An electron spectroscopic determination of theL I energy in the elements Sodium (Z=11) to Copper (Z=29)

Energies of atomic electrons in theK andL shells of eighteen elements of low atomic numbers have been measured by electron spectroscopy. Tabulated values for theL _I energies are shown to be in need of considerable revision. AluminumKα radiation is shown to have high potentialities for ESCA studies.     

Necessary and sufficient conditions for a matrix to be causative in a nonstationary Markov chain

Given a sequence of transition matrices for a nonstationary Markov chain, a matrix whose product on the right of a transition matrix yields the next transition matrix is called a causative matrix. A causative matrix is strongly causative if successive products continue to yield stochastic matrices. This paper presents necessary and sufficient conditions for a matrix to be causative and strongly causative with respect to an invertible transition matrix, by considering the causative matrix as a linear transformation on the rows of the transition matrix.     

Error estimates for a galerkin approximation of a parabolic control problem

Summary Numerical approximation of a parabolic control problem with a Neumann boundary condition control is considered. The observation is the final state. The numerical approximation is based on backward discretization with respect to time and a Galerkin method in the space variables. Optimal (except for a logarithmic term) L² error estimates are derived for the optimal state. Certain error estimates for the optimal control are also given. Entrata in Redazione il 4 maggio 1977. This work was supported by the Norwegian Research Council for Science and the Humanities.     

Optimal conditions for the reduction of selenate to selenite by hydrochloric acid

Summary The rate of reduction of Se(VI) to Se(IV) by hydrochloric acid was studied as a function of the acid concentration, temperature and reaction time. The reaction product Se(IV) was measured with the hydride generation-atomic absorption technique. The results show that for 10 mol/l HCl a complete reduction is achieved within 15 min at 60°C. The activation energy of the apparent first-order reaction was calculated from the results, and a value of 83 kJ mol^–1 was obtained.

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Optimale Bedingungen für die Reduktion von Selenat zu Selenit mit Salzsäure

     

Wave induced vibrations of gravity platforms: a stochastic theory

This paper presents a consistent stochastic method to evaluate wave induced vibrations of offshore platforms with special emphasis on gravity type structures. The wavy sea surface is idealized as a stationary and homogeneous stochastic Gaussian (or semi-Gaussian) field. The wave loading processes are treated by applying the concepts of probabilistic potential theory and the stochastic linearization method. The structure is modelled according to the finite element method using boundary spring-dashpot elements to idealize the soil-foundation system. The linearized equations of motion are solved by the frequency response method accounting properly for the temporal and spatial structure of waves as well as for time dependent system function. Numerical results for a 170m high concrete platform are presented including a parametric study of effects due to the shape of the wave spectral density.     

On optimal parameter estimation in credibility

The present paper is concerned with optimal estimation of the 1st and 2nd order structural moments appearing in credibility formulas. In a recent paper De Vylder has treated the problem in the case of multinormal conditional distributions under quite restrictive assumptions. He minimizes, within a certain restricted class of unbiased estimators, the variance (or the sum of variances if the estimand is a matrix) and next replaces all structural moments (up to fourth order) in the solution by estimates based on the data. This paper is an attempt to simplify the method and extend it so as to make it applicable in more general situations. By suitable choice of a (sufficient) set of statistics and a suitable parametrization, the powerful theory of estimation in linear models can be employed, which makes cumbersome minimization procedures superfluous. The theory is applied to the cases with binomial. Poisson, compound Poisson, and multinormal conditional distributions. Some simulation studies have been performed to assess the performance of the estimators.