The Existence of Zeros of Multivalued Functionals,Coincidence Points,and Fixed Points in $$f$$ -Quasimetric Spaces

Mathematical Notes - The notion of a $$\lambda$$ -generalized-search multivalued functional on an $$f$$ -quasimetric space is introduced. An existence theorem for zeros of such functionals is...     

Mechanism of Interaction of γ-Halogenated Salts of Pyrylium and Benzopyrylium with Aromatic Amines

Stoichiometry and kinetics of reactions of 2,6-diphenyl-4-chloropyrylium, 4-chloroflavylium, 4-bromoflavylium, and 4-iodoflavylium perchlorates with nucleophiles N,N-dimethylaniline and n-phenylenediamine are studied using cyclic voltammetry and spectroscopy. Nucleophilic substitution in these compounds proceeds via the formation of a charge-transfer complex, which converts into a radical ion pair as a result of the electron transfer. Heterolytic clevage of the C–Hal bond occurs at the stage of pyranyl (flavanyl) radical.     

Classification of Two-Dimensional Surfaces with Zero Normal Torsion in Four-Dimensional Spaces of Constant Curvature

We introduce the notion of normal torsion of a surface at a point along a given direction in a Riemannian space. We give a complete classification of surfaces in four-spaces of constant curvature having zero normal torsion.     

Estimates of Petersson's inner squares of cusp forms and arithmetic applications

Uniform estimates are given for Petersson's inner squares of cusp forms in the case of increasing levels and weights. The considered cusp forms are newforms or cusp forms occurring in the theta series associated with positive definite quadratic forms. Arithmetic applications of the obtained estimates are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 168, pp. 158–179, 1988.     

Oxidation of 4-H-selenopyrans

Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, p. 996, July, 1991.     

Applications of the petersson formula for a bilinear form in fourier coefficients of cusp forms

Let S_k(Γ₀(N),χ) be the space of holomorphic Γ₀(N) forms of integral weight k and character χ. Let fj(z), 1≤j≤v _2k ^new (p), be the set of normalized newforms of S_2k(Γ₀(p),1), where p is a prime, and let $L_j (s) = L_{f_i } (s)$ be the L-function of fj(z). It is proved that $$\sum\limits_{1 \leqslant j \leqslant v_{2k}^{new} (p)} {L_j^2 (\tfrac{1}{2}) \ll p\log ^4 p \cdot \log \log p} , p \to \infty$$ where 2k≥4. Errors in an earlier paper (R?Mat, 1989, 4A65) are corrected. Bibliography: 11 titles.     

Distribution of the values of multiplicative functions modulo a prime number

One investigates the distributions of the values of the modified sum of divisors being a real character mod Q, relative to nonzero residue classes mod , 3 being a prime number. One considers in more detail the case of the function 2^–2r₂(n), where r₂(n) is the number of representations of n by a sum of two squares.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 93, pp. 218–224, 1980.     

Integrable billiards model important integrable cases of rigid body dynamics

Abstract—A generalized billiard is considered, in which a point moves on a locally flat surface obtained by isometrically gluing together several plane domains along boundaries being arcs of confocal quadrics. Under this motion, a point moves from one domain to another, passing through the glued boundaries. Many integrable cases of rigid body dynamics with appropriate parameter values at certain levels of integrals are modeled by classical or generalized billiards; in the paper, Liouville equivalence is proved by comparing Fomenko–Zieschang invariants.     

Topological Obstacles to the Realizability of Integrable Hamiltonian Systems by Billiards

Doklady Mathematics - We introduce the following classes of integrable billiards: elementary billiards, topological billiards, billiard books, billiards with a potential, with a magnetic field, and...