Early physics reach of the ATLAS detector

The European Physical Journal C - The first year of data taking at ATLAS should be a very challenging and rewarding time. It will include commissioning of the detector and many interesting physics...     

The motion of charged test particles in general relativity

We derive, from the Einstein-Maxwell field equations, the Lorentz equations of motion with radiation reaction for a charged mass particle moving in a background gravitational and electromagnetic field by utilizing a line element for the background space-time in a coordinate system specially adapted to the world line of the particle. The particle is introduced via perturbations of the background space-time (and electromagnetic field) which are singular only on the source world line.     

Change points in heavy‐tailed multivariate time series: Methods using precision matrices

We propose two robust data‐driven techniques for detecting network structure change points between heavy‐tailed multivariate time series for situations where both the placement and number of change points are unknown. The first technique utilizes the graphical lasso method to estimate the change points, whereas the second technique utilizes the tlasso method. The techniques not only locate the change points but also estimate an undirected graph (or precision matrix) representing the relationship between the time series within each interval created by pairs of adjacent change points. An inference procedure on the edges is used in the graphs to effectively remove false‐positive edges, which are caused by the data deviating from normality. The techniques are compared using simulated multivariate t‐distributed (heavy‐tailed) time series data and the best method is applied to two financial returns data sets of stocks and indices. The results illustrate the method's ability to determine how the dependence structure of the returns changes over time. This information could potentially be used as a tool for portfolio optimization.     

Expanding the repertoire of cyclopropenium ion phase transfer catalysis: Benzylic fluorination

The application of cyclopropenium ion as a phase transfer catalyst for benzylic fluorination in high yields is reported. Integral to the mechanisms of these fluorination reactions was the role of in situ derived cyclopropenium fluoride complexes, the existence of which was supported by ¹H, ¹⁹F NMR and UV–Vis spectroscopy. Density functional theory calculations were applied to gain insight into the mechanism of these reactions.     

Chlorotris(2,4,6‐trimethylphenyl)tin(IV) and its ethanol hemisolvate

Chloro­tris(2,4,6‐tri­methyl­phenyl)­tin(IV), crystallizes from ethanol as solvent‐free needles, [Sn(C₉H₁₁)₃Cl], (I), and as the hemisolvate, [Sn(C₉H₁₁)₃Cl]·0.5C₂H₆O, (II). The asymmetric unit in (I) has three independent mol­ecules, whereas in (II), there are two [Sn(C₉H₁₁)₃Cl] mol­ecules together with one ethanol molecule. In the unit cell of (II), the ethanol mol­ecules lie in channels between stacks of (Mes)₃SnCl mol­ecules (Mes is 2,4,6‐tri­methyl­phenyl) and each ethanol mol­ecule is disordered (0.50:0.50) over two positions. A comparison of the structures of the title compounds and other (Mes)₃SnX (X = F, Br or I) systems with those of the tri­phenyl­tin analogues shows that the steric requirements of the o‐CH₃ groups are met by a flattening of the SnC₃ skeleton and increases in the average Sn—X and Sn—C values. Comparing Sn—X data for (Mes)₃SnX (X = F, Cl, Br or I) systems with values for the tris(o‐methoxy­phenyl)­tin analogues suggests that the Sn—F distance of 1.961 Å in (Mes)₃SnF may well be characteristic of sterically unhindered four‐coordinate Ar₃SnF systems.     

Zur Bestimmung und Trennung des Chroms und zur Analyse von Chrom enthaltenden Substanzen

Ohne Zusammenfassung     

Null strings and complex Einstein-Maxwell fields with cosmological constant

Previous results of two of us (J. P. and I. R.) concerning left-degenerate Einstein-flat complex space-times, and preliminary results concerning the electromagnetic field [1], are here generalized and worked out in some detail for the system of Einstein-Maxwell equations with a cosmological constant. On the assumption that there exists a congruence of totally null surfaces, the system is reduced to a pair of equations for two unknown functions.On leave of absence from the University of Warsaw, Warsaw, Poland.     

Some neglected niches in the understanding and teaching of numbers and number systems

Cultural questions have attended arithmetic since it began to develop in ancient times. They include possible differences between integers and non-integral numbers and in operating with them, religious and mystical uses and interpretations, the roles of zero, extensions to infinite numbers, and representing numbers by numerals in ways which aid calculation (including the use of algebra). The selection of historical examples given here concentrates on aspects of numbers which are not well known but which could be used in teaching, either at school or undergraduate level. Comments on educational utility are given, mostly at the end of each section; the word “student” refers to learners of all ages.