Combined intra-intermolecular criss-cross cycloaddition of a new fluorinated unsymmetrical allenylazine with alkynes

The reaction of a new fluorinated unsymmetrical allenylazine with dimethyl acetylenedicarboxylate and phenylacetylene affords the combined intra-intermolecular criss-cross cycloaddition products, 2,3-disubstituted-1,10-diazatricyclo[5.2.1.0^4,10]deca-2,6-diene derivatives. The products contain three fused five-membered rings with two nitrogen atoms within an unsaturated heterocyclic system. The structures were assigned using 2D NMR correlations and in the case of the phenylacetylene adduct by X-ray structure analysis.     

Orbital formal normal forms for general Bogdanov-Takens singularity

We solve completely the problem of classification of germs of complex planar vector fields with nilpotent singularity with respect to formal orbital equivalence.     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Lyapunov-type inequalities for nonlinear systems

In this paper, by using elementary analysis, we establish some new Lyapunov-type inequalities for nonlinear systems of differential equations, special cases of which contain the well-known equations such as Emden-Fowler-type and half-linear equations. The inequalities obtained here can be used as handy tools in the study of qualitative behaviour of solutions of the associated equations.     

Anodic stripping coulometry with collection for absolute trace analysis of lead, using flow-through electrochemical cells with porous working electrodes

Summary Flow-through electrochemical cells with porous working electrodes made of crushed reticulated vitreous carbon and plated with mercury were used for absolute analysis of trace amounts of lead by anodic stripping coulometry with collection (ASCWC) in a flow system. The role of mercury coating, flow rate and pH were investigated. The coulombic content of the collection peak corresponded to the theoretical values calculated by Faraday's law in a concentration range from about 10^–9 to 10^–6 mol/l. The relative error and the relative standard deviation was +0.15% and 0.8%, respectively for 2×10^–6 mol/l analyte concentration. The absolute detection limit (3 s) was 0.1 ng of Pb, the linear response range 7×10⁴. One leave from: Department of Analytical Chemistry, Slovak Technical University, CS-812 37 Bratislava, Czechoslovakia     

Crystal and molecular structures of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine.

The crystal structure of 1-[3-(3,4-dimethoxyphenyl)-2-propenoyl]pyrrolidine (C15H19NO3) (I) has been determined by X-ray analysis. It crystallizes orthorhombic space group Pbca with a = 24.295(3), b = 15.086(3), c = 7.552(3)A, V = 2768(1)A3, Z = 8, Dcalc = 1.254 g/cm3, mu = (Mo K(alpha)) = 0.87 cm(-1). The title compound has analgesic activity of cycloaliphatic amine part. The molecule is deviated from planar configuration.     

Thermal analysis of renal stones

The chemical composition of 200 renal stones, collected from Taxila, Rawalpindi and Islamabad regions in Pakistan, was determined by thermogravimetric (TG) and differential thermal analysis (DTA) techniques. The thermal curves show weight losses at various temperatures indicating dehydration and decomposition phenomena of renal stones. Results were compared with qualitative data obtained by IR analysis which confirmed the chemical composition of various stones in the solid state. The thermal curves helped in the differentiation of various kinds of water held by stones and their chemical composition was obtained by weight loss during pyrolysis. It was found that 26.5% of the stones were pure whewellite, 3% weddellite, 13% uric acid anhydrous, 7.5% struvite, 2.5% ammonium acid urate, 0.5% cystine and 47% stones had mixed composition. In the mixed state the most frequent combinations were those of calcium oxalate with uric acid (14.5%) and with phosphates (27.5%).

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Zusammenfassung Mittels TG und DTA wurde die chemische Zusammensetzung von 200 Nierensteinen untersucht, die in den Gebieten Taxila, Rawalpindi und Islamabad in Indien gesammelt wurden. Die Thermogramme zeigen Masseverluste bei verschiedenen Temperaturen, die auf Dehydratation und Zersetzung der Nierensteine hinweisen. Die Ergebnisse wurden mit den qualitativen Resultaten aus der IR-Analyse verglichen, welche die chemische Zusammensetzung der verschiedenen Steine im festen Zustand bekräftigte. Die Thermogramme halfen bei der Unterscheidung von verschieden gebundenem Wasser, ihre chemische Zusammensetzung wurde durch Gewichtsverlust bei der Pyrolyse bestimmt. Man fand, daß 26.5 % der Steine aus reinem Whewellit bestanden, 3 % aus Weddellit, 13 % aus anhydrierter Harnsäure, 7.5 % aus Struvit, 2.5 % aus Ammmoniumhydrogenurat, 0.5 % aus Cystin und 47 % der Steine hatten eine gemischte Zusammensetzung. Die häufigsten Kombinationen der Mischzusammensetzungen waren Calciumoxalat mit Harnsäure (14.5 %) und mit Phosphaten (27.5 %).

     

Hochschild cohomology and “smoothness” in monoidal categories

We introduce and investigate the properties of Hochschild cohomology of algebras in an abelian monoidal category M. We show that the second Hochschild cohomology group of an algebra in M classifies extensions of A up to an equivalence. We characterize algebras of Hochschild dimension 0 (separable algebras), and of Hochschild dimension ≤1 (formally smooth algebras). Several particular cases and applications are included in the last section of the paper.     

Simulated cosmic strings in a “big bang” in superfluid3He at 100 μK

During studies of the impact of single neutrons on superfluid³He at around 100μK we have measured the thermal energy released in the superfluid following the nuclear reaction, n+³He→p+³H+764keV. However, we find that the measured energy deposited in the quasiparticle system shortly after this reaction is substantially less than what we expect. We believe that this energy deficit represents that energy which has gone into the creation of vortices, in analogy to the creation of cosmic strings in the early universe via the Kibble mechanism. Furthermore, from the magnitude of the deficit, we can infer the vortex density which compares favorably with that predicted in Zurek’s scenairo.