On the finite element approximation of incompressible flows of an electrically conducting fluid

We consider the finite element approximation of incompressible flows field of an electrically conducing fluid in the presence of a magnetic where it is assumed that this field is prescribed. A weak form is chosen that is similar in some respects to a weak form used by many authors for the Navier-Stokes equations. Existence and uniqueness results are presented for the weak problem. A finite element Algorithm is given for the approximate solution of the weak problem and error estimates are derived.     

Crystal and molecular structure of the triflate salt of diprotonated 1,4,8,11-tetrakis(2-hydroxyethyl)-1,4,8,11-tetraazacyclotetradecane, [C10H22N4(CH2CH2OH)4 2+]−[CF3SO3 −]2: geometry of a diprotonated octadenate ligand

The title complex crystallizes in the centrosymmetric monoclinic space group P2₁/n with Z=2. The cation is the diprotonated derivative of the neutral octadentate macrocyclic ligand C₁₀H₂₀N₄(CH₂CH₂OH)₄; the two protonated nitrogen atoms are as far apart as is possible in the 14-membered ring (1-and 8-positions) so as to minimize electrostatic repulsions. Each of the [C₁₀H₂₂N₄(CH₂CH₂OH)₄ ²⁺] cations is involved in hydrogen bonding (through the four hydroxy groups) to oxygen atoms on four different peripheral [CF₃SO₃ ⁻] anions.     

Nonautonomous locally Lipschitz continuous functional differential equations in spaces of continuous functions

A local existence and uniqueness result for the functional differential equation in a Banach space X (FDE) $$\begin{gathered} x\prime (t) \in f(t)x(t) + g(t)x_t ,0 \leqslant t \leqslant T, \hfill \\ x_0 = \phi \in C( - R,0;X) \hfill \\ \end{gathered} $$ is obtained, for the case where the operatorsf(t) satisfy only a local dissipativity condition and the operatorsg(t) are only locally Lipschitz continuous. The conditions include equations defined on cones.     

Random reals and the relation 171-1171-1171-1

It is consistent that ₁(₁,(:n))² holds in any random extension for n finite and countable.     

Analysis of classes of compounds of environmental concern: III. Organochlorine pesticides

Forty five organochlorine pesticides (currently listed in EPA Method 8081A) have been chromatographed on DB-5/DB-1701 and SPB-5/SPB-1701 column pairs which were in each case connected to an inlet splitter and separate electron capture detectors. Thirteen additional compounds were evaluated for their suitability as internal standards or surrogate compounds for incorporation into Method 8081A. Method reproducibility and linearity are discussed, and results are presented for extracts of six real samples spiked with fifteen organochlorine pesticides and analyzed using the dual-column, dual-detector arrangement.     

Principal component and decomposition analysis of multicomponent mixtures of carcinogenic fluorophores

A series of binary and tertiary mixtures of polycyclic aromatic hydrocarbons is analyzed by using principal component and decomposition analysis of molecular fluorescence spectra. The results demonstrate the ability to determine the number and identity of species that are present. Failures caused by high correlation among spectra are considered.     

Rapid phosphine exchange on 1.5-nm gold nanoparticles

Triphenylphosphine-cappped, 1.5-nm gold nanoparticles "Au(101)(PPh(3))(21)Cl(5)" prepared following Hutchison's procedure (Weare, W. W.; Reed, S. M.; Warner, M. G.; Hutchison, J. E. J. Am. Chem. Soc. 2000, 122, 12890) undergo rapid exchange of capping ligand phosphine with dissociated and added phosphine in dichloromethane solvent at 298 K. Remarkably, while the (1)H NMR spectrum resonances of the attached phosphine are broad, characteristic of a range of incompletely averaged environments, the (31)P NMR spectrum (observable only at 213 K and below) exhibits a single, narrow resonance indicating that all of the phosphorus atoms are magnetically equivalent.