Diophantine inequalities and quasi-algebraically closed fields

Consider a form g(x ₁,...,x _s ) of degree d, having coefficients in the completion of the field of fractions associated to the finite field . We establish that whenever s > d ₂, then the form g takes arbitrarily small values for non-zero arguments . We provide related results for problems involving distribution modulo , and analogous conclusions for quasi-algebraically closed fields in general.     

PyFrag 2019—Automating the exploration and analysis of reaction mechanisms

We present a substantial update to the PyFrag 2008 program, which was originally designed to perform a fragment-based activation strain analysis along a provided potential energy surface. The original PyFrag 2008 workflow facilitated the characterization of reaction mechanisms in terms of the intrinsic properties, such as strain and interaction, of the reactants. The new PyFrag 2019 program has automated and reduced the time-consuming and laborious task of setting up, running, analyzing, and visualizing computational data from reaction mechanism studies to a single job. PyFrag 2019 resolves three main challenges associated with the automated computational exploration of reaction mechanisms: it (1) computes the reaction path by carrying out multiple parallel calculations using initial coordinates provided by the user; (2) monitors the entire workflow process; and (3) tabulates and visualizes the final data in a clear way. The activation strain and canonical energy decomposition results that are generated relate the characteristics of the reaction profile in terms of intrinsic properties (strain, interaction, orbital overlaps, orbital energies, populations) of the reactant species. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.     

Synthesis of Floridoside

Floridoside (2-O-glycerol-α-D-galactopyranoside) is a natural glycerol glycoside found in red algae and is believed to play important roles in carbon storage, transport, and assimilation and in the regulation of osmotic balance. We describe here a rapid, high-yield, and high-stereoselectivity synthesis of floridoside in which the key step involves the 1,2-cis O-glycosylation of 1,3-dibenzylglycerol with ethyl 2,3,4,6-tetra-O-benzyl-1-thio-β-D-galactopyranoside using iodonium dicollidine perchlorate (IDCP) or N-iodosuccinimide/trimethylsilyl triflate (NIS/TMSOTf) as promoters.     

High pressure vapor–liquid equilibrium measurements of carbon dioxide with naphthalene and benzoic acid

High pressure vapor–liquid equilibrium data for binary systems of carbon dioxide with naphthalene and benzoic acid were measured at three different temperatures for each system. Experimental temperatures and pressures ranged from 373 to 458 K and 0 to 22 MPa, respectively. Dew points were also measured for naphthalene in the CO₂ rich region. The data measured provides valuable solubility information and is used to derive gas–solvent group interaction parameters for the predictive Soave–Redlich–Kwong equation of state.     

The self‐assembling zwitterionic form of L‐phenylalanine at neutral pH

The title zwitterion (2S)‐2‐azaniumyl‐1‐hydroxy‐3‐phenylpropan‐1‐olate, C₉H₁₁NO₂, also known as L‐phenylalanine, was characterized using synchrotron X‐rays. It crystallized in the monoclinic space group P2₁ with four molecules in the asymmetric unit. The 0.62 Å resolution structure is assumed to be closely related to the fibrillar form of phenylalanine, as observed by electron microscopy and electron diffraction. The structure exists in a zwitterionic form in which π–π stacking and hydrogen‐bonding interactions are believed to form the basis of the self‐assembling properties.     

Liquid injection field desorption/ionization of transition metal fluoride complexes

Metal fluoride complexes that are extremely sensitive to air and water have been characterized by liquid injection field desorption/ionization (LIFDI) mass spectrometry. Dilute solutions of fluoride complexes of nickel, rhodium, titanium, zirconium and ruthenium in toluene and tetrahydrofuran were examined by LIFDI methods on a time-of-flight mass spectrometer. All the spectra of nickel, titanium and zirconium complexes exhibited the molecular ion as base peak. The ruthenium and rhodium complexes showed [M−HF]⁺ as base peaks but the molecular ions were easily detected. The nickel complexes do not provide useful mass spectra by EI or ESI methods. Only the titanium and zirconium species showed evidence of the fluoride ligands in the ESI spectra. Two new nickel fluoride complexes are formed by C-F activation reactions with 2,3,5,6-tetrafluoro-4-dimethylaminopyridine and 2,3,5,6-tetrafluoro-4-methoxypyridine yielding trans-NiF{2-C₅NF₃(4-NMe₂)}(PEt₃)₂ and trans-NiF{2-C₅NF₃(4-OMe)}(PEt₃)₂, respectively. The crystal structure of trans-NiF{2-C₅NF₃(4-NMe₂)}(PEt₃)₂ shows typical square planar coordination at nickel with an Ni-F distance of 1.8521(9) Å.     

Sums and Differences of Two Cubic Polynomials

 When f(x) is a cubic polynomial with integral coefficients, we show that almost all integers represented as the sum or difference of two values of f(x), with , are thus represented essentially uniquely. (Received 18 January 1999; in revised form 17 May 1999)