Scalar and neutrino fields in the Gödel universe

Some properties of the Gödel universe are demonstrated, such as closed timelike lines, and new coordinates are found. The scalar and neutrino field equations are solved and the eigenvalue spectra are calculated. The scalar field has a discrete spectrum, but the neutrino field has, in addition, a continuous spectrum due to the coupling of neutrino spin and rotation in the Gōdel universe. The mode solutions do not form a complete set for either the scalar or neutrino fields; therefore, a quantum field theory cannot be constructed in the usual manner.     

Control of density fluctuations and electron transport in the reversed-field pinch

Contrary to what has been observed thus far collision-induced light scattering (CILS) can be completely polarized. This exceptional behavior characterizes the very far wing of the binary CILS spectrum by gaseous helium. This conclusion is drawn from an experimental study of the depolarization ratio of He (2) in a much extended, previously unexplored, spectral domain. Our analysis shows that this property, unique thus far, is mainly due to an almost perfect cancellation between polarization and exchange pair polarizability contributions to the depolarized spectrum, taking place at internuclear distances shorter than the atomic diameter.     

Momentum transport from nonlinear mode coupling of magnetic fluctuations

A cause of observed anomalous plasma momentum transport in a reversed-field pinch is determined experimentally. Magnetohydrodynamic theory predicts that nonlinear interactions involving triplets of tearing modes produce internal torques that redistribute momentum. Evidence for the nonlinear torque is acquired by detecting the correlation of momentum redistribution with the mode triplets, with the elimination of one of the modes in the triplet, and with the external driving of one of the modes.     

Qualitative properties of modified equations

Suppose that a consistent one-step numerical method of orderr is applied to a smooth system of ordinary differential equations.Given any integer m 1, the method may be shown to be of orderr + m as an approximation to a certain modified equation. Ifthe method and the system have a particular qualitative propertythen it is important to determine whether the modified equationsinherit this property. In this article, a technique is introducedfor proving that the modified equations inherit qualitativeproperties from the method and the underlying system. The techniqueuses a straightforward contradiction argument applicable toarbitrary one-step methods and does not rely on the detailedstructure of associated power series expansions. Hence the conclusionsapply, but are not restricted, to the case of Runge-Kutte methods.The new approach unifies and extends results of this type thathave been derived by other means: results are presented forintegral preservation, reversibility, inheritance of fixed points.Hamiltonian problems and volume preservation. The techniquealso applies when the system has an integral that the methodpreserves not exactly, but to order greater than r. Finally,a negative result is obtained by considering a gradient systemand gradient numerical method possessing a global property thatis not shared by the associated modified equations.     

Regioselective and enantiospecific rhodium-catalyzed allylic alkylation reactions using copper(I) enolates: synthesis of (-)-sugiresinol dimethyl ether

The transition metal-catalyzed allylic alkylation represents a fundamentally important cross-coupling reaction for the construction of ternary carbon stereogenic centers. We have developed a regioselective and enantiospecific rhodium-catalyzed allylic alkylation of acyclic unsymmetrical allylic alcohol derivatives using copper(I) enolates to prepare beta-substituted ketones. This protocol represents a convenient asymmetric Claisen rearrangement surrogate in which alpha-substituted enolates permit the introduction of an additional stereogenic center. The synthetic utility of this transformation was highlighted in the construction of a trans-1,2-disubstituted cyclohexene and the total synthesis of (-)-sugiresinol dimethyl ether. Finally, we anticipate that copper(I) enolates may prove useful nucleophiles in related metal-catalyzed reactions.     

Enantioselective total synthesis of the antitumor macrolide rhizoxin D

The convergent, highly enantioselective synthesis of rhizoxin D, a natural product possessing potent antitumor and antifungal bioactivity, is described. The C(1)-C(9) fragment of the molecule was synthesized utilizing a threefold pseudosymmetric intermediate ultimately derived from gamma-butyrolactone. The central core of rhizoxin D was prepared via a chiral resolution/asymmetric aldol protocol. Several methods for the generation of the polyene fragment were explored, and the side-chain was ultimately prepared from serine in six steps. The unification of the left and right wings of the molecule was achieved using a one-step olefination protocol, and the macrocyclization was carried out using a Horner-Emmons olefination at the C(2)-C(3) olefin.     

Discrimination of Methionine Sulfoxide and Sulfone by Human Neutrophil Elastase

Human neutrophil elastase (HNE) is a uniquely destructive serine protease with the ability to unleash a wave of proteolytic activity by destroying the inhibitors of other proteases. Although this phenomenon forms an important part of the innate immune response to invading pathogens, it is responsible for the collateral host tissue damage observed in chronic conditions such as chronic obstructive pulmonary disease (COPD), and in more acute disorders such as the lung injuries associated with COVID-19 infection. Previously, a combinatorially selected activity-based probe revealed an unexpected substrate preference for oxidised methionine, which suggests a link to oxidative pathogen clearance by neutrophils. Here we use oxidised model substrates and inhibitors to confirm this observation and to show that neutrophil elastase is specifically selective for the di-oxygenated methionine sulfone rather than the mono-oxygenated methionine sulfoxide. We also posit a critical role for ordered solvent in the mechanism of HNE discrimination between the two oxidised forms methionine residue. Preference for the sulfone form of oxidised methionine is especially significant. While both host and pathogens have the ability to reduce methionine sulfoxide back to methionine, a biological pathway to reduce methionine sulfone is not known. Taken together, these data suggest that the oxidative activity of neutrophils may create rapidly cleaved elastase “super substrates” that directly damage tissue, while initiating a cycle of neutrophil oxidation that increases elastase tissue damage and further neutrophil recruitment.