Very short F—H⋯F hydrogen bond in l‐argininium fluoride hydrogen fluoride

There are two symmetry‐independent formula units of the title compound, C₆H₁₅N₄O₂⁺·F^?·HF, per cell. Both cations have a zwitterionic form, protonated at both the guanidyl and amino groups. The two symmetry‐independent cations differ in their conformation. In one of them the C_γ atom is in a gauche position to both the amino and carboxyl groups, while in the other this atom is trans to the amino group. The two anions have very similar geometry. The F^? ions are strongly hydrogen bonded to an HF molecule [F—H?F 2.233 (2) and 2.248 (3) Å], thereby forming an asymmetric non‐linear bifluoride anion. These F?F distances are the shortest reported for an asymmetric HF₂^? anion.     

C—H⃛π interactions in 9‐(n‐do­decylamino­methyl)­anthracene

The title compound, C₂₇H₃₇N, which is intended to be included in the structure of a sulfon­amide porphyrin for the preparation of Langmuir–Blodgett films, consists of a do­decyl chain linked to an anthracene mol­ecule through an amino­methyl group. The angle between the least‐squares plane of the anthracene and the do­decyl chain is 11.44 (8)°. The mol­ecules are arranged in zigzag layers head‐to‐head, with the hydro­carbon chains side‐by‐side. The structure is stabilized by C—H?π interactions, the strongest having an H?centroid distance of 2.63 Å.     

Benzyl 5‐carboxy‐4‐ethyl‐3‐methyl­pyrrole‐2‐carboxyl­ate

In the title compound, C₁₆H₁₇NO₄, the benzyl­oxy­carbonyl group is anti to the pyrrolic N atom. The mol­ecules are joined into head‐to‐head dimers by hydrogen bonds involving the carboxyl­ic acid groups. There is orientational disorder of these groups over two positions with approximately equal occupancy. A weaker hydrogen bond between the pyrrolic N atom and the carbonyl O atom of the benzyl­oxy­carbonyl group joins the dimers into chains running parallel to the [110] direction.     

2,4‐Dibromo‐3‐methoxy‐6‐nitrobenz­aldeyde: effect of substituents on ring geometry

In the title compound, C₈H₅Br₂NO₄, the endocyclic angles of the ring deviate significantly from the ideal value of 120°. The substituents deviate from the plane of the ring, with large twist angles for the aldehyde, nitro and methoxy groups. The geometry of the mol­ecule in the crystal is compared with that of the isolated mol­ecule, as given by a self‐consistent field molecular‐orbital Hartree–Fock calculation. Only weak hydrogen bonds of the C—H?Br and C—H?O types are present in the crystal structure.     

A completion problem over the field of real numbers

Let F be a field. Almost 25 years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [A_i,j], i,j{1,2}, where A_1,1 and A_2,2 are square submatrices, when some of the blocks A_i,j are fixed and the others vary [cf. Linear Multilinear Algebra 2 (1975) 357]. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira's problem where the blocks A_1,2,A_2,1 are fixed and the others vary.     

Cycloisomerization of Olefins in Water

Preparative reactions that occur efficiently under dilute, buffered, aqueous conditions in the presence of biomolecules find application in ligation, peptide synthesis, and polynucleotide synthesis and sequencing. However, the identification of functional groups or reagents that are mutually reactive with one another, but unreactive with biopolymers and water, is challenging. Shown here are cobalt catalysts that react with alkenes under dilute, aqueous, buffered conditions and promote efficient cycloisomerization and formal Friedel–Crafts reactions. The constraining conditions of bioorthogonal chemistry are beneficial for reaction efficiency as superior conversion at low catalyst concentration is obtained and competent rates in dilute conditions are maintained. Efficiency at high dilution in the presence of buffer and nucleobases suggests that these reaction conditions may find broad application.     

Subspaces and Subgroups in Five-Dimensional Gravity

A systematic investigation of the one- and two-dimensional subspaces of the potential space in the projective field theory is made. From the one-dimensional subspaces some stationary charged solutions can be generated. The two-dimensional subspaces have an isometry group SU(1,1) which corresponds to the Einstein equations in vacuum, an O(2,1) group which corresponds to stationary charged solutions with constant scalar field, and an Abelian group which has no counterpart in the Einstein-Maxwell theory.     

Geodesics around oscillatons

Oscillatons are spherically symmetric solutions to the Einstein–Klein–Gordon equations. These solutions are non-singular, asymptotically flat, and with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around of an oscillatonic field. Bound orbits are found for particular values of the particles' angular momentum L and their initial radial position r ₀. It is found that the radial coordinate of such particles oscillates in time and we are able to predict the corresponding oscillating period as well as its amplitude. We carry out this study for the quadratic V(φ) = m _Φ Φ²/2 scalar field potential. We discuss possible ways to follow in order to connect this kind of studies with astrophysical observations.     

Acceleration property for the columns of the E-algorithm

A convergence acceleration result for the E-algorithm is proved for sequences such that the error has an asymptotic expansion on a scale of comparison for which a determinantal relation holds. This result is also generalized to the vector case.     

Kinetic modeling studies of ethylene polymerization reactions using supported chromium catalysts

Kinetic models for ethylene polymerization based on a general coordination–insertion mechanism, in which either a monocoordinated species or a bicoordinated species could lead to migratory insertion, were constructed. These models were implemented through the solution of a set of differential equations resulting from the material balances for all the species involved. The application of these kinetic models to monomer consumption for different supported catalysts produced very good fittings and allowed the estimation of the kinetic rate constants of each elementary step. Although the same kinetic scheme was used to describe all the observations, the results of the fitting showed that the supported chromium species behaved very differently according to the support. Only in the case of the silica‐supported catalysts was mechanical fragmentation of the particles observed during the course of the reaction, and this implied the inclusion of a new term in the model. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3464–3472, 2004