Дано новое доказательство теоремы Понселе о бицентрических многоугольниках, основанное на обобщении понятия ортоцентра для $n$-угольника. Отмечены некоторые свойства бицентрических многоугольников и найдены обобщения формулы Эйлера, связывающей радиусы вписанной и описанной окружностей и расстояние между их центрами для выпуклых $n$-угольников при $n=4, 5, 6$, а также для невыпуклого пятиугольника. В заключение рассматривается конструкция из трех связанных между собой бицентрических пятиугольников. Библиография: 6 названий.
This paper describes a class of convex compact sets K in C(n) having the following uniqueness property: K is the unique support of every analytic functional for which it is a support.
For any odd number n greater-than-or-equal-to 1003, the authors construct an infinite 2-generator group each of whose proper subgroups is contained in a cyclic subgroup of order n . This result strengthens analogous results of Ol'shanskii for prime n > 10(75) and Atabekyan and Ivanov for odd n > 10(80). The proof is carried out in the original language of Novikov-Adyan theory. Bibliography: 6 titles.
It is shown that there exists a Levi-flat surface in C2 with boundary on a given two-dimensional sphere that lies in the boundary of a strictly pseudoconvex domain and is totally real everywhere except at a finite number of elliptic and hyperbolic points.
Generators and relations of the groups of birational automorphisms are described for six classes of (k-minimal) rational surfaces. For surfaces F with rho := rk Pic F = 2, d := K(F)2 = 3, 4 and rho = 1 , F(k) = phi, d = 9 relations between the already known generators are described, and for surfaces with rho = 1 , F(k) = phi , d = 8, 6 and rho = 2, F(k) = phi, d = 8 generators and relations are described.
The traditional method for constructing criteria for completeness with respect to reducibility is by describing the property of (in general, weakened) productiveness satisfied by the complement of a set which is complete with respect to the given reducibility. Originally this property was tied to the reducibility of a creative set to the complete set. Such a method appeals directly to the universality of the creative set in the class of all recursively enumerable sets.However, for several reducibilities it is possible to determine the completeness of a recursively enumerable set from the fact that a certain set of degree below the degree of the creative sets is reducible to the given set. This second, "test" set is, of course, not recursively enumerable. In addition, in place of the property of effective nonrecursive enumerability which productive sets have, it is possible to substitute variants of the property of diagonal nonrecursiveness, although not for all reducibilities.In this paper we examine the connection between these two approaches-specifically, between different weakenings of the property of productiveness on the one hand, and diagonal nonrecursiveness on the other-and we present results obtained by these methods for Turing and truth-table reducibilities.
A proof is given for the theorem of Novikov and the author on the existence of a closed nonselfintersecting extremal for a single-valued functional corresponding to the motion of a charged particle in a strong magnetic field on a Riemannian manifold homeomorphic to the 2-sphere, and an analogue in the case of multivalued functionals is also proved.
This paper strengthens a theorem due to A. Dold on the algebraic properties of sequences of integers which are Lefschetz numbers of the iterates of a continuous map from a finite polyhedron to itself. The realizability of sequences satisfying Dold's condition at a single fixed point of a continuous map on R3 is proved. Indices of a fixed point (under iteration) are investigated in the case of a smooth mapping. A linear lower bound on the number of periodic points of a smooth map, which strengthens a result of Shub and Sullivan, is obtained.
A general (not necessarily local) boundary value problem is considered for an elliptic l x l system on the plane of nth order containing only leading terms with constant coefficients. By a method of function theory developed for elliptic s x s systems of first order partial derivative PSI/partial derivative y - J partial derivative PSI/partial derivative x = 0 with a constant triangular matrix J = (J(ij))1s, Im J(ii) > 0 ; this problem is reduced to an equivalent system of integrofunctional equations on the boundary. In particular, a criterion that the problem be Noetherian and a formula for its index are obtained in this way. All considerations are carried out in the smooth case when the boundary of the domain has no corner points, while the boundary operators act in spaces of continuous functions.
A solution of a parabolic equation without an initial condition is determined in terms of the right side in a semi-infinite cylinder. It is assumed that the coefficients of the equation do not depend on time. An estimate of the solution is given in terms of the right side of the equation, which estimate contains a weighted exponential function of time.
Under suitable conditions countable solvability of the problem -u(tt) + DELTA-u - g(u, r, t) = h(r, t) in B(pi), u(x, t) = u(x, t + T), T > 0, u(partial derivative B(pi), t) = 0, where B(pi) subset-of R(N) is a ball of radius pi, is proved.
The author discusses classes of periodic functions of variables that are either piecewise monotonic or piecewise monotonic in the sense of Hardy, and clarifies the connections, for such functions, between the property of belonging to space, , and the convergence of series of their trigonometric Fourier coefficients, We establish the existence, when 1$ SRC=http://ej.iop.org/images/0025-5726/39/3/A02/tex_im_2240_img5.gif/>, of certain results that differ from the one-dimensional case.
The author constructs mappings between bundles on an elliptic surface and bundles on an elliptic surface that has been modified by a logarithmic transformation. These mappings are applied to the study of the moduli varieties of bundles with c1 = 0 on elliptic surfaces.
An algorithm is found that decides, for an arbitrary system of semigroup identities, whether the orders of the finite semigroups satisfying the system are bounded by a function (or a recursive function) of the number of generators.
This paper introduces a new method of representing pseudo-Boolean algebras by implication structures of a special type or by partially ordered sets. This is used to construct four sequences of pseudo-Boolean algebras. Their properties and the properties of the logics prescribed by the sequences are studied. The connection between these logics and the logic consisting of the realizable propositional formulas is established, and a problem posed by Hosoi and Ono is solved.
New classes of Heun's functions that are eigenfunctions of a two-parameter spectral problem with boundary conditions at singular points of Heun's equation are introduced. The asymptotics of the spectrum and of Heun's functions are studied.
