The generic condition is generic

We consider the generic condition for vectors—both null and non-null—at a fixed pointp of a spacetime, and ask just how generic this condition is. In a general spacetime, if the curvature is not zero at the pointp, then the generic condition is found to be generic in the mathematical sense that it holds on an open dense set of vectors atp; more specifically, if there are as many as five non-null vectors in general position atp which fail to satisfy the generic condition, then the curvature vanishes atp. If the Riemann tensor is restricted to special forms, then stronger statements hold: An Einstein spacetime with three linearly independent nongeneric timelike vectors atp is flat atp. A Petrov type D spacetime may not have any nongeneric timelike vectors except possibly those lying in the plane of the two principal null directions; if any of the non-null vectors in such a plane are nongeneric, then so are all the vectors of that plane, as well as the plane orthogonal to it.     

Sequential flow analysis coupled with ACSV for on-line monitoring of cobalt in the marine environment

The development of a compact instrument for on-line measurement of trace metals in seawater is described. The system is based on adsorptive cathodic stripping voltammetry (ACSV), and on the concept of sequential flow analysis, to perform on-line measurements with controlled perturbation of natural equilibria of the element. The design combines a low volume flow cell with a miniature solenoid pump and valves to achieve low power consumption. The flow segmentation is time-controlled and the detection step takes place in a well-defined part of the flow stream where reagent and sample occur mixed. The system was tested on the determination of cobalt in seawater but it is likely that the same technique can be used to determine other metals detectable by CSV. The determination range was 6–1050 pmol/L cobalt with a detection limit (3σ) of 6 pmol/L. The measurement rate was about 60 h^–1. Comparative measurements were carried out using continuous flow analysis. The apparatus was used continuously on board a ship to determine the distribution pattern of cobalt in surface waters off the coast of California.     

Coupling routes to hexafluoro-1,3-butadiene, substituted-1,3-fluorine-containing butadienes and fluorinated polyenes

Hexafluoro-1,3-butadiene was readily prepared via a variety of self-coupling processes, such as Cu(0) mediated self-coupling of iodotrifluoroethene, Pd(0) catalyzed coupling of iodotrifluoroethene with the trifluorovinylzinc reagent, and CuBr₂ mediated coupling of the trifluorovinylzinc reagent. Perfluoro-2,3-dimethyl-1,3-butadiene was readily synthesized by the reaction of pentafluoropropenyl-2-zinc reagent with either CuBr₂ or FeCl₃. Alternatively, perfluoro-2,3-dimethyl-1,3-butadiene was prepared by oxidation of the pentafluoropropenyl-2-copper reagent with dioxygen. Cu(0) mediated coupling of an (E)-substituted ,β-difluoro-β-iodostyrene provided the first useful route to a (Z)(Z)-1,4-diaryl-1,3-tetrafluorobutadiene. Extension of the Cu(0) mediated coupling methodology to a perfluorodienyl iodide demonstrated a useful stereospecific route to perfluoropolyenes.     

An upper bound for permanents of nonnegative matrices

A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently, of the author, states that the maximum of the permanent of a matrix whose rows are unit vectors in lp is attained either for the identity matrix I or for a constant multiple of the all-1 matrix J.The conjecture is known to be true for p=1 (I) and for p?2 (J).We prove the conjecture for a subinterval of (1,2), and show the conjectured upper bound to be true within a subexponential factor (in the dimension) for all 1<p<2. In fact, for p bounded away from 1, the conjectured upper bound is true within a constant factor.     

Microwave-assisted highly diastereoselective synthesis of oxazolidines derived from ketones and aminoalcohols

A number of oxazolidines derived from ketones and aminoalcohols have been prepared in excellent yields using microwave irradiation. In most cases, conventional reflux failed to provide any of the desired products.     

The reactions of alkoxy radicals with O2. II. n-C3H7O radicals

n-C₃H₇ONO was photolyzed with 366 nm radiation at ?26, ?3, 23, 55, 88, and 120°C in a static system in the presence of NO, O₂, and N₂. The quantum yields of C₂H₅CHO, C₂H₅ONO, and CH₃CHO were measured as a function of reaction conditions. The primary photochemical act is and it proceeds with a quantum yield ?₁ = 0.38 ± 0.04 independent of temperature. The n-C₃H₇O radicals can react with NO by two routes The n-C₃H₇O radical can decompose via or react with O₂ via Values of k₄/k₂ ? k_4b/k₂ were determined to be (2.0 ± 0.2) × 10¹⁴, (3.1 ± 0.6) × 10¹⁴, and (1.4 ± 0.1) × 10¹⁵ molec/cm³ at 55, 88, and 120°C, respectively, at 150-torr total pressure of N₂. Values of k₆/k₂ were determined from ?26 to 88°C. They fit the Arrhenius expression: For k₂ ? 4.4 × 10^?11 cm³/s, k₆ becomes (2.9 ± 1.7) × 10^?13 exp{?(879 ± 117)/T} cm³/s. The reaction scheme also provides k_4b/k₆ = 1.58 × 10¹⁸ molec/cm³ at 120°C and k_8a/k₈ = 0.56 ± 0.24 independent of temperature, where      

Prediction of bubble concentration profiles in vertical turbulent two-phase flow

In vertical bubbly flow, the bubbles are not distributed evenly across the flow section. Several investigators have observed a wall-skewed bubble concentration profile in a vertical upward flow. This paper presents an analysis that predicts this type of bubble distribution by incorporating into the equation of motion a lateral force due to the relative velocity of the two phases and the eddy diffusivity of the liquid. Comparison of analysis and experiment shows good agreement.