A spiral hollow jet of an ideal liquid

It is assumed in the theory of water outlets that the flow corresponding to the given head is the maximum possible [1] (the principle of maximum flow). The available experimental evidence only qualitatively reproduces the relations between the parameters implied by this principle, whereas numerical calculations agree very satisfactorily [2]. This indicates doubt as to whether the principle is exact. Here Moiseev's method [3] is used to ascertain the meaning of the relationships implied by the principle of maximum flow when used to calculate the potential flow of an ideal liquid in a centrifugal ejector. The resulting formula agrees well with experiment.     

Large deflection of thin plates in cylindrical bending – Non-unique solutions

Considered in this paper is the large deflection of a thin beam. One end of the beam is fixed (clamped) to a rigid wall, while the other end is placed on a flat surface of arbitrary orientation. It is shown that under certain conditions, the solution to the deflected shape of the plate is not unique. Conditions for the existence of multiple solutions are identified. Numerical methodologies are developed to obtain the multiple solutions. Experiments were conducted to verify the numerical predictions. Excellent agreements are found between the predicted deflection and the experimental measurements.     

On best-approximation polynomials in the Hausdorff metric

A definition of the Hausdorff alternance is given. In its terms we give a sufficient condition for an algebraic polynomial to have minimal deviation from a function f in the Hausdorff α-metric. A condition under which a polynomial P_n is the unique best-approximation polynomial for a function f and a necessary condition for P_n to have minimal deviation from f are given. Similar theorems for 2π-periodic functions are formulated. Bibliography: 3 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 130–143.     

Synchrotron radiation of charged particles passing through the boundary between two media

The radiation of charged particles moving in a circle perpendicular to the boundary between two media is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 51–57, May, 1977.     

Determination of the strength of the intramolecular electric field of the NO2 group by the NQR method

Conclusions Comparison of the investigated NQR spectra of the halogen atoms in a series of methane nitro derivatives with the field constants of the halogen atoms makes it possible to estimate the averaged intramolecular electric field created by the NO₂ group.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 769–772, April, 1981.     

Radiation of relativistic electrons in a magnetic undulator

Expressions are obtained for the spectral-angular characteristics of the radiation in two limiting cases: 1 and 1 ( is the angle of deflection of the electron in the field, and is the energy of the electron in units of mc²). It is shown that in the latter case the maximum of the radiation occurs at higher harmonics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 88–91, October, 1973.In conclusion the authors thank Professor A. A. Sokolov for useful discussions.