An example in connection with the Jacobian conjecture

Translated from Matematicheskie Zametki, Vol. 47, No. 1, pp. 127–136, January, 1990.     

Multivariate cardinal interpolation with radial-basis functions

For a radial-basis function?∶?→? we consider interpolation on an infinite regular lattice , tof∶? ⁿ→?, whereh is the spacing between lattice points and the cardinal function , satisfiesX(j)=δ _oj for allj∈? ⁿ. We prove existence and uniqueness of such cardinal functionsX, and we establish polynomial precision properties ofI _h for a class of radial-basis functions which includes \(\varphi (r) = r^{2q + 1} \) , \(\varphi (r) = r^{2q} \log r,\varphi (r) = \sqrt {r^2 + c^2 } \) , and \(\varphi (r) = 1/\sqrt {r^2 + c^2 } \) whereq∈? ₊. We also deduce convergence orders ofI _hf to sufficiently differentiable functionsf whenh→0.     

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.     

Threshold anomaly in doubletn-d scattering

The behaviour of the doubletn-d scattering phase shift ₂(k) at energies close to the three-particle threshold is studied analytically and numerically. The scattering parameters possess an anomaly associated with the low energy of the singletN-N virtual state. The anomaly manifests itself both as a bend in the energy dependence of the functionk cot(Re ₂) in the range around 0.5 MeV and in the nonstandard behaviour of the break-up cross section near the threshold.     

Phase-space analysis of alternating Δβ couplers

A geometrical method for determining the power transfer between piecewise uniform, alternating , twin-core linear directional couplers is presented. Phase space provides the basis for the method.     

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.     

Analysis, synthesis, and perception of voice quality variations among female and male talkers

Voice quality variations include a set of voicing sound source modifications ranging from laryngealized to normal to breathy phonation. Analysis of reiterant imitations of two sentences by ten female and six male talkers has shown that the potential acoustic cues to this type of voice quality variation include: (1) increases to the relative amplitude of the fundamental frequency component as open quotient increases; (2) increases to the amount of aspiration noise that replaces higher frequency harmonics as the arytenoids become more separated; (3) increases to lower formant bandwidths; and (4) introduction of extra pole zeros in the vocal-tract transfer function associated with tracheal coupling. Perceptual validation of the relative importance of these cues for signaling a breathy voice quality has been accomplished using a new voicing source model for synthesis of more natural male and female voices. The new formant synthesizer, KLSYN88, is fully documented here. Results of the perception study indicate that, contrary to previous research which emphasizes the importance of increased amplitude of the fundamental component, aspiration noise is perceptually most important. Without its presence, increases to the fundamental component may induce the sensation of nasality in a high-pitched voice. Further results of the acoustic analysis include the observations that: (1) over the course of a sentence, the acoustic manifestations of breathiness vary considerably--tending to increase for unstressed syllables, in utterance-final syllables, and at the margins of voiceless consonants; (2) on average, females are more breathy than males, but there are very large differences between subjects within each gender; (3) many utterances appear to end in a "breathy-laryngealized" type of vibration; and (4) diplophonic irregularities in the timing of glottal periods occur frequently, especially at the end of an utterance. Diplophonia and other deviations from perfect periodicity may be important aspects of naturalness in synthesis.