A note on the necessary conditions for the algebraic Riccati equation

We derive some useful and easily computable necessary conditionsfor the existence of a positive semi-definite solution to thealgebraic Ricatti equation (ARE). A motivating example is givento highlight the usefulness of the conditions for controllerand observer designs for nonlinear systems. Further, an upperbound on the trace of the solution to the ARE is also derived.     

Properties of nonparametric estimators of autocovariance for stationary random fields

Summary We introduce nonparametric estimators of the autocovariance of a stationary random field. One of our estimators has the property that it is itself an autocovatiance. This feature enables the estimator to be used as the basis of simulation studies such as those which are necessary when constructing bootstrap confidence intervals for unknown parameters. Unlike estimators proposed recently by other authors, our own do not require assumptions such as isotropy or monotonicity. Indeed, like nonparametric function estimators considered more widely in the context of curve estimation, our approach demands only smoothness and tail conditions on the underlying curve or surface (here, the autocovariance), and moment and mixing conditions on the random field. We show that by imposing the condition that the estimator be a covariance function we actually reduce the numerical value of integrated squared error.     

Recent radiochemical studies of the fission process

This article summarizes the recent radiochemical investigations on mass, charge kinetic energy and fragment angular distributions in low energy fission of actinides.     

Study of the reaction of chalcone analogs of dehydroacetic acid and o-aminothiophenol: synthesis and structure of 1,5-benzothiazepines and 1,4-benzothiazines

Treatment of α,β-unsaturated carbonyl compounds, obtained by the reaction of DHA and aromatic (or heteroaromatic) aldehydes, with o-aminothiophenol results in the formation of 1,5-benzothiazepines and/or 1,4-benzothiazines depending upon the reaction conditions and structure of the aldehydes. The products were characterized by the combined use of multinuclear 1D and 2D NMR and GIAO/DFT calculations of ¹H, ¹³C and ¹⁵N chemical shifts. The tautomerism of these compounds in solution was determined, they have an exocyclic CC double bond.     

New accurate design data for a suspended microstrip line

New design data for an open suspended microstripline is reported. Two most commonly used substrate materials, namely RT-Duroid (_r=2.22) and fused quartz (_r=3.78) are considered. Effects of dispersion and strip thickness are included in the results which are based on a fullwave spectral-domain analysis. The data, which is computed over the complete practical ranges of frequency and parameter values, is much more reliable than the currently available quasistatic results.     

Synthesis of 1,3-bis(N,N-difluoroamino)adamantane: addition of difluoramino radicals to 1,3-dehydroadamantane

1,3-Dehydroadamantane undergoes a facile reaction with tetrafluorohydrazine to give 1,3-bis(N,N-difluoroamino)adamantane, the product of 1,3-NF₂ radical addition.     

Kinetics and mechanism of the complex formation between oxalatopentaamminecobalt(III) and aluminium(III) and gallium(III); a comparative study

Summary The reversible complex formation between oxalatopentaammine cobalt(III), aluminium(III) and gallium(III) was investigated by the stopped flow technique at 30 ± 0.1 °C and I = 1.0 mol dm^–3. The reactivity sequence: Ga^III > Al^III is observed, however, the major path for gallium(III) was (NH3)₅CoC₂O₄H²⁺ + GaOH²⁺ (NH₃)₅CoC₂O₄-Ga⁴⁺ + H₂O. The formation and dissociation rate constants of the binuclear species have been compared with the analogous data for iron(III) and nickel(II) reported earlier. The results reflect the fact that the half-bonded exalato moiety of (NH₃)₅CoC₂O _inf4 ^p+ acts as a chelating agent for the metal ions.Author to whom all correspondence should be directed.     

A convenient synthesis of linear pyranocoumarins. Xanthyletin and 3-Phenylxanthyletin

A convenient synthesis of linear pyranocoumarins, viz., 8,8-dimethyl-2H,8H-benzo[1,2-b; 5,4-b]dipyran-2-one (xanthyletin,1) and 8,8-dimethyl-3-phenyl-2H,8H-benzo[1,2-b; 5,4-b]dipyran-2-one (3-phenylxanthyletin,2) is described. The key steps are blocking the 8-position of appropriate 7-hydroxy-2H-1-benzopyran-2-one derivatives with iodine and 1,1-dimethyl-2-propynylation followed by cyclisation.

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Ein einfacher Syntheseweg zu linearen Pyranocumarinen. Xanthyletin und 3-Phenylxanthyletin

Zusammenfassung Es wird ein vorteilhafter Weg zur Synthese von linearen Pyranocumarinen am Beispiel von Xanthyletin und 3-Phenylxanthyletin gezeigt. Das Syntheseprinzip besteht in einer Blockierung der 8-Position des entsprechenden 7-Hydroxy-2H-1-benzopyran-2-ons mit Jod und einer 1,1-Dimethyl-2-propinylierung mit nachfolgender Cyclisierung.