A Kinematic Formula for Affine Diameters and Affine Medians of a Convex Set

For a planar convex set K with C ²-smooth boundary, the area of the set of the points lying on a given number of affine diameters of K is estimated. As a corollary, it is proved that the area of K is at most pM² /4\pi M^2 /4 , where M is the largest length of a chord of K halving the area of K. Bibliography: 2 titles.     

Knaster's problem on continuous maps of a sphere into Euclidean space

A survey of known results and additional new ones on Knaster's problem: on the standard sphere S^n–1Rⁿ find configurations of points A₁, , A_k, such that for any continuous map fS^n–1R^m one can find a rotation a of the sphere S^n–1 such that f(a(A₁)==f(a(A_k)) and some problems closely connected with it. We study the connection of Knaster's problem with equivariant mappings, with Dvoretsky's theorem on the existence of an almost spherical section of a multidimensional convex body, and we also study the set {a S0(n)f(a(A₁))==f(a(A_k))} of solutions of Knaster's problem for a fixed configuration of points A₁, , A_kS^n–1 and a map fS^n–1R^m in general position. Unsolved problems are posed.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 167, pp. 169–178, 1987.     

Quasielastic nucleon and hyperon production by neutrinos and antineutrinos with energies below 30 GeV

The cross sections of neutrino and antineutrino quasielastic reactions \(vn \to \mu ^ - p,\bar vp \to \mu ^ + n,\bar vp \to \mu ^ + \Lambda\) were studied in the neutrino energy range between 3 and 30 GeV. In comparison withV-A theory axial mass parameters ofM _A =(1.06±0.05±0.14) GeV/c² from neutrino andM _A =(0.71±0.10±0.20) GeV/c² from antineutrino data were found. The total cross-section for the hyperon production process can be described byM _A =1.0 GeV/c².     

Final results on μe-pair production in neutrino interactions in the SKAT freon bubble chamber experiment

We present the final results from the search for μe pairs produced in neutrino interactions using the freon filled bubble chamber SKAT. The rate of μ^? e ⁺ pairs to charged current events above the charm threshold is \(R_{\mu ^ - e^ + } = (4.8 \pm 1.1)10^{ - 3} \) . Assuming charm particle production to be the origin of the positron we calculate \(R_{\Lambda _c^ + } = (6.2 \pm 3.1)10^{ - 2} \) andR _D =(2.8±0.9)10^?2. We observe no considerable μ^? e ^? pair production above the background. In the regionE _v >3 GeV,p _μ,e >1.0 GeV/c andp _μ>p _e we find with a 90% confidence level the limit \(R_{\mu ^ - e^ - }< 1.7 10^{ - 4} \) .     

Fluorine absorption spectra and some fluorides in condensed state

The absorption spectra of liquid F₂, NF₃, N₂F₄, CF₄, BF₃, NF₃, SF₆ have been obtained at diminished temperatures in the near ultra-violet region of the spectrum. It is shown that the absorption spectrum does not differ from the spectra in the gaseous phase, therefore the elementary absorption act is characterized by the cross section of photon absorption by an individual molecule. The absorption cross sections of the above mentioned molecules are represented in the liquid phase, which do not differ strongly from absorption cross sections of these molecules in the gaseous phase. The dependence of the absorption cross sections of liquid fluorine on its concentrations in solutions with N₂, Ar, NF₃, O₂ at - 196°C has been studied. The cross sections of photon absorption by the fluoride molecule in different liquid media with small fluorine concentrations have been obtained.     

Properties of multiplicity distributions in νA and\bar v A intersections atE_{\begin{array}{*{20}c} {( - )} \\ v \\ \end{array} }< 30GeV

We present data on the multiplicity structure of inclusive charged hadron production in charged current neutrino and antineutrino freon interactions in the energy range 3–30 GeV resulting from an experiment with the bubble chamber SKAT. Average multiplicities, dispersions and correlation coefficients are investigated. Furthermore, KNO-scaling is studied and average net charges are calculated in different kinematical regions. Our data are compared with results from \(\begin{array}{*{20}c} {( - )} \\ v \\ \end{array} \) -interactions on an isoscalar target of “free” nucleons to study the influence of nuclear effects.     

A New Method to Study the Structure of NMR Signals Detected with the Aid of Modulation Procedure

Technical Physics - A need to study the structure of the NMR signals detected with the aid of the modulation method is substantiated. Specific features of the detection of the NMR signals using the...     

Parallelepipeds and centrally symmetric hexagonal prisms circumscribed about a three-dimensional centrally symmetric convex body

Let K be a three-dimensional centrally symmetric compact convex set of unit volume. It is proved that K is contained in a centrally symmetric hexagonal prism (or a parallelepiped) of volume 4