chinense was evaluated, obtaining the best results with the leaf extract. Gold and silver nanoparticles synthesized using leaf extract (AuNPs-leaf and AgNPs-leaf, respectively) were characterized by UV-visible spectrophotometry (UV-Vis), Fourier Transform Infrared Spectroscopy with Attenuated Total Reflection (FTIR-ATR), X-ray Photoelectron Spectroscopy (XPS), Ultra Hight Resolution Scanning Electron Microscopy coupled to Energy-Dispersive X-ray spectroscopy (UHR-SEM-EDX) and Transmission Electron Microscopy (TEM), and tested for their antioxidant and antimicrobial activities. In addition, different metabolites involved in the synthesis of nanoparticles were analyzed. We found that by the use of extracts derived from the leaf, we could generate stable and easy to synthesize AuNPs and AgNPs. The AuNPs-leaf were synthesized using microwave radiation, while the AgNPs-leaf were synthesized using UV light radiation. The antioxidant activity of the extract, determined by ABTS, showed a decrease of 44.7% and 60.7% after the synthesis of the AuNPs-leaf and AgNPs-leaf, respectively. After the AgNPs-leaf synthesis, the concentration of polyphenols, reducing sugars and amino acids decreased by 15.4%, 38.7% and 46.8% in the leaf extract, respectively, while after the AuNPs-leaf synthesis only reducing sugars decreased by 67.7%. These results suggest that these groups of molecules are implicated in the reduction/stabilization of the nanoparticles. Although the contribution of these compounds in the synthesis of the AuNPs-leaf and the AgNPs-leaf was different. Finally, the AgNPs-leaf inhibited the growth of S. aureus, E. coli, S. marcescens and E. faecalis. All of them are bacterial strains of clinical importance due to their fast antibiotic resistance development.     

Elucidation of urinary metabolites of fluoxymesterone by liquid chromatography-tandem mass spectrometry and gas chromatography-mass spectrometry

The suitability of liquid chromatography tandem mass spectrometry (LC-MS/MS) and gas chromatography mass spectrometry (GC-MS) for the elucidation of fluoxymesterone metabolism has been evaluated. Electrospray ionization (ESI) and collision induced dissociation (CID) fragmentation in LC-MS/MS and electron impact spectra (EI) in GC-MS have been studied for fluoxymesterone and two commercially available metabolites. MS(n) experiments and accurate mass measurements performed by an ion-trap analyser and a QTOF instrument respectively have been used for the elucidation of the fragmentation pathway. The neutral loss scan of 20 Da (loss of HF) in LC-MS/MS has been applied for the selective detection of fluoxymesterone metabolites. In a positive fluoxymesterone doping control sample, 9 different analytes have been detected including the parent compound. Seven of these metabolites were also confirmed by GC-MS including 5 previously unreported metabolites. On the basis of the ionization, the CID fragmentation, the accurate mass of the product ions and the EI spectra of these analytes, a tentative elucidation as well as a proposal for the metabolic pathway of fluoxymesterone has been suggested. The presence of these compounds has also been confirmed by the analysis of five other positive fluoxymesterone urine samples.     

The Synthesis of B2(SIDip)2 and its Reactivity Between the Diboracumulenic and Diborynic Extremes

A new compound with the formula L‐B₂‐L wherein the stabilizing ligand (L) is 1,3‐bis[diisopropylphenyl]‐4,5‐dihydroimidazol‐2‐ylidene (SIDip) has been synthesized, isolated, and characterized. The π‐acidity of the SIDip ligand, intermediate between the relatively non‐acidic IDip (1,3‐bis[diisopropylphenyl]imidazol‐2‐ylidene) ligand and the much more highly acidic CAAC (1‐[2,6‐diisopropylphenyl]‐3,3,5,5‐tetramethylpyrrolidin‐2‐ylidene) ligand, gives rise to a compound with spectroscopic, electrochemical, and structural properties between those of L‐B₂‐L compounds stabilized by CAAC and IDip. Reactions of all three L‐B₂‐L compounds with CO demonstrate the differences caused by their respective ligands, as the π‐acidities of the CAAC and SIDip carbenes enabled the isolation of bis(boraketene) compounds (L(OC)B‐B(CO)L), which could not be isolated from reactions with B₂(IDip)₂. However, only B₂(IDip)₂ and B₂(SIDip)₂ could be converted into bicyclic bis(boralactone) compounds.     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

Synthesis of novel C-2 substituted pyrimidine nucleoside analogs

A series of 2-(2-oxoalkylidene)-4(1H)-pyrimidinone nucleoside analogs were synthesized by the addition of the lithium enolates of methylketones to 2,5′- and 2,2′-anhydrouridines and to 2,5′-anhydrothymidines. Alternatively, 2-thiouridine was alkylated with bromomethyl ketones to yield 2-(2-oxoalkyl)thio-4(1H)-pyrimidinone ribofuranosides in good yields. These intermediates were subsequently transformed into the title compounds via an Eschenmoser sulfur extrusion reaction. The 2-(2-oxoalkylidene)-4-(1H)-pyrimidinone nucleoside analogs exhibit enol proton signals in their ¹H nmr spectra indicative of hydrogen bonding between N-3 and keto oxygen. These structures offer functional groups with potential for Watson-Crick hydrogen bonding.     

Fragment-asperity interaction model for earthquakes

A model for earthquake dynamics consisting of two rough profiles interacting via fragments filling the gap is introduced, the fragments being produced by the local breakage due to the interaction of the local plates. The irregularities of the fault planes can interact with the fragments between them to develop a mechanism for triggering earthquakes. The fragment size distribution function comes from a nonextensive formulation, starting from first principles. An energy distribution function, which gives the Gutenberg-Richter law as a particular case, is analytically deduced.     

Transition‐Metal π‐Ligation of a Tetrahalodiborane

The reaction of tetraiododiborane (B₂I₄) with trans‐[Pt(BI₂)I(PCy₃)₂] gives rise to the diplatinum(II) complex [{(Cy₃P)(I₂B)Pt}₂(μ₂:η³:η³‐B₂I₄)], which is supported by a bridging diboranyl dianion ligand [B₂I₄]^2?. This complex is the first transition‐metal complex of a diboranyl dianion, as well as the first example of intact coordination of a B₂X₄ (X=halide) unit of any type to a metal center.     

Boryl‐Functionalized σ‐Alkynyl and Vinylidene Rhodium Complexes: Synthesis and Electronic Properties

The synthesis, reactivity, and properties of boryl‐functionalized σ‐alkynyl and vinylidene rhodium complexes such as trans‐[RhCl(?C?CHBMes₂)(PiPr₃)₂] and trans‐[Rh(C?CBMes₂)(IMe)(PiPr₃)₂] are reported. An equilibrium was found to exist between rhodium vinylidene complexes and the corresponding hydrido σ‐alkynyl complexes in solution. The complex trans‐[Rh(C?CBMes₂)(IMe)(PiPr₃)₂] (IMe=1,3‐dimethylimidazol‐2‐ylidene) was found to exhibit solvatochromism and can be quasireversibly oxidized and reduced electrochemically. Density functional calculations were performed to determine the reaction mechanism and to help rationalize the photophysical properties of trans‐[Rh(C?CBMes₂)(IMe)(PiPr₃)₂].