Uniqueness of embedding into a Gaussian semigroup on a nilpotent Lie group

This research was partially supported by the Hungarian Foundation for Scientific Researchers under grant number OTKA-T4047/1992.     

Scheduling crackdowns on illicit drug markets

This paper presents an analytical approach for scheduling crackdowns on street-corner drug markets. The crackdown scheduling problem is shown to be NP-complete. We then provide efficient optimal algorithms for several special cases and approximation algorithms for the general case. These results show that the optimal strategy is to give priority to markets that take longer to bring down and which require low levels of post-crackdown maintenance. The results are then extended to incorporate dealer displacement between drug markets.     

Parameter estimation of selfsimilarity exponents

The characteristic feature of operator selfsimilar stochastic processes is that a linear rescaling in time is equal in the sense of distributions to a linear operator rescaling in space, which in turn is characterized by the selfsimilarity exponent. The growth behaviour of such processes in any radial direction is determined by the real parts of the eigenvalues of the selfsimilarity exponent. We extend an estimation method of Meerschaert and Scheffler [M.M. Meerschaert, H.-P. Scheffler, Moment estimator for random vectors with heavy tails, J. Multivariate Anal. 71 (1999) 145-159, M.M. Meerschaert, H.-P. Scheffler, Portfolio modeling with heavy tailed random vectors, in: S.T. Rachev (Ed.), Handbook of Heavy Tailed Distributions in Finance, Elsevier Science B.V., Amsterdam, 2003, pp. 595-640] to be applicable for estimating the real parts of the eigenvalues of the selfsimilarity exponent and corresponding spectral directions given by the eigenvectors. More generally, the results are applied to operator semi-selfsimilar processes, which obey a weaker scaling property, and to certain Ornstein-Uhlenbeck type processes connected to operator semi-selfsimilar processes via Lamperti's transformation.     

Ozonation of 3β-acetoxy-5α-chloro-cholestane in solution. X-ray study of 3β-acetoxy-5α-chloro-14-cholestene-ozonide.

A selected saturated steroid derivative has been subjected to ozonation in solution. As the main reaction product 14,15-ozonide has been isolated in crystalline form whose structure has been unambiguously confirmed by the X-ray difraction method.     

Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes

Summary First we give a construction of bridges derived from a general Markov process using only its transition densities. We give sufficient conditions for their existence and uniqueness (in law). Then we prove that the law of the radial part of the bridge with endpoints zero derived from a special multidimensional Ornstein--Uhlenbeck process equals the law of the bridge with endpoints zero derived from the radial part of the same Ornstein--Uhlenbeck process. We also construct bridges derived from general multidimensional Ornstein--Uhlenbeck processes.     

The application of instrumental methods in the study of recent lacustrine sediments

Atomic absorption spectrophotometry, differential scanning calorimetry, differential thermal analysis, thermogravimetric analysis, and infrared spectroscopy, combined with oxidizable carbon determinations and pollen counting, were applied in the paleoecological study of lacustrine sediments taken from some lakes in Northern Ireland. Details of the techniques, and the methods of sampling and sample preparation are described, and the results discussed. Such studies reveal valuable information on past environments.     

The reaction of alkoxides with dicobalt octacarbonyl: Trapping of the Co(I) intermediate in the disproportionation (“base reaction”) with a hardLewis base

Dicobalt octacarbonyl reacts with alcoholates (RO^–) yielding alkoxycarbonylcobalt tetracarbonyls,ROC(O)Co(CO)₄.

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Reaktion von Alkoxiden mit Dicobaltoctacarbonyl: Abfangen des Co(I) Zwischenproduktes in der Disproportionierung (Basen-Reaktion) mit einer hartenLewis Base (Kurze Mitteilung)

Zusammenfassung Dicobaltoctacarbonyl reagiert mit Alkoxiden (RO^–) zu Alkoxycarbonylcobalt tetracarbonylen,ROC(O)Co(CO)₄.

     

New Routes to Oxindole Derivatives

A new, practical synthesis of the antirheumatic oxindole derivative, tenidap, has been elaborated. The new approach has initiated studies on the mechanism of the acylation reactions of oxindoles. Methods have been developed for the synthesis of 1-[alkoxy(or aryloxy)carbonyl]- and 1,3-di[alkoxy(or aryloxy)carbonyl]oxindoles starting from oxindoles. The route designed for tenidap has provided a facile access to several analogues, too.On another front, new reaction conditions are described, which turn Wenkerts synthesis of 3-alkyloxindoles (by Raney nickel induced alkylation of oxindoles with alcohols) into a highly efficient synthetic tool. The method has been extended to the synthesis of 3-alkyloxindoles from isatins and to the preparation of 3-(-hydroxyalkyl)oxindoles from oxindoles and isatins.     

Efficient syntheses of the versatile phthalide building blocks, 5,6-diaminoisobenzofuran-1(3H)-one and 5H,7H-furo[3,4-f][2,1,3]benzothiadiazol-5-one

A new and efficient synthesis of 5,6-diaminophthalide and a novel thiadiazolophthalide has been accomplished. Both molecules are useful starting compounds for the construction of more complex heterocyclic systems and for the preparation of bioisosteres of methylenedioxyphenyl derivatives.