Comparison of two-dimensional polynomials

A necessary and sufficient condition for comparison with a weight of two-dimensional polynomials is obtained.     

Comparison of polynomials and almost hypoellipticity

The paper investigates the hypoellipticity of polynomials in terms of comparisons.     

Method for investigation of parameters of X-ray beams diffracted from a single crystal in the presence of temperature gradient

A method for investigation of the parameters of X-ray beams pumped from the transmission direction into the reflection one depending on the value of applied temperature gradient is proposed. An increase in the integral intensity of diffracted X-ray beam is due to both the overthrowing effect inside the Darwin table and an increase in the angular width of beam. It is shown that it is possible to determine to a high accuracy the value of temperature gradient, beginning with which the angular width of the pumped X-ray beam increases.     

Effects of scanning speed on the laser beam profile measurements by vibrating wire

For measuring laser beam profiles, a vibrating wire monitor (VWM) has been introduced. The measurements were carried out at different speeds of scan. Preliminary estimates were made for the calculation of the VWM response times with respect to the thermal losses along the wire, and radiative and convective losses. These estimates, however, do not determine the difference between the beam profile and the frequency response of the VWM for a given scan rate. To evaluate the reliability of the frequency response of the VWM, comparisons between forward and reverse beam scans at different speeds have been used. The results of these scans are used to correct the thermal inertia in the frequency response of the VWM.     

Photochemistry of unsaturated lactones. 2. Photoannelation of 2-acetyl-3,4,4-trimethyl-2-buten-4-olide by terminal alkynes

The photochemical cycloaddition of 2-acetyl-3,4,4-trimethyl-2-buten-4-olide to 1-heptyne and 1-chloro-2-propyne was carried out. The reaction gives isomeric cycloadducts of the head to head and head to tail types. The influence of solvent on the directivity of the reaction was investigated. The possibility was shown of using the cycloadducts obtained in the synthesis of difficulty available polyfunctionally substituted butanolides and heterocyclic compounds containing a spirocyclobutene fragment.For Communication 1, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1315–1320, October, 1986.     

Study of angular width of an X-ray beam fully pumped from quartz single crystal in the presence of temperature gradient

We investigate the cross section of transmitted X-ray beam diffracted by reflecting atomic planes (10–11) of a SiO₂ single crystal in Laue geometry for different values of temperature gradient applied to the crystal. It is shown that the angular width of a fully pumped X-ray beam depends on the distance between the source and the studied sample and decreases with the increase in this distance.