Calculations on bound and autoionizing states,and continuum radiative properties for Li− and Na−

Semi-empirical model potential calculations have been performed for bound and continuum properties of Li^? and Na^?. The calculated electron affinities of the 2s²¹S state of Li^? and the 3s²¹S and 3p²³P^e states of Na^? are in agreement with the calculations of Norcross and with experimental data. Positions of possible autoionizing states are calculated using projection and root stabilization methods. The Stieltjes imaging method of Langhoff is employed to compute the photodetachment cross sections of Li^? and Na^? and the results are in excellent agreement with the close-coupling calculations of Moores and Norcross. A comparison of variational and numerical results for the coupled time-dependent Hartree-Fock photoionization of helium shows that good Stieltjes imaging results can be obtained with a very small basis set for the variational calculation. The continuous photoemission profile for the 3p²³P^e state of Na^? is also obtained.     

FRIEDEL-CRAFTS-Reaktionen der C7-, C8- und C12-Cycloalkane mit Kohlenmonoxid

The reaction of cycloheptane, cyclooctane, and cyclododecane with carbon monoxide under pressure in the presence of anhydrous aluminium chloride has been investigated. Cycloheptane leads to acetylcyclohexane and trans-2-methyl-cyclohexane carboxylic acid as main products. Cyclooctane yields 3- and trans-4-acetyl-methylcyclohexane and various dimethylcyclohexane carboxylic acids. From cyclododecane a mixture of numerous ketones has been obtained besides a mixture of acids.     

Symmetriegerechte Basisvektoren für Permutationsdarstellungen aller endlichen Punktgruppen der Dimensionen 3 und 2

Zusammenfassung Es seiG eine endliche Untergruppe der orthogonalen Gruppe (det=±1) des ^k mitk=2 oder 3 undN eine endliche Menge von Punkten des ^k , welche unterG invariant ist. Dies gibt Anlass zu einer Permutationsdarstellung vonG im Vektorraum der komplexen Funktionen aufN.In Abschn. 3 wird für eine symmetriegerechte Basis angegeben. Dabei sind die Funktionswerte jeweils exakt tabelliert.

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Let G be a finite subgroup of the orthogonal group (det=±1) of ^k wherek=2 or 3 and letN be a finite set of points of ^k , which is invariant underG. In this way one gets a permutation representation ofG in the vector space of the complex functions onN.In Section 3, a symmetry adapted basis is given for , where the function values are tabulated exactly.

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Im Buch [1] wurden lediglich die Diedergruppen behandelt (in Abschn. 3.1).     

Nonparametric estimation based on censored observations of a Markov renewal process

Summary Uniform consistency and weak convergence is proved of estimators of the transition probabilities of an arbitrary finite state space Markov renewal process, based on n independent and identically distributed right censored realizations of the process. The approach uses the theory of stochastic integrals and counting processes. It is shown how the results may be extended to the non-identically distributed case and to general censorship under suitable conditions.     

Reflectivity and transmitivity of a spatially dispersive crystal

The reflectivity and transmitivity of a spatially dispersive crystal for S-polarized incident light are calculated for a microscopical model in which the interaction among the crystal planes is assumed to fall exponentially with distance. The angle of incidence is arbitrary and the deduced formulae are valid from X-ray to the visible light region. The generalization to the more complicated models is briefly discussed. For solving the problem an algebraic formulation of the Ewald dynamical theory of diffraction is used.     

Rotational band crossings in the actinides

In the actinides bothi _13/2 protons andj _15/2 neutrons are close to the Fermi surface. At rapid rotation these high-j particles will unpair and align their orbital angular momentum along the axis of rotation giving rise tos-bands that cross the ground-state band. Coulomb excitation of the odd nuclei ₂₃₇ ⁹³ Np (established up to the 45/2⁺ state) and ₂₃₅ ⁹² U (established up to the 51/2^? state) provides specific information about these band crossings: From the saturating alignment of the odd high-j particle in both nuclei at intermediate rotational frequencies we find the aligned angular momentum of thei _13/2 protons-band to be 6.6? while the corresponding value for thej _15/2 neutrons-band is 5.5?. At more rapid rotation above ?ω=0.18 MeV we observe additional alignment in²³⁵U. This is ascribed to the interaction of the protons-band. From the gradual onset of the additional alignment we deduce that forZ=92 the protons-band interacts strongly with the ground-state band and from a comparison of the actual amount of alignment with the full value of 6.6? we estimate the crossing to occur around ?gw _c ^p =0.25 MeV.     

Methods of Wall Charge Determination in External Electrode Gas Discharges. II. Preliminary Tests,Comparison of Methods,Distributions

First experiments with the arrangement described in part I of this paper resulted in three spurious effects: shifting of characteristic values due to ageing effects, dissymmetric behaviour of wall charges and currents with respect to the voltage pulse sign, and backfiring. The comparison between the direct and the indirect methods demonstrated the sensitivity of the indirect ones to uncertainties and variations in effective cell capacities. The wall charge density distributions are axially symmetric and can be described in the electrode range by ? (x) = ae.     

A note on the stack size of regularly distributed binary trees

Assume that in one unit of time a node is stored in the stack or is removed from the top of the stack during postorder-traversing of a binary tree. If all binary trees are equally likely the average stack size aftert units of time and the variance is computed as a function of the proportion=t/n.Part of this paper was presented at the 6th Colloquium on Automata, Languages and Programming, ICALP' 79, July 1979.     

Nonlinear renormalization-group analysis applied to the hydrodynamic light scattering spectrum of4He belowT λ

We calculate the observable critical temperature dependence of the transport coefficients entering the hydrodynamic form of the dynamic structure factor of⁴He belowT . Application of our recently introduced nonlinear renormalization-group analysis yields quantitative agreement with previous light scattering experiments in the hydrodynamic region. This resolves a long-standing problem in the critical dynamics below the superfluid transition of⁴He.Supported in part by the Fonds zur Förderung der wissenschaftlichen Forschung     

Minkowski parallel-translation and their coordinatization

In a Minkowski plane with parallelisms ₊ and _– one postulates triple transitivity of ₊ -preserving bijections of points onto _– points such that circles map on circles. This postulate corresponds almost exactly to Axiom G of [2]. A coordinatization may then be accomplished by introduction of a quaternary operation, after a coordinate frame consisting of three distinct concircular points has been fixed. All circles except those in one derived affine plane are points (x,y) with y=[x,a,b,c]. This derived plane then turns out to be a nearfield-plane. The quaternary operation satisfies [x,a,b,c]=[x–a,0,0,1]c+b. In a symmetric Minkowski plane, which, in view of [1], is coordinatized by a commutative field, y=[x,a,b,c] becomes (x–a)(y–b)=c, yielding the well known hyperbola model.Dedicated to Werner Burau on his 70th birthdayPresented to the Conference on Geometry, University of Haifa, March 10, 1975.