Hilbert’s Tenth Problem for function fields of varieties over algebraically closed fields of positive characteristic

Let K be the function field of a variety of dimension ?? 2 over an algebraically closed field of odd characteristic. Then Hilbert??s Tenth Problem for K is undecidable. This generalizes the result by Kim and Roush from 1992 that Hilbert??s Tenth Problem for the purely transcendental function field ${{{\overline{\mathbb{F}}_p}}(t_1,t_2)}$ is undecidable when p?>?2.     

CAS SCF and contracted CI calculations on the HO3 radical

CAS SCF and CCI calculations have been performed in order to establish the existence or non-existence of the HO₃ radical. The potential surface for the dissociation reaction, HO₃ → O₂(³Σ) + OH, along one chosen coordinate has been calculated. The calculations show that although the wavefunctions describing the short-distance and long-distance states are of different character, the energies are the same and the curve connecting the states is very flat. There is probably no barrier towards dissociation of the radical. However, the existence of HO₃ can still not be excluded.     

On the use of nitrite in the determination of halogen in organic compounds

Summary A few properties of nitrite are cited which are useful for the determination of halogens and perhaps also of sulfur in organic compounds. Procedures using this reagent for the determination of chlorine and bromine in ordinary organic compounds and compounds containing mercury, using flask combustion, and a procedure for microdetermination of chlorine and bromine using combustion and subsequent hydrogenation are described.

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Zusammenfassung Einige Eigenschaften des Nitrits werden erwähnt, die es für die Bestimmung der Halogene und möglicherweise auch des Schwefels in organischen Verbindungen geeignet erscheinen lassen. Arbeitsvorschriften für die Verwendung dieses Reagens bei der Bestimmung von Chlor und Brom in gewöhnlichen organischen Verbindungen und Organo-Quecksilberverbindungen mit Hilfe der Kolbenverbrennung werden beschrieben. Ebenso wird auch ein Verfahren zur Mikrobestimmung von Chlor und Brom durch Verbrennung und nachfolgende Hydrierung angegeben.

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Résumé L'auteur cite quelques propriétés des nitrites qui sont utiles pour la détermination des halogènes et peut être également du soufre dans les composés organiques. Il décrit des techniques de détermination du chlore et du brome dans les composés organiques courants et dans les composés contenant du mercure par combustion en fiole, et une technique de microdosage du chlore et du brome par combustion suivie d'hydrogénation, dans lesquelles ce réactif est utilisé.

     

Experimental and theoretical characterization of the valence isomerization of Bi-2H-azirin-2-yls to diazabenzenes

3,4-diazidocyclobutenes 16 were prepared from the corresponding dihalides. Some of these diazides, such as parent compound 16 d and phenyl-substituted derivatives 16 c,f, underwent spontaneous stereoselective electrocyclic ring opening below room temperature, whereas the tetraalkyl derivatives of 16 had to be heated to force the same reaction. In most cases, the resulting 1,4-diazidobuta-1,3-dienes 8 were isolated to study their photochemical transformation into bi-2H-azirin-2-yls 9 via intermediate mono-azirines 17. Except for starting materials with a low number of substituents such as 9 d and 9 f, title compounds 9 underwent a thermal valence isomerization which led exclusively to pyridazines 18 at surprisingly low temperatures. Based on quantum-chemical calculations for the parent bi-2H-azirinyl-2-yl 9 d at the UB3LYP/6-31+G(d) and MR-MP2/TZV(2df,2p) levels, the valence isomerization process is best explained by simultaneous homolytic cleavage of both C--N single bonds of 9 to generate energetically favorable N,N' diradicals 26, which cyclize to 18. The theoretical studies indicate also that one stereoisomer of 9, namely, the rac compound, should undergo valence isomerization more easily than the other, which is in conformity with different rates of these rearrangement reactions found experimentally. For the tetramethyl-bi-2H-azirin-2-yls 9 g, which are better models for the experimentally studied compounds, simultaneous homolytic cleavage of both C--N single bonds is also predicted by the calculations, although the intermediate diradicals 26 g are significantly higher in energy than those of the parent system 9 d.     

Quantification of 31 illicit and medicinal drugs and metabolites in whole blood by fully automated solid-phase extraction and ultra-performance liquid chromatography–tandem mass spectrometry

An efficient method for analyzing illegal and medicinal drugs in whole blood using fully automated sample preparation and short ultra-high-performance liquid chromatography–tandem mass spectrometry (MS/MS) run time is presented. A selection of 31 drugs, including amphetamines, cocaine, opioids, and benzodiazepines, was used. In order to increase the efficiency of routine analysis, a robotic system based on automated liquid handling and capable of handling all unit operation for sample preparation was built on a Freedom Evo 200 platform with several add-ons from Tecan and third-party vendors. Solid-phase extraction was performed using Strata X-C plates. Extraction time for 96 samples was less than 3 h. Chromatography was performed using an ACQUITY UPLC system (Waters Corporation, Milford, USA). Analytes were separated on a 100 mm?×?2.1 mm, 1.7 μm Acquity UPLC CSH C₁₈ column using a 6.5 min 0.1 % ammonia (25 %) in water/0.1 % ammonia (25 %) in methanol gradient and quantified by MS/MS (Waters Quattro Premier XE) in multiple-reaction monitoring mode. Full validation, including linearity, precision and trueness, matrix effect, ion suppression/enhancement of co-eluting analytes, recovery, and specificity, was performed. The method was employed successfully in the laboratory and used for routine analysis of forensic material. In combination with tetrahydrocannabinol analysis, the method covered 96 % of cases involving driving under the influence of drugs. The manual labor involved in preparing blood samples, solvents, etc., was reduced to a half an hour per batch. The automated sample preparation setup also minimized human exposure to hazardous materials, provided highly improved ergonomics, and eliminated manual pipetting.

Langmuir-Blodgett monolayers of gold nanoparticles with amphiphilic shells from V-shaped binary polymer arms

Gold nanoparticles functionalized with amphiphilic polybutadiene-poly(ethylene glycol) (PB-PEG) V-shaped arms formed stable Langmuir monolayers at the air-water and the air-solid interfaces. At these interfaces, the binary arms vertically segregated into a dense polymer corona, which surrounded the gold nanoparticles, preventing their large-scale agglomeration and keeping individual nanoparticles well-separated from each other and forming flattened, pancake nanostructures. The presence of both PEG and PB chains in the close proximity to the gold core was confirmed by surface enhanced Raman spectroscopy, whereas the AFM phase contrast images revealed the presence of 2 nm gold cores surrounded by the polymer shell with the diameter of 11 nm. We suggest that the amphiphilic shell drives their spontaneous organization into discrete 2D pancake-like hybrid structures that measured up to 10 microm in diameter and had a high packing density of gold clusters.     

Heat Content Asymptotics for Operators of Laplace Type with Spectral Boundary Conditions

Let P be an operator of Dirac type and let D=P ² be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for D.