Extension of the York field decomposition to general gravitationally coupled fields

We extend the York decomposition analysis of the initial value constraints to general gravitationally coupled classical field theories. The decomposition is found to be particularly useful in solving the constraint equations for all theories of current physical interest. These include Einstein gravity or Einstein-Cartan (torsion) gravity coupled to the massive or massless version of the following: general scalar (including Klein-Gordon, Brans-Dicke, and Higgs), Dirac spin 1/2, Maxwell (Proca) and Yang-Mills (any gauge group). We show in detail how the program works for the general Yang-Mills field and for the Einstein-Cartan-Proca field.     

Quantitation of ortho‐cresyl phosphate adducts to butyrylcholinesterase in human serum by immunomagnetic‐UHPLC‐MS/MS

Tri‐ortho‐cresyl phosphate (ToCP) is an anti‐wear, flame retardant additive used in industrial lubricants, hydraulic fluids and gasoline. The neurotoxic effects of ToCP arise from the liver‐activated metabolite 2‐(o‐cresyl)‐4H‐1,3,2‐benzodioxaphosphoran‐2‐one (cresyl saligenin phosphate or CBDP), which inhibits esterase enzymes including butyrylcholinesterase (BChE). Following BChE adduction, CBDP undergoes hydrolysis to form the aged adduct ortho‐cresyl phosphoserine (oCP‐BChE), thus providing a biomarker of CBDP exposure. Previous studies have identified ToCP in aircraft cabin and cockpit air, but assessing human exposure has been hampered by the lack of a laboratory assay to confirm exposure. This work presents the development of an immunomagnetic‐UHPLC‐MS/MS method for the quantitation of unadducted BChE and the long‐term CBDP biomarker, oCP‐BChE, in human serum. The method has a reportable range from 2.0 ng/ml to 150 ng/ml, which is consistent with the sensitivity of methods used to detect organophosphorus nerve agent protein adducts. The assay demonstrated high intraday and interday accuracy (≥85%) and precision (RSD ≤ 15%) across the calibration range. The method was developed for future analyses of potential human exposure to CBDP. Analysis of human serum inhibited in vitro with CBDP demonstrated that the oCP‐BChE adduct was stable for at least 72 h at 4, 22 and 37 °C. Compared to a previously reported assay, this method requires 75% less sample volume, reduces analysis time by a factor of 20 and demonstrates a threefold improvement in sensitivity. Published 2015. This article is a U.S. Government work and is in the public domain in the USA.     

Bis-[3]Ferrocenophanes with Central >E−E’< Bonds (E,E’=P,SiH): Preparation,Properties, and Thermal Activation

A series of bis-[3]ferrocenophanes of the general type Fe(C₅H₄E’)₂E−E(E'C₅H₄)₂Fe (E=P, SiH and E’=PtBu, NneoPentyl, NSi(CH₃)₃) with an isolobal molecular framework have been prepared and characterized by heteronuclear NMR spectroscopy and X-ray crystallography. The thermal dissociation behavior with respect to homolytic fission of the central bond generating phosphorus centered radicals was investigated using EPR spectroscopy and quantum chemical calculations.     

A geometric introduction to the two-loop renormalization group flow

The Ricci flow has been of fundamental importance in mathematics, most famously through its use as a tool for proving the Poincaré conjecture and Thurston’s geometrization conjecture. It has a parallel life in physics, arising as the first-order approximation of the renormalization group flow for the nonlinear sigma model of quantum field theory. There recently has been interest in the second-order approximation of this flow, called the RG-2 flow, which mathematically appears as a natural nonlinear deformation of the Ricci flow. A curvature flow arising from quantum field theory seems to us to capture the spirit of Yvonne Choquet-Bruhat’s extensive work in mathematical physics, and so in this commemorative article we give a geometric introduction to the RG-2 flow. A number of new results are presented as part of this narrative: short-time existence and uniqueness results in all dimensions if the sectional curvatures K _ij satisfy certain inequalities; the calculation of fixed points for n =  3 dimensions; a reformulation of constant curvature solutions in terms of the Lambert W function; a classification of the solutions that evolve only by homothety; an analogue for RG flow of the 2-dimensional Ricci flow solution known to mathematicians as the cigar soliton, and discussed in the physics literature as Witten’s black hole. We conclude with a list of open problems whose resolutions would substantially increase our understanding of the RG-2 flow both physically and mathematically.     

Asymptotic Gluing of Asymptotically Hyperbolic Solutions to the Einstein Constraint Equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.     

An efficient one-pot synthesis of coumarin-amino acid derivatives as potential anti-inflammatory and antioxidant agents

Abstract

A series of seven coumarinyl-amino acid ester conjugates have been synthesized and characterized by NMR (¹H and 13C) and mass spectra. Further, the compounds were investigated for their therapeutic applications such as anti-inflammatory and antioxidant activities. Among the synthesized compounds most of the analogs showed good efficiency compared with the standard.     

Gluing initial data sets for general relativity

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Second, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.     

On the determination of Cauchy surfaces from intrinsic properties

We consider the problem of determining from intrinsic properties whether or not a given spacelike surface is a Cauchy surface. We present three results relevant to this question. First, we derive necessary and sufficient conditions for a compact surface to be a Cauchy surface in a spacetime which admits one. Second, we show that for a non-compact surface it is impossible to determine whether or not it is a Cauchy surface without imposing some restriction on the entire spacetime. Third, we derive conditions for an asymptotically flat surface to be a Cauchy surface by imposing the global condition that it be imbedded in a weakly asymptotically simple and empty spacetime.This research was supported in part by the National Science Foundation grants PHY 70-022077 and PHY 76-20029 as well as the National Aeronautics and Space Administration grant NGR 21-002-010National Science Foundation Pre-doctoral Fellow