Surgery and the Spinorial τ-Invariant

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ _n }, where Λ _n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ _n . Also, below Λ _n the values of τ cannot accumulate from above when varied over all manifolds of dimension n.     

Pricing of Claims in Discrete Time with Partial Information

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller’s price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively.     

Switching from "absorption within transparency" to "transparency within transparency" in an electromagnetically induced absorption dominated transition

The absorption of a resonant coupling laser driving a closed degenerate two-level system in an atomic cesium beam was investigated as a function of the detuning of a second laser probing the same transition. The measurements were performed for four different polarization combinations of the two laser beams. Except for the beams of counterrotating polarizations all coupling-laser absorption profiles showed "absorption within transparency," i.e., the absorption in the region around the two-photon resonance was smaller than the absorption corresponding to the one-photon transition induced by the coupling laser, and an extra absorption peak was observed on this curve at the two-photon resonance. With regard to the beams of counterrotating polarizations we observed a switch from absorption within transparency to "transparency within transparency" when the probe-laser power exceeded the constant coupling-laser power. In other words, the cesium ensemble became mostly transparent to the coupling-laser beam at the two-photon resonance.     

Antiaromatic spacer-bridged bisfluorenyl dications generated by superacid induced ionization

Derivatives of the dication of tetrabenzo[5.5]fulvalene were prepared with phenyl and ethynyl spacers through ionization of the appropriate bis-methylethers. The antiaromaticity shown by the parent dication was demonstrated for these dications with spacers, although it was attenuated by the presence of the spacer. It was substantially greater than that of fluorenyl monocations with similar substituents. Antiaromaticity was evaluated through comparison of (1)H NMR shifts with those of acyclic analogues, through nucleus independent chemical shifts, and through magnetic susceptibility exaltation. Although the fluorenyl systems are separated by spacers, the antiaromaticity of one system is affected by the other remote fluorenyl system. An explanation for this interaction may lie in the ability of a remote cationic substituent to attenuate delocalization in the spacer. The use of spacers is designed to prevent side reactions in less stable antiaromatic dications, allowing exploration of a number of species that have previously been inaccessible.     

Determination of total chromium in phosphate rocks by ion chromatography

Chromium(VI) is one of seven elements which is classified in the fertilizer industry as being harmful to plants and biological systems. Phosphate rocks represent the raw material for complex fertilizer production in the world. This paper investigates for the first time the determination of total chromium in phosphate rocks by ion chromatography. The developed analytical method involves the digestion of phosphate rocks with nitric acid followed by sample treatment of the resulting solution. The digestion solution obtained was treated with an oxidising agent (potassium peroxosulphate) to convert all chromium to the hexavalent state. The analytical method developed utilizes anion-exchange ion chromatography to achieve the separation and spectrophotometric post-column reaction for detection with diphenylcarbazide. The relative standard of deviation from analytical data comparison of six different phosphate rocks with atomic absorption spectrometry and inductively coupled plasma atomic emission spectrometry techniques, and cross-analysis data against an internationally certified phosphate rock standard were between 0.58 and 1.45%. Calibration curve between 0.2 and 0.9 μg/ml was excellent, and the method has a detection limit for Cr(VI) of 0.05 ng. The developed method offers a fast, a reliable and an alternative procedure for the determination of total chromium in phosphate rock deposits by ion chromatography.     

Reactivities of the Prism‐Shaped Diamondoids [1(2)3]Tetramantane and [12312]Hexamantane (Cyclohexamantane)

Functionalized nanodiamonds : Various functional groups have been incorporated into the structures of the naturally occurring diamondoids [1(2)3]tetramantane and [12312]hexamantane (cyclohexamantane), which represent hydrogen‐terminated prism‐shaped nanodiamonds (see picture). The attachment points define the use of these diamond‐like molecules as geometric building blocks for a variety of applications.

     

Scattering measurements from a dissolving bubble

A laboratory-scale study on acoustic scattering from a single bubble undergoing dissolution in undersaturated fresh water is presented. Several experiments are performed with the acoustic source driven with five-cycle tone bursts, center frequency of 120 kHz, to insonify a single bubble located on axis of the combined beam of the set of transducers. The bubble is placed on a fine nylon thread located in the far field of the transducer set, arranged in bistatic configuration, in a tank filled with undersaturated water. Backscattered waveforms from the bubble target are acquired every few seconds for several hours until the bubble has completely dissolved, and detailed dissolution curves are produced from the acoustic data. The rate of bubble dissolution is calculated using the solution developed by Epstein and Plesset [J. Chem. Phys. 18, 1505-1509 (1950)]. The results of the experiments performed are in agreement with the calculations.     

Determination of iodine in seafood by inductively coupled plasma/mass spectrometry.

A method was developed for determination of total iodine content in different standard reference materials (SRMs) and seafood products by inductively coupled plasma/mass spectrometry (ICP/MS). If iodine is present as iodide and nitric acid is used in the wet digestion system, the observed signal is not stable when iodine is measured by ICP/MS at m/z 127. To stabilize the iodine signal, 3% ammonia solution (1 + 1, v/v) was added to the digest. The limit of quantitation of the method, defined as 6 times the standard deviation in the blank solution (n = 20) was estimated to be 15 mg/kg (using 0.2 g dry mass and a dilution factor of 50). The precision, expressed as repeatability of the iodine concentration, varied between 3.2 and 12% in SRMs, with concentrations of 4.70-0.17 mg/kg dry matter. The described method was compared with a method using tetramethylammonium hydroxide extraction. Both methods showed good precision and trueness by analyses of SRMs. The 2 methods were used to determine iodine in seafood from the Barents Sea, the Norwegian Sea, and the North Sea. The results showed great variation between different fish species as well as between individuals within a species. The lowest values of iodine were recorded in muscle of ling (Molva molva) with a mean of 0.07 mg/kg fresh weight and a variation between 0.03 and 0.11 mg/kg fresh weight. The highest values were found in cod (Gadus morhua) from the Barents Sea, with a mean of 2.5 mg/kg and a variation between 0.7 and 12.7 mg/kg fresh weight.