On a method of constructing the solutions of boundary-value problems of the theory of bendings of surfaces of positive curvature

A new method is proposed for constructing the solutions of boundary-value problems of Riemann-Hilbert type for noncanonical linear and quasilinear first-order elliptic systems in a simply connected bounded region of the plane. For a linear boundary condition we obtain complete results; for a nonlinear boundary condition we study the solvability in a neighborhood of zero. Applications are given to the problem of isometric transformations of a surface diffeomorphic to the disk and having positive curvature all the way to the boundary under prescribed boundary conditions.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 56–82.     

Nonclassical states generated via four-wave mixing

The nonclassical properties of quantum fields generated by four- or three-wave mixing are investigated on the basis of assumptions of two-photon coherent (squeezed) input states and the approximation of strong pumping. The influence of losses is shown supposing the model of mutually independent phonon reservoirs. The possibility of producing squeezed and sub-Poisson light outputs is demonstrated in single or superposed modes using computer solutions.The author wishes to acknowledge helpful discussions with Dr. J. Peina and Dr. M. Kárská.     

Effect of multijunction grill length on its lower hybrid current drive efficiency

The distance between the junction of subsidiary waveguides in the main waveguide and the grill mouth has an important influence upon the spectrum of radiated waves, the total reflection coefficient, the power distribution among the separate waveguides and the actual phases of incident waves. This effect is nearly as important as that of the phase shift between the adjacent waveguides and it is necessary to carry out optimization with respect to this parameter in the grill design.     

Optical constants of titanium and silicon dioxide films

In this paper a study of optical constants of titanium and silicon dioxide films prepared in Balzers BAK 600 and BA 510 conventional high-vacuum apparatus is described. Both the dispersion and the geometrical thickness were determined from normal reflectance spectrum by adapted general algorithm of the statistical interpretation of measured data. The dependence of optical constants on oxygen pressure for both materials and the evaporation rate dependence for titanium dioxide were obtained. The time changes of these constants were also measured.     

Low energy restrictions for a flipped left-right symmetric model

I consider some low energy restrictions for a “flipped” left-right symmetric model containing exotic fermions ofE ₆ and a right-handedW-boson, all with oddR-parity. The new interactions due toW _R-exchange have no significant impact on rare kaon decays, because theW _R does not couple tod,s,b quarks. On the other hand,W _R exchanges might induce rare processes like \(D - \bar D\) mixing, \(D^0 \to \mu \bar \mu ,D^0 \to \mu \bar e,\mu \to e\gamma ,\mu \to 3e\) , and μN→eN. It turns out that the strongest bound is obtained from \(D - \bar D\) mixing. With reasonable extra assumptions, it is found that the exotic right-handed W-boson is likely to be heavier than 500 to 1500 GeV.     

The effective action of a spin 1/2 field in the background of a nontopological soliton

We generalize a new method of calculating the effective action for fields in a spherically symmetric background to the case of a spin 1/2 field whose mass is a function ofr=|x|, as it is the case in the nontopological soliton model of Friedberg and Lee. The quantum corrections to the soliton energy are sizeable, of the same order as the bound state energies that stabilize the soliton.     

Crystal structure and vibrational spectra of hydrazinium (2+) tri-μ-fluoro bis[pentafluorozirconate (IV)] fluoride and vibrational spectra of its hafnium analogue

Monoclinic (N₂H₆)₃Zr₂F₁₃·F crystallizes in space group P2₁-C ₂ ² (No. 4) with unit cell dimensionsa=5.670(1),b=10.984(2),c=10.601(2) Å,=93.88(1)°,V=658.7(4) ų andZ=2. Two different types of N₂H₆ ²⁺ ions are present. One is involved in strong H-bonds to F^– ions in infinite chains running along the a axis (the shortest N-F distance is 2.437(5) Å), and the other links the structure through weaker bi- and trifurcated H-bonds to fluorine ligands of the Zr₂F₁₃ ^5– ions. The N-N bond lengths range from 1.430(5) to 1.446(5) Å with apparently no meaningful correlation to the type of N₂H₂ ²⁺ ions. The Zr₂F₁₃ ^5– ions have very nearly C₂ point symmetry and are formed by joining two distorted bicapped trigonal prisms of ZrF₈-units through a common face. Distances of Zr-F terminal bonds range from 2.015(2) to 2.112(2) Å and of bridging bonds from 2.133(2) to 2.212(2) Å. (N₂H₆)₃Hf₂F₁₃·F is isomorphous. The vibrational spectra of the two compounds are nearly identical, with the exception of a strong infrared band, which is assigned to a stretching mode with the moving central atom within the anion. The anion part of the spectrum is simple, showing broad unresolved bands. The cation part shows two types of N₂H₆ ^– ions. H-Bonding is strongly present in the spectra, but no simple correlations with the H-bond strength is evident.     

Crystal and molecular structure of crenatine carbonate

The crystal and molecular structure of 1-ethyl-4-methoxy-9H-pyrido[3,4b]indole (crenatine) carbonate C₁₄H₁₄N₂O·H₂CO₃, (MS, m/z 226)M _R 288.3, a-carboline alkaloid, has been determined from X-ray diffraction data. The compound crystallizes in the space group Pbca with cell parameters:a=11.616(4),b=18.450(8),c=12.992(5)Å,V=2784(2)ų,Z=8,D _calc=1.375 g cm^–3, (MoK)=0.71069Å,(Mo K)=0.94 cm^–1,F(000)=1216,R/R _w =8.2/10.3% for 1099 reflections. The ring system of the-carboline nucleus is planar. The title compound shows a two center hydrogen bond between the indole N-H group and the oxygen atom of a carbonate group. The structure does not display hydrogen bonding between-carboline groups but rather a bonding network involving the carbonate group.     

Impulse systems with fixed moments of shocks of general position: The structure of the set of moments of the shocks

Ordinary differential equations with impulse action are considered at fixed moments of time when finite limits points are admitted to the set of moments of the shocks. The topological structure of this set is clarified: it must be resolvable, in particular nowhere dense in R.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 3, pp. 378–383, March, 1990.     

Electron Emission from Clean Solid Surfaces by Fast Ions

Total backward electron yields from 27 elemental, non-crystalline, clean solids were measured during bombardment by H⁺-, H-, H-, He⁺- and Ar⁺-ions in the energy range from 100 keV to 800 keV. The yields were found to exhibit an oscillatory dependence on the atomic number of the target material correlated with the periods of the periodic system. These Z₂-oscillations are relatively insensitive to the type of projectile and the impact energy at the high projectile energies of this experiment. Present theories of electron emission cannot explain the main experimental results. The reasons for this failure are discussed.