Structural features and transport processes of superionic conductors based on tin(II) fluoride

The thermal behavior and transport properties of lead(II) tetrafluorostannate(II) have been investigated by impedance spectroscopy,¹⁹F NMR and high hydrostatic pressure techniques. It is shown that these experimental methods are powerful tools to clarify ionic transport processes in the investigated solid electrolytes with predominant fluorine mobility. Paper presented at the 3rd Euroconference on Solid State Ionics, Teulada, Sardinia, Italy, Sept. 15–22, 1996     

Influence of hydrostatic pressure on the lifetimes of polymers

Under uniaxial tension, the lifetimes of polymers under hydrostatic pressure are longer than under atmospheric pressure. This effect is attributed to a change in the failure mechanism under pressure owing to retardation of the free-radical chain reaction of breakage of the macromolecules under omnidirectional compression.A. F. Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 207–213, March–April, 1976.     

Splitting the Pasch axiom

On the basis of the theory ^– of Pasch-free 2-dimensional geometry, Pasch's axiom is shown to be equivalent to the conjunction of the following two axioms: In any right triangle the hypotenuse is greater than the leg and If AOB is right, B lies between O and C, and D is the footpoint of the perpendicular from B to AC, then the segment OA is greater than the segment BD. This represents an attempt to split the Pasch axiom with respect to ^–. Only the question whether the second of the above two axioms is really weaker than Pasch's axiom, remains open.     

Common supports as fixed points

A family S of sets in R ^d is sundered if for each way of choosing a point from rd+1 members of S, the chosen points form the vertex-set of an (r–1)-simplex. Bisztriczky proved that for each sundered family S of d convex bodies in R ^d , and for each partition (S , S ), of S, there are exactly two hyperplanes each of which supports all the members of S and separates the members of S from the members of S . This note provides an alternate proof by obtaining each of the desired supports as (in effect) a fixed point of a continuous self-mapping of the cartesian product of the bodies.     

Exact theory of the (Einstein) gravitational field in an arbitrary background space-time

The Lagrangian based theory of the gravitational field and its sources at the arbitrary background space-time is developed. The equations of motion and the energy-momentum tensor of the gravitational field are derived by applying the variational principle. The gauge symmetries of the theory and the associated conservation laws are investigated. Some properties of the energymomentum tensor of the gravitational field are described in detail and the examples of its application are given. The desire to have the total energymomentum tensor as a source for the linear part of the gravitational field leads to the universal coupling of gravity with other fields (as well as to the self-interaction) and finally to the Einstein theory.     

Intensity measurement for Kβ η satellites in the radiative auger effect

Calculations have been performed on the integral shapes of the K lines, which are long-wave satellites of the K ₁ lines, for Cl, Ti, and Fe, where allowance has been made for interference between states in the 2p^–1 and 3p^–2p configurations. The calculations show that these satellites represent short-wave branches of the K lines strengthened by the 3p-1s transition with simultaneous M electron ejection. The strong interference between the amplitudes of these processes in the final state means that it is in principle quite impossible to speak of the intensities of the K satellites without stating how they are isolated from the measured spectrum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 34–39, September, 1984.