On the probability distribution of data at points in real complete intersection varieties

We show several estimates on the probability distribution of some data at points in real complete intersection varieties: norms of real affine solutions, condition number of real solution of real systems of multi-variate polynomial equations and convergence radius of Newton's operator for under-determined system of multi-variate polynomial equations.     

Eine Approximation der Binomialverteilung durch die Normalverteilung der Ordnung 1/n

Summary The class (1) of transformations of a binomial variablek is studied. The famous De Moivre-Laplace local and integral limit theorems are generalized for the asymptotically standardized transformations (2). The transformation (4) respectively (3) is singled out as the only one with an error of order 1/n. Besides it is shown, that the error term of ordern ^–1/2 of the identical transformation, the angular transformation, and the logarithmic transformation are in proportion to 1/6, –1/12, and –1/3. Results on the influence of a correction of unbiasedness are mentioned in the last section. Such corrections allow a slight improvement of our new transformation.     

Zur Existenz von separablen stochastischen Prozessen

Ohne ZusammenfassungK. L. Chung und J. L. Doob haben bereits im April 1965 im wesentlichen die Aussage von Satz 2 für T=R in Proposition 33 ihrer Arbeit Fields, Optionality and Measurability, Amer. J. Math. 87, 397–424 (1965) mit Hilfe völlig anderer Methoden bewiesen. Dabei benutzen sie unser Kriterium (2.4) als Definition der SeparabilitÄt.     

Self-consistent-field CNDO/BW cluster model of covalent solids

We have suggested a parametrization scheme for the self -consistent CNDO/BW method suitable to model the electronic structure of perfect and locally perturbed covalent solids. By working on small clusters we have carried out calculations for diamond perfect crystal and for nitrogen replacing a carbon atom in the lattice. The results show that the methos is accurate to calculate one electron energy-eigenvalues and total energies.     

Buchbesprechung

Ohne Zusammenfassung     

Does QCD have infrared renormalons?

We give a naïve perturbative proof of the existence of infrared renormalons for large distance asymptotically free theories. We argue that the extension of the result for small distance asymptotically free theories is not obvious. Indeed we do not find infrared renormalons for QCD.