On the fragmentation modes in PMO analyses

The molecular species 1,1- and 1,2-disubstituted alkenes have been used as model systems for a comparative discussion of the results obtained with quantitative orbital analyses using different fragmentation modes. It is shown that when indices of the overall energy effects are used, the results of a quantitative orbital analysis are independent of the chosen fragmentation mode. On the other hand, the results of such analysis can depend on the fragmentation mode when indices of partial energy effects are used.     

On a new class of multiplicative pseudo-random number generators

In the computing literature, there are few detailed analytical studies of the global statistical characteristics of a class of multiplicative pseudo-random number generators.We comment briefly on normal numbers and study analytically the approximately uniform discrete distribution or (j,)-normality in the sense of Besicovitch for complete periods of fractional parts {x _{0 1} ⁱ /p} on [0, 1] fori=0, 1,..., (p–1)p^–1–1, i.e. in current terminology, generators given byx _{n+1 1} x _n mod p wheren=0, 1,..., (p–1)p ^–1–1,p is any odd prime, (x ₀,p)=1, ₁ is a primitive root modp ², and 1 is any positive integer.We derive the expectationsE(X, ),E(X ², ),E(X _nX_n+k); the varianceV(X, ), and the serial correlation coefficient k. By means of Dedekind sums and some results of H. Rademacher, we investigate the asymptotic properties of k for various lagsk and integers 1 and give numerical illustrations. For the frequently used case =1, we find comparable results to estimates of Coveyou and Jansson as well as a mathematical demonstration of a so-called rule of thumb related to the choice of ₁ for small k.Due to the number of parameters in this class of generators, it may be possible to obtain increased control over the statistical behavior of these pseudo-random sequences both analytically as well as computationally.     

Models and paradoxes in quantum chemistry

Ten different, unexpected features of the classificatory results of quantum mechanics are discussed as well as the question whether the Schrödinger equation only applies to sufficiently small systems which can be indiscernibly reproduced and possess assembly porperties.Dedicated to Professor H. Hartmann on occasion of his sixtieth birthday 4. May 1974.     

Theoretical study of the potential energy curves of the diatomic radicals MeIIX. III. Application to MgCl,CaF and CaCl radicals and some preliminary remarks

The series of calculations of the potential energy curves of the diatomic radicals Me_IIX (Me_II = second group metal, X = halogen), has been extended to MgCl, CaF and CaCl. The calculations have been performed according to a stepwise procedure, outlined in previous works. The presently available results allow comparisons for the first members of the series.     

“In-situ” monitoring activation and reaction on very absorbing catalytic solid by DRIFT spectrometer

The FTIR's well-known advantages are strongly shown by the use of new infrared techniques. Both advantages of FTIR and diffuse reflectance make this coupling particularly important in the development of infrared studies.Sensitivity and rapidity of the FTIR spectrometer, added to the extremely simple preparation of the sample, allowed by diffuse reflectance attachment, give a high performing tool particularly in catalysis in the view of understanding the catalytic reactions mechanisms. We have chosen thein-situ study of two catalytic systems active in selective hydrogénation of dienes: a copper-chromium oxide and Cu/Al₂O₃ .     

An investigation of the reliability of the Galerkin-Petrov method

The Galerkin-Petrov method is applied to the determination of the ground state energy of the beryllium atom. The basis set of the coordinate subspace consists of correlated wavefunctions of the combined configuration-interaction-Hylleraas type. The basis set of the projective subspace is of the configuration-interaction type. The usefulness of a previously proposed way of characterization of pairs of subspaces has been further confirmed. Experience in constructing close pairs of subspaces gathered in the case of two-electron systems is used for the larger system. Two methods for constructing pairs of subspaces are used in the calculations.     

Polarographic determination of microgram amounts of thorium(IV)

Summary Among various salt solutions tested 0.01 N LiNO₃ proved to be most suitable as supporting electrolyte for the polarographic determination of microgram amounts of thorium. Well-developed, maxima-free and reproducible waves were obtained for a Th(IV) concentration range of 1.4–23 g/ml. The minimum detectable limit of the element was 0.8 g/ml. No relationship has been found between Th(IV) and H⁺-ion concentration.

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Polarographische Bestimmung von Mikrogramm-Mengen Thorium(IV)

Zusammenfassung Von verschiedenen untersuchten Salzlösungen hat sich als Grundelektrolyt 0,01 N LiNO₃-Lösung als am günstigsten erwiesen. Es wurden damit gut ausgebildete, maxima-freie und reproduzierbare Stufen für einen Konzentrationsbereich von 1,4–23 g Th(IV)/ml erhalten. Die Nachweisgrenze betrug 0,8 g Th(IV) in 1 ml Lösung. Es wurde kein Zusammenhang zwischen Thoriumkonzentration und H⁺-Ionenkonzentration nachgewiesen.