Study of M4,5N4,5N4,5 auger energy shifts of Cs and I in free CsI molecules

High-resolution electron beam excited M_4,5N_4,5N_4,5 Auger electron spectra of Cs and I have been measured from CsI vapour. The Auger energies of both Cs and I observed from gaseous CsI are higher than the corresponding free-atom energies due to extra-atomic relaxation. The molecular Auger results have been compared with corresponding photoelectron measurements and free-atom data. Estimates for extra-atomic relaxation energies have been extracted from the changes of the Auger parameter between molecular and atomic species and from the difference between experimental energies and energies calculated with a relativistic Dirac-Fock program, applying the point-charge model for the CsI molecule.     

Computations on the growth of the first factor for prime cyclotomic fields II

It is shown by computing thath(p) — the first factor of the class number of the prime cyclotomic fieldk(exp(2i/p)) — is strictly increasing for 19p1097.     

A Phragmén — Lindelöf principle for subsolutions of quasi — linear equations

Quasi — linear elliptic equations of homogeneous type are studied in this paper. The equation satisfies uniform ellipticity and growth conditions. A Phragmén — Lindelöf principle is proved by a combined technique of Ladyenskaya-Ural'ceva and Moser. This technique makes it possible to estimate the growth of the maximum modulus of a subsolution in general unbounded domains.     

Normal Auger spectra of Br in alkali bromide molecules

Molecular Auger electron spectra following the bromine 3d ionization in gas-phase alkali bromides and in HBr were studied both experimentally and theoretically. The AES for HBr and CsBr were measured using photoexcitation, and for LiBr, NaBr, and KBr by using electron impact. These results are compared with the theoretical spectra from nonrelativistic ab initio calculations and one-center approximation and with the spectra of Br(-), computed with the multiconfiguration Dirac-Fock method.     

Chaos in the one-dimensional gravitational three-body problem

We have investigated the appearance of chaos in the one-dimensional Newtonian gravitational three-body system (three masses on a line with -1/r pairwise potential). In the center of mass coordinates this system has two degrees of freedom and can be conveniently studied using Poincare sections. We have concentrated in particular on how the behavior changes when the relative masses of the three bodies change. We consider only the physically more interesting case of negative total energy. For two mass choices we have calculated 18 000 full orbits (with initial states on a 100x180 lattice on the Poincare section) and obtained dwell time distributions. For 105 mass choices we have calculated Poincare maps for 10x18 starting points. Our results show that the Poincare section (and hence the phase space) divides into three well defined regions with orbits of different characteristics: (1) There is a region of fast scattering, with a minimum of pairwise collisions. This region consists of 'scallops' bordering the E=0 line, within a scallop the orbits vary smoothly. The number of the scallops increases as the mass of the central particle decreases. (2) In the chaotic scattering region the interaction times are longer, and both the interaction time and the final state depend sensitively on the starting point on the Poincare section. For both (1) and (2) the initial and final states consist of a binary + single particle. (3) The third region consists of quasiperiodic orbits where the three masses are bound together forever. At the center of the quasiperiodic region there is a periodic orbit discovered (numerically) by Schubart in 1956. The stability of the Schubart orbit turns out to correlate strongly with the global behavior.     

Calculations of millimeter wave depolarization due to melting layer and rain

A model for calculating the total depolarization due to the melting layer and rain is proposed under the assumption that oblate spheroidal melting particles and raindrops have the same orientation. The melting layer is composed of the melting particles which are made up from the mixture of ice, air and water. The specific attenuation and the specific phase shift both for the melting layer and for rain are given in the power lawaR ^b form for the rain rates 0R12.5 mm/h and the parameters are tabled over the frequency range of 1–100 GHz. Using the model, the numerical calculation of the depolarization is possible for three drop size distributions.     

p-Laplacian Inclusions via Fixed Points for Multifunctions in Posets

We consider the Dirichlet problem for elliptic differential inclusions involving the p-Laplacian and governed by multivalued nonlinearities bounded above and below by single-valued monotone functions not necessarily continuous. The aim of this note is to provide existence and comparison results for the problem under consideration without imposing further regularity assumptions. The main tools used in the proof of our results are existence and comparison results for extremal solutions of (single-valued) nonlinear elliptic equations, and an abstract comparison principle for fixed points of multivalued operators in partially ordered sets (posets).     

Inverse cationic ITP for separation of methadone enantiomers with sulfated β‐cyclodextrin as chiral selector

Chiral ITP of the weak base methadone using inverse cationic configurations with H⁺ as leading component and multiple isomer sulfated β‐CD (S‐β‐CD) as leading electrolyte (LE) additive, has been studied utilizing dynamic computer simulation, a calculation model based on steady‐state values of the ITP zones, and capillary ITP. By varying the amount of acidic S‐β‐CD in the LE composed of 3‐morpholino‐2‐hydroxypropanesulfonic acid and the chiral selector, and employing glycylglycine as terminating electrolyte (TE), inverse cationic ITP provides systems in which either both enantiomers, only the enantiomer with weaker complexation, or none of the two enantiomers form cationic ITP zones. For the configuration studied, the data reveal that only S‐methadone migrates isotachophoretically when the S‐β‐CD concentration in the LE is between about 0.484 and 1.113 mM. Under these conditions, R‐methadone migrates zone electrophoretically in the TE. An S‐β‐CD concentration between about 0.070 and 0.484 mM results in both S‐ and R‐methadone forming ITP zones. With >1.113 mM and < about 0.050 mM of S‐β‐CD in the LE both enantiomers are migrating within the TE and LE, respectively. Chiral inverse cationic ITP with acidic S‐β‐CD in the LE is demonstrated to permit selective ITP trapping and concentration of the less interacting enantiomer of a weak base.     

Subordinate solutions and spectral measures of canonical systems

The theory of 2×2 trace-normed canonical systems of differential equations on ?⁺ can be put in the framework of abstract extension theory, cf. [9]. This includes the theory of strings as developed by I.S. Kac and M.G. Kre?n. In the present paper the spectral properties of such canonical systems are characterized by means of subordinate solutions. The theory of subordinacy for Schrödinger operators on the halfline ?⁺, was originally developed D.J. Gilbert and D.B. Pearson. Its extension to the framework of canonical systems makes it possible to describe the spectral measure of any Nevanlinna function in terms of subordinate solutions of the corresponding trace-normed canonical system, which is uniquely determined by a result of L. de Branges.