Complex relativity and real solutions. III. Real type-N solutions from complexN ⊗N ones

Einstein's vacuum field equations are integrated in complex relativity in a major subcase of the class whose Weyl tensor is of the type NN, i.e., when the left and right Weyl spinors and are each of typeN. The subcase is the complex equivalent of the real nontwisting case. Five separate families of solutions are found. Three of these are complexified versions of the two families of plane-fronted waves and the Robinson-Trautman real type-N metrics and two are complex solutions which do not have any real slices of Lorentz signature. Before the equations are integrated, the relevant general theory and equations are developed in a tetrad frame which is well suited to the discussion of these and a wider class of complex solutions and is called aleft quarter flat frame. The relationship between this frame and the coordinates used and some other frames and coordinates, including the complexified version of the frame often used for real type-N metrics, is discussed.     

Kinetic and analytical study on precipitation reactions with110AgNO3 of some di (β-chloroethyl) amine derivates and hydrochlorides with esters of N-(p-aminobenzoyl)-L-aspartic acid as carriers from dimethylformamide-water solution

The kinetics of precipitation reactions with¹¹⁰AgNO₃ of some di (β-chlorethyl) amine derivates and hydrochlorides with esters of N-(p-aminobenzoyl)-L-aspartic acid as carriers in dimethylformamide-water mixture, were studied. The rate constants of these reactions were of the order of 10^?4 1 · mol^?1 · min^?1. The concentrations of the corresponding hydrochloride solutions were measured by radiometric titration with¹¹⁰AgNO₃ solution of given concentration.     

Complex relativity and real solutions II: Classification of complex bivectors and metric classes

This paper continues the examination of real metrics and their properties from the viewpoint of complex relativity as initiated by McIntosh and Hickman [1]. Tetrads of real metrics can be formally complexified by complex coordinate transformations and tetrad rotations and their properties investigated from the viewpoint of complex relativity. First, complex bivectors are examined and classified, partly by using the fundamental quadric surface of a metric in projective complex 3-space P³-an elegant but not well-known method of investigating the null structure of a metric. A generalization of the Mariot-Robinson theorem from real relativity is then given and related to various canonical forms of complex bivectors. The second part of the paper discusses four classes of complex metrics. Real metrics of the first class are ones with a null congruence whose wave surfaces have equal curvature. The second class, a subcase of the first one, is the main one; it contains integrable double Kerr-Schild metrics. Different, but equivalent, definitions of such metrics are given from various viewpoints. Two other subcasses are also discussed. The nonexpanding typs-D vacuum metric is considered and it is shown how complex transformations may be made to write it (and subcases) in double (or single) Kerr-Schild form.     

Improved alkylation and product stability in phosphotriester formation through quinone methide reactions with dialkyl phosphates

Investigating reactions of functionalized p-quinone methides continues to advance our design of a reagent being developed for controlled, in situ modification of DNA via phosphodiester alkylation. Previously reported investigations of p-quinone methides derived from catechols allowed for trapping of isolable trialkyl phosphates for characterization and mechanistic information. However, lactone formation with these derivatives required long reaction times, resulting in an unfavorable mixture of trialkyl phosphate and hydrolysis products. To enhance the rate and efficacy of trialkyl phosphate formation and trapping, a phenol derived p-quinone methide has been designed to enforce a conformation favoring lactonization of the dialkyl phosphate alkylated intermediate. The relative rates of phosphodiester alkylation and subsequent trapping of the phosphotriester adduct have been examined by UV and (1)H NMR analysis for p-quinone methide precursor 1 and the corresponding control, 1'. The incorporation of a methyl group at the meta-position of 1 (relative to 1') significantly improves the rate of lactionization to provide a much higher yield of the desired product, lactonized phosphotriester 5. The control reaction with 1' afforded only a minor amount of the corresponding lactonized trialkyl phosphate 5'.     

Expanding the thioglycoligase strategy to the synthesis of alpha-linked thioglycosides allows structural investigation of the parent enzyme/substrate complex

For the first time, the thioglycoligase strategy has been successfully applied to alpha-glycosidases. The alpha-thioglycoligases derived from the family 31 glycosidases, alpha-xylosidase from E. coli (YicI) and alpha-glucosidase from Sulfolobus solfataricus, catalyze thioglycoligase reactions using alpha-glycosyl fluorides and deoxythioglycosides as donors and acceptors, respectively, in yields up to 86%. In addition, we describe the Michaelis complex of YicI using one of the thioglycosides as a nonhydrolyzable substrate analogue and discuss the structural insights this yields into the specificity and mechanism of family 31 alpha-glycosidases and the molecular basis of an associated genetic disease.     

Unambiguous determination of the ionization state of a glycoside hydrolase active site lysine by 1H-15N heteronuclear correlation spectroscopy

We have investigated the lysine side chain amines in the 34 kDa catalytic domain from Cellulomonas fimi beta-(1,4)-glycosidase Cex (or CfXyn10A) using 1H-detected 15N heteronuclear correlation NMR spectroscopy. Signals from the 1Hzeta ( approximately 8 ppm) and 15Nzeta ( approximately 35 ppm) of Lys302 in the unmodified enzyme and Lys47 in a trapped cellobiosyl-enzyme intermediate were detected in a 1H-15N HMQC spectrum (pH 6.5 and 30 degrees C). The amine of Lys302 forms a buried ion pair, and that of Lys47 is hydrogen bonded to the cellobioside. Both lysines are positively charged, as unambiguously demonstrated by the splitting of their 15Nzeta signals into quartets (|1JNH| approximately 75 Hz) in a 1H-15N HSQC spectrum recorded without 1H decoupling during 15N evolution. Qualitative insights into the dynamic properties of these lysines are also provided by the deviations of their quartet intensity ratios from that of approximately 3:1:1:3 expected for a highly mobile amine. On the basis of the observed ratios of approximately 1:1:1:1 for the quartet of Lys302 and approximately 0.5:1:1:0.5 for Lys47, the amine of the latter active site residue is most rigidly positioned. Signals from at least 8 and 10 additional positively charged, mobile amines in Cex were observed at 10 degrees C and pH 6.5 and 5.6, respectively. By using conditions of reduced temperature, slightly acidic pH, and low general base concentrations, as well as water flipback pulses to minimize the effects of hydrogen exchange, 1H-15N correlation experiments provide a sensitive route to directly investigate the charge states and dynamic properties of the N-terminal and side chain amines in proteins and protein complexes.     

Approach to the synthesis of cladiell-11-ene-3,6,7-triol

[reaction: see text] The synthesis of an advanced intermediate in the synthesis of the title compound has been achieved. Key steps include an Ireland-Claisen rearrangement to install the C7 tertiary alcohol stereocenter, an SN2' reaction of an alkoxymethyl Cu reagent, and a diastereoselective Re-catalyzed allylic alcohol transposition.     

Conical square function estimates and functional calculi for perturbed Hodge-Dirac operators in <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">P</Emphasis></Superscript>

Perturbed Hodge-Dirac operators and their holomorphic functional calculi, as investigated in the papers by Axelsson, Keith and the second author, provided insight into the solution of the Kato square-root problem for elliptic operators in L² spaces and allowed for an extension of these estimates to other systems with applications to non-smooth boundary value problems. In this paper, we determine conditions under which such operators satisfy conical square function estimates in a range of L ^p spaces, thus allowing us to apply the theory of Hardy spaces associated with an operator to prove that they have a bounded holomorphic functional calculus in those L ^p spaces. We also obtain functional calculus results for restrictions to certain subspaces, for a larger range of p. This provides a framework for obtaining L ^p results on perturbed Hodge Laplacians, generalising known Riesz transform bounds for an elliptic operator L with bounded measurable coefficients, one Sobolev exponent below the Hodge exponent, and L ^p bounds on the square-root of L by the gradient, two Sobolev exponents below the Hodge exponent. Our proof shows that the heart of the harmonic analysis in L² extends to L ^p for all p ∈ (1,∞), while the restrictions in p come from the operator-theoretic part of the L² proof. In the course of our work, we obtain some results of independent interest about singular integral operators on tent spaces and about the relationship between conical and vertical square functions.