Analysis and optimization against buckling of beams interacting with elastic foundation

We consider an infinite continuous elastic beam that interacts with linearly elastic foundation and is under compression. The problem of the beam buckling is formulated and analyzed. Then the optimization of beam against buckling is investigated. As a design variable (control function) we take the parameters of cross-section distribution of the beam from the set of periodic functions and transform the original problem of optimization of infinite beam to the corresponding problem defined at the finite interval. All investigations are on the whole founded on the analytical variational approaches and the optimal solutions are studied as a function of problems parameters.     

The diffraction phenomenon in consecutive parametric processes

The manifestation of diffraction effects in two coupled three-frequency collinear processes in the presence of a single intense pump wave in a nonlinear optical crystal with a regular domain structure is considered. A set of three coupled parabolic equations is solved by the Fourier transform method. Attention is focused on the analysis of the functions of image conversion from a signal frequency to a new frequency and to the image gain. It was established that the influence of the subsequent process of image conversion by means of frequency mixing weakly affects the initial process of nondegenerate parametric interaction.     

A study of C60F48 solvates with alkanes by differential scanning calorimetry

The behavior of the C₆₀F₄₈ fluorofullerene—a compound with maximum fluorine content that can be synthesized in pure form through direct fluorination—is investigated in alkane solutions. The kinetics of formation of C₆₀F₄₈ crystal solvates at solid-phase equilibrium with a saturated solution is studied by differential scanning calorimetry (DSC) and thermogravimetry. The composition of the crystal solvates and the temperatures and enthalpies of their decomposition are determined. It is found that the C₆₀F₄₈ solvates formed upon crystallization from saturated solutions of pentane, hexane, and heptane are more stable than the hexagonal solvates (with octane, nonane, decane, and undecane). The latter solvates undergo decomposition into the initial fluorofullerene and liquid hydrocarbon at temperatures below the boiling points of the hydrocarbons.     

Coherent pion production in neutrino and antineutrino interactions on nuclei of heavy freon molecules

Studying the coherent diffractive production of pions in neutrino and antineutrino scattering off the nuclei of freon molecules we have observed for the first time in one experiment all three states of the isospin triplet of the axial part of the weak charged and neutral currents. For the corresponding cross sections we derive $$\begin{array}{*{20}c} {\sigma _{coh}^v (\pi ^ + ) = (106 \pm 16) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ {\sigma _{coh}^{\bar v} (\pi ^ - ) = (113 \pm 35) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}and} \\ {\sigma _{coh}^v (\pi ^0 ) = (52 \pm 19) \cdot 10^{ - 40} {{cm^2 } \mathord{\left/ {\vphantom {{cm^2 } {\left\langle {nucl.} \right\rangle }}} \right. \kern-\nulldelimiterspace} {\left\langle {nucl.} \right\rangle }}} \\ \end{array} $$ . Comparing our data with theoretical predictions based on the standard model of weak interactions we find reasonable agreement. Independently from any model of coherent pion production we determine the isovector axial vector coupling constant to be |β|=0.99±0.20.     

Inclusive study of neutrino and antineutrino interactions with nuclei at energiesE_v^{( - )} \leqq 30 GeV

Neutrino and antineutrino charged current reactions are studied inclusively at energies below 30 GeV using the freon filled bubble chamber SKAT at the Serpukhov accelerator. Data are given for the nucleon structure functions and the differential spectradσ/dy. The results are compared with predictions of the Quark-Parton Model and Quantum Chromodynamics.     

Neutron to proton cross section ratios in neutrino and antineutrino charged current reactions forE ν<30 GeV

Using the freon filled bubble chamber SKAT at the Serpukhov accelerator we study event charge distributions in neutrino and antineutrino charged current reactions in the (anti)neutrino energy region from 3–30 GeV. We derive from the data the total cross section ratios of reactions on neutrons to reactions on protonsR _ν=2.24±0.18 and \(R_{\bar v} = 0.43\) in agreement with the predictions of the quark parton model. These values agree also with other experimental results at different energies. For neutrino reactions we study additionally the differential distributions in Bjorken variablesx andy.     

Affine cross-polytopes inscribed in a convex body

Let X be an affine cross-polytope, i.e., the convex hull of n segments A ₁ B ₁,…, A _n B _n in \mathbbRⁿ {\mathbb{R}^n} that have a common midpoint O and do not lie in a hyperplane. The affine flag F(X) of X is the chain O ∈ L ₁ ⊂⋯ ⊂ L _n = \mathbbRⁿ {\mathbb{R}^n} , where L _k is the k-dimensional affine hull of the segments A ₁ B ₁,…, A _k B _k , k ≤ n. It is proved that each convex body K ⊂ \mathbbRⁿ {\mathbb{R}^n} is circumscribed about an affine cross-polytope X such that the flag F(X) satisfies the following condition for each k ∈{2,…, n}:the (k−1)-planes of support at A _k and B _k to the body L _k ∩ K in the k-plane L _k are parallel to L _k −1.Each such X has volume at least V(K)/2 ^n(n−1)/2. Bibliography: 5 titles.