Singularities and conjugate points in FLRW spacetimes

Conjugate points play an important role in the proofs of the singularity theorems of Hawking and Penrose. We examine the relation between singularities and conjugate points in FLRW spacetimes with a singularity. In particular we prove a theorem that when a non-comoving, non-spacelike geodesic in a singular FLRW spacetime obeys conditions (39) and (40), every point on that geodesic is part of a pair of conjugate points. The proof is based on the Raychaudhuri equation. We find that the theorem is applicable to all non-comoving, non-spacelike geodesics in FLRW spacetimes with non-negative spatial curvature and scale factors that near the singularity have power law behavior or power law behavior times a logarithm. When the spatial curvature is negative, the theorem is applicable to a subset of these spacetimes.     

Enantioselective protonation of catalytically generated chiral enolates as an approach to the synthesis of alpha-chloroesters

Treatment of alpha,alpha-dichloroaldehydes with various phenols in the presence of chiral triazolium salt catalysts and excess base results in the synthesis of alpha-chloro aryl esters in good yield and enantioselectivity. The reaction is tolerant of various functionality on the aldehyde as well as several electronically diverse phenols. The product chloroesters were further transformed into chloroacid, chlorohydrin, and azidoesters with nearly complete retention of enantioselectivity.     

The separation of inorganic isomeric cis-trans compounds by paper chromatography and the effect of configuration on rf values

It has been established that of all the inorganic isomeric cis–trans compounds that have been separated by paper chromatography up to the present, the cis isomers have higher rf values than the trans, forms On the basis of this regularity, a new method has been suggested for the determination of the configuration of inorganic isomeric cis-trans compounds     

Decarbonylative cross-coupling of cyclic anhydrides: introducing stereochemistry at an sp3 carbon in the cross-coupling event

Treatment of cyclic anhydrides with stoichiometric amounts of nickel-neocuproine complex generates alkylcarboxylato-nickelalactones upon extrusion of CO. These metalacycles undergo cross-coupling with arylzinc reagents. The generated CO is sequestered in situ by a nickel-dppb complex. The overall sequence effects a secondary sp3(electrophile)-sp2(nucleophile) cross-coupling and allows for control of stereochemistry during the bond-forming event.     

“True Transformations Relativity” and Electrodynamics

Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach, which we call the true transformations (TT) relativity. In this approach a physical quantity in the four-dimensional spacetime is mathematically represented either by a true tensor (when no basis has been introduced) or equivalently by a coordinate-based geometric quantity comprising both components and a basis (when some basis has been introduced). This invariant approach is compared with the usual covariant approach, which mainly deals with the basis components of tensors in a specific, i.e., Einstein's coordinatization of the chosen inertial frame of reference. The third approach is the usual noncovariant approach to SR in which some quantities are not tensor quantities, but rather quantities from 3+1 space and time, e.g., the synchronously determined spatial length. This formulation is called the apparent transformations (AT) relativity. It is shown that the principal difference between these approaches arises from the difference in the concept of sameness of a physical quantity for different observers. This difference is investigated considering the spacetime length in the TT relativity and spatial and temporal distances in the AT relativity. It is also found that the usual transformations of the three-vectors (3-vectors) of the electric and magnetic fields E and B are the AT. Furthermore it is proved that the Maxwell equations with the electromagnetic field tensor F^ab and the usual Maxwell equations with E and B are not equivalent, and that the Maxwell equations with E and B do not remain unchanged in form when the Lorentz transformations of the ordinary derivative operators and the AT of E and B are used. The Maxwell equations with F^ab are written in terms of the 4-vectors of the electric E^a and magnetic B^a fields. The covariant Majorana electromagnetic field 4-vector ^a is constructed by means of 4-vectors E^a and B^a and the covariant Majorana formulation of electrodynamics is presented. A Dirac like relativistic wave equation for the free photon is obtained.     

Bayesian characterization of multiple-slope sound energy decays in coupled-volume systems

Due to recent developments in concert hall design, there is an increasing interest in the analysis of sound energy decays consisting of multiple exponential decay rates. It has been considered challenging to estimate parameters associated with double-rate (slope) decay characteristics, and even more challenging when the coupled-volume systems contain more than two decay processes. To meet the need of characterizing energy decays of multiple decay processes, this work investigates coupled-volume systems using acoustic scale-models of three coupled rooms. Two Bayesian formulations are compared using the experimentally measured sound energy decay data. A fully parameterized Bayesian formulation has been found to be capable of characterization of multiple-slope decays beyond the single-slope and double-slope energy decays. Within the Bayesian framework using this fully parameterized formulation, an in-depth analysis of likelihood distributions over multiple-dimensional decay parameter space motivates the use of Bayesian information criterion, an efficient approach to solving Bayesian model selection problems that are suitable for estimating the number of exponential decays. The analysis methods are then applied to a geometric-acoustics simulation of a conceptual concert hall. Sound energy decays more complicated than single-slope and double-slope nature, such as triple-slope decays have been identified and characterized.     

Organocatalytic hydroacylation of unactivated alkenes

N-Heterocyclic carbenes interact with aldehydes to generate the Breslow intermediate, a rendering of the prototypical electrophile into a nucleophile (umpolung). Recent work has indicated that these intermediates may also add to simple, unpolarized alkenes. The use of a chiral precatalyst leads to the generation of the derived adducts with high yields and very high selectivities.     

Observation of a two-dimensional halogen-bonded cocrystal at sub-monolayer coverage using synchrotron X-ray diffraction

The formation of two-dimensional halogen-bonded layers of 4,4'-bipyridyl and 1,4-diiodotetrafluorobenzene was observed on a graphite surface at sub-monolayer coverage using synchrotron X-ray diffraction; the use of the diffraction technique enabled, for the first time, the measurement of I···N halogen bonding distances in a two-dimensional cocrystal and the identification of the halogen bonding interaction in the monolayer.     

Hydrogen bonding topology influences gelating properties of malonamides

Preparation, structural characterisation and topology of hydrogen bonding networks of bis(phenylglycinol)malonamide, as well as its Cα mono- and dialkyl-substituted derivatives are described. Their hydrogen bonding motifs are described in view of their gelling properties. Topology of hydrogen bonding typical of malonamide gelators is compared with those of well-examined oxalamide gelators.