Approximation Methods for Solving the Cauchy Problem

In this paper we give some new results concerning solvability of the 1-dimensional differential equation y′ = f(x, y) with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if f is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution. Finally, some applications are given.     

Arc Discharge in a Channel with Transparent Walls at Intense Flow Rates of a Plasma Forming Gas

The arc discharge was studied in a transparent channel at an intense flow rate of nitrogen, hydrogen, air, carbon dioxide in the current range 100–1500 A. The internal diameter of the porous channel varied from 10 to 34 mm, the length - from 50 to 150 mm, the air and nitrogen flow rates - from 0.05 to 1.5 kg/s, hydrogen - from 0.005 to 0.05 kg/s. The electric field strength in the arc channel reached a value of 300 V/cm for N₂ and 500 V/cm for H₂. The effect of plasma thermochemical non-equilibrium was discovered.     

The influence of photodissociated N2O in pulsed-laser deposition of Y-Ba-Cu-O films

Pulsed-laser deposition of YBa₂Cu₃O₇ in N₂O permits lowering of the substrate temperature with respect to deposition in O₂ atmosphere. Additional photodissociation of N₂O near the substrate surface deteriorates the superconducting properties of deposited films.On leave from: Institute of Applied Physics of the Academy of Sciences of the USSR, SU-603600 Nishni Nowgorod, USSR     

Band structures in73Se

Excited states of⁷³Se have been investigated up to spin, 21/2 using techniques of in-beamγ-ray spectroscopy in connection with the⁷⁰Ge(α, n) reaction. Mean lifetimes of 12 levels have been determined applying Doppler-shift andγ-RF-methods. Five different bands have been identified that reflect a variety of different excitation modes. The decoupled 9/2⁺ band is likely to correspond to an oblate deformation while the 5/2⁺ band is interpreted as a strongly coupled prolate band built on the Nilsson configuration [422] 5/2⁺. The 3/2^? band is a strongly coupled band built on the [301] 3/2^} configuration.Nuclear reactions:⁷⁰Ge(α,n),E=14, 16, 18, 19, 20MeV; measuredE _γ,I _γ,σ(E _γ,θ),γγ-coin, linear polarization, DSA,γ(t).⁷⁵Se deduced levels,I, π, τ, δ(E2/M1), B(σλ). Enriched targets, Ge detectors.     

Optical waveguide analysis using modified Airy functions

We review a little-used but powerful method of solving the scalar wave equation. It uses a modification of the well-known Airy functions, which are easily calculated on desktop computers. The techniques are reminiscent of the WKBJ methodology, but the solution, although approximate, is much more useful than the traditional WKBJ solution and can be used with almost as much ease. Re method is extremely powerful but, to our knowledge, is not used in the optics community. It is useful in analyzing integrated optical waveguide components.     

Serial magnetic resonance imaging in patients following acute myocardial infarction.

The detection of serial changes in magnetic resonance (MR) signal intensity of the heart following acute myocardial infarction may provide a useful method of characterizing tissue healing. Fourteen patients with acute Q-wave infarction underwent T2-weighted, spin-echo cardiac imaging during hospitalization, followed by one or more additional MR studies (total 31) over a 6- to 27-wk period (mean: 3 mo). Visual assessment of the images demonstrated a gradual reduction in signal intensity and localization of the bright signal to the subendocardium of the infarction region over the three-mo study period. A quantitative measurement of signal intensity (infarction/normal myocardium) fell from 1.81 +/- 0.42 on the initial study to 1.34 +/- 0.37 (p less than 0.05) at a mean of 14 wk. Two patients had an increase in signal intensity on the follow-up study and both patients had been readmitted with acute coronary syndromes. In summary, characterization of changes in signal intensity may provide a useful method of assessing myocardial healing following acute myocardial infarction. Further studies are indicated to determine the prognostic significance of these parameters.     

Homogeneous symplectic structures of second order on loop spaces and symplectic connections

Scientific Industrial Association, All-Union Scientific Research Institute of Physicotechnical and Radiotechnical Measurements. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 25, No. 2, pp. 65–67, April–June, 1991.