Binuclear cyclopentadienylcobalt sulfur and phosphinidene complexes Cp2Co2E2 (E = S, PX): Comparison with their Iron carbonyl analogues

Density functional theory studies on a series of Cp₂Co₂E₂ derivatives (E = S and PX; X = H, Cl, OH, OMe, NH₂, NMe₂) predict global minimum butterfly structures with one Co-Co bond for the “body” of the butterfly and four Co-E bonds at the edges of the “wings” of the butterfly. Tetrahedrane structures with both Co-Co and E-E bonds are higher in energy for Cp₂Co₂S₂ and Cp₂Co₂(PH)₂ and are not found in the other systems. This differs from the corresponding Fe₂(CO)₆S₂ and Fe₂(CO)₆(PX)₂ derivatives where tetrahedrane structures are predicted to be the lowest energy structures for all cases except X = NR₂ and OH and such a tetrahedrane structure is found experimentally for Fe₂(CO)₆S₂. The butterfly structures for the Cp₂Co₂E₂ derivatives are of two types. For Cp₂Co₂(PX)₂ (X = H, OH, OMe, NH₂, NMe₂) the lowest energy structures are unsymmetrical butterflies Cp₂Co₂(P)(PX₂) with two X groups on one phosphorus atom and a lone pair on the other (naked) phosphorus atom. Related low-energy unsymmetrical butterfly Fe₂(CO)₆(P)(PX₂) structures, not observed in previous theoretical studies, are now found for the corresponding Fe₂(CO)₆(PX)₂ derivatives. Symmetrical butterfly singlet diradical structures with one X group on each phosphorus atom in relative cis or trans positions are also found for the Cp₂Co₂(PX)₂ derivatives and are the global minima for Cp₂Co₂(PCl)₂ as well as Cp₂Co₂S₂. In all cases the cis structures are of lower energy than the corresponding trans structures. Rhombus structures having neither Co-Co nor E-E bonds are also found for all of the Cp₂Co₂(PX)₂ derivatives but always at higher energies than the butterfly structures, ranging from 17 to 29 kcal/mol above the global minima.     

Detection of heteroplasmy in individual mitochondrial particles

Mitochondrial DNA (mtDNA) mutations have been associated with disease and aging. Since each cell has thousands of mtDNA copies, clustered into nucleoids of five to ten mtDNA molecules each, determining the effects of a given mtDNA mutation and their connection with disease phenotype is not straightforward. It has been postulated that heteroplasmy (coexistence of mutated and wild-type DNA) follows simple probability rules dictated by the random distribution of mtDNA molecules at the nucleoid level. This model has been used to explain how mutation levels correlate with the onset of disease phenotype and loss of cellular function. Nonetheless, experimental evidence of heteroplasmy at the nucleoid level is scarce. Here, we report a new method to determine heteroplasmy of individual mitochondrial particles containing one or more nucleoids. The method uses capillary cytometry with laser-induced fluorescence detection to detect individual mitochondrial particles stained with PicoGreen, which makes it possible to quantify the mtDNA copy number of each particle. After detection, one or more particles are collected into polymerase chain reaction (PCR) wells and then subjected to real-time multiplexed PCR amplification. This PCR strategy is suitable to obtain the relative abundance of mutated and wild-type mtDNA. The results obtained here indicate that individual mitochondrial particles and nucleoids contained within these particles are not heteroplasmic. The results presented here suggest that current models of mtDNA segregation and distribution (i.e., heteroplasmic nucleoids) need further consideration.     

Determination of methylamines and trimethylamine-N-oxide in particulate matter by non-suppressed ion chromatography

An ion chromatography method with non-suppressed conductivity detection was developed for the simultaneous determination of methylamines (methylamine, dimethylamine, trimethylamine) and trimethylamine-N-oxide in particulate matter air samples. The analytes were well separated by means of cation-exchange chromatography using a 3 mM nitric acid/3.5% acetonitrile (v/v) eluent solution and a Metrosep C 2 250 (250 mm × 4 mm i.d.) separation column. The effects of the different chromatographic parameters on the separation were also investigated. Detection limits of methylamine, dimethylamine, trimethylamine, and trimethylamine-N-oxide were 43, 46, 76 and 72 μg/L, respectively. The relative standard deviations of the retention times were between 0.42% and 1.14% while the recoveries were between 78.8% and 88.3%. The method is suitable for determining if methylamines and trimethylamine-N-oxide are a significant component of organic nitrogen aerosol in areas with high concentration of these species.     

On Balazard,Saias, and Yor’s equivalence to the Riemann Hypothesis

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t)$S\left(t\right)$ in the theory of the Riemann zeta-function.     

Isoperimetric domains of large volume in homogeneous three-manifolds

Given a non-compact, simply connected homogeneous three-manifold X   and a sequence _{Ωn}n${\{{\Omega }_n\}}_n$ of isoperimetric domains in X   with volumes tending to infinity, we prove that, as n→∞$n\to \infty$:

(1)

The radii of the _Ωn${\Omega }_n$ tend to infinity.     

On local regularization for an inverse problem of option pricing

We explore the theoretical and numerical application of local regularization methods to an ill-posed inverse problem arising from financial option pricing. In addition, we provide an algorithm and show results through numerical examples.     

Classification of doubly-periodic minimal surfaces of genus zero

We prove that if the quotient surface of a properly embedded doubly–periodic minimal surface in ℝ³ has genus zero, then the surface is one of the classical Scherk examples. Oblatum 30-IX-1998 & 18-II-2000?Published online: 30 October 2000     

Two sample applications of a classical isoperimetric problem of the calculus of variations to fluid mechanical problems in fluidization and spouting

This paper is devoted to outlining precisely the basic mathematics of a classical isoperimetric problem of the calculus of variations and showing how significant fluid mechanical problems in fluidization and spouting can be addressed using this approach.