Cylindric multipartitions and level-rank duality

We show that a multipartition is cylindric if and only if its level rank-dual is a source in the corresponding affine type $A$ crystal. This provides an algebraic interpretation of cylindricity, and completes a similar result for FLOTW multipartitions.Comment: 7 pages, 7 figure

Observational Aspects of Symmetries of the Neutral B Meson System

We revisit various results, which have been obtained by the BABAR and Belle Collaborations over the last twelve years, concerning symmetry properties of the Hamiltonian, which governs the time evolution and the decay of neutral B mesons.We find that those measurements, which established CP violation in B meson decay, 12 years ago, had as well established T (time-reversal) symmetry violation. They also confirmed CPT symmetry in the decay (T_CPT = 0) and symmetry with respect to time-reversal (epsilon? = 0) and to CPT (delta? = 0) in the B0 ?B0bar oscillation.Comment: Original arguments and conclusions unchanged. Relation to other work explained in more detail. 2 references adde

gsbDesign: An R Package for Evaluating the Operating Characteristics of a Group Sequential Bayesian Design

The R package gsbDesign provides functions to evaluate the operating characteristics of Bayesian group sequential clinical trial designs. More specifically, we consider clinical trials with interim analyses, which compare a treatment with a control, and where the endpoint is normally distributed. Prior information can either be specified for the difference of treatment and control, or separately for the effects in the treatment and the control groups. At each interim analysis, the decision to stop or continue the trial is based on the posterior distribution of the difference between treatment and control. The decision at the final analysis is also based on this posterior distribution. Multiple success and/or futility criteria can be specified to reflect adequately medical decision-making. We describe methods to evaluate the operating characteristics of such designs for scenarios corresponding to different true treatment and control effects. The characteristics of main interest are the probabilities of success and futility at each interim analysis, and the expected sample size. We illustrate the use of gsbDesign with a detailed case study

2,4,6-Trifluoro­benzoic acid

In the title compound, C7H3F3O2, the C—C—C angles in the ring are greater than 120° for F-bonded C atoms [123.69 (13), 123.88 (12) and 123.66 (12)°]. In the crystal, inter­molecular O—H⋯O hydrogen bonds between carboxyl groups give rise to the formation of a centrosymmetric dimer, while dispersive F⋯O contacts [2.8849 (16) Å] connect the dimers into infinite strands along the a axis

Sodium p-toluenesulfinate tetra­hydrate

The title compound, Na+·C7H7O2S−·4H2O, is the hydrate of the sodium salt of para-toluene­sulfinic acid. The mol­ecular geometry around the sulfur atom is tetra­hedral with X–S–Y angles spanning a range of 102.23 (6)–110.04 (6)°. In the crystal, the water mol­ecules connect the sodium cations into chains along the b axis via O—H⋯O hydrogen bonds. An inter­molecular O—H⋯π inter­action is also observed

Ethyl­triphenyl­phospho­nium bromide dihydrate

In the crystal structure of the title hydrated bromide salt, C20H20P+·Br−·2H2O, O—H⋯Br and O—H⋯O hydrogen bonds as well as C—H⋯Br contacts connect the different components into a three-dimensional network. In the cation, the aromatic rings make dihedral angles of 55.24 (5), 76.16 (4) and 85.68 (4)°

(3-Amino­phen­yl)methanol

In the title compound, C7H9NO, a derivative of benzyl alcohol, the endocyclic C—C—C angles are in the range 119.50 (12)–121.04 (12)°. In the crystal, mol­ecules are linked by N—H⋯O hydrogen-bond inter­actions, forming an extended two-dimensional framework parallel to ab. O—H⋯N inter­actions are also observed

5-Amino­pentan-1-ol

The title compound, C5H13NO, is an aliphatic amino­alcohol with both functional groups residing on terminal C atoms. Apart from the hy­droxy group, all non-H atoms are nearly co-planar, the maximum deviation of an atom taking part in the least-squares plane defined by the mentioned non-H atoms being 0.029 (1) Å. In the crystal, O—H⋯N and N—H⋯O hydrogen bonds connect the mol­ecules, forming a three-dimensional network

Bis(piperidin-1-yl)methanone

The title compound, C11H20N2O, is a urea derivative bearing two piperidine moieties in place of the amino groups. The mol­ecule shows approximate non-crystallographic C 2 symmetry. The six-membered rings adopt 1 C 4 and 4 C 1 conformations and their mean planes make a dihedral angle of 35.87 (5)°. In the crystal, inter­molecular C—H⋯O contacts connect the mol­ecules into infinite strands along the a axis

2-[(4-Methyl­phen­yl)sulfan­yl]aniline

The least-squares planes defined by the aromatic moieties in the title aniline derivative, C13H13NS, are nearly perpendicular to each other, forming a dihedral angle of 87.80 (7)°. Apart from a weak intramolecular N—H⋯S hydrogen bond, a co-operative set of N—H⋯N hydrogen bonds present in the crystal structure leads to the formation of tetra­meric units