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A full description of the ring of unitary bordisms with the action of Z_p and of the ring of all admissible collections of fixed submanifolds under the action of Z_p is given in terms of generators and relations. The calculations are based on a special choice of polynomial generators in the ordinary ring of unitary bordisms and Poincaré duality in bordism theory. Bibliography: 3 titles.

This paper studies the question of decomposition of a closed nonorientable two-dimensional manifold of arbitrary genus into maximal connected components (cells), consisting of trajectories which behave "similarly" in the sense of stability of orbits and in the sense of geometrical equivalence. 2 figures. Bibliography: 20 references.

The author shows that in the well-known Radon-Nikodým theorem it is possible to drop the requirement that the space under consideration has σ-finite measure. The author also gives a partial solution to the problem formulated in a somewhat new fashion concerning the representation of a set function as an integral. Bibliography 4 items.

Recently the paper of Homma (Yokohama Math. J. 14 (1966), 47-54; MR 36 #892) which implies the possibility of piecewise linear approximation of piecewise linear manifolds in codimensions higher than two was found to contain an error, so that it is at present unclear whether the proof of this result can be completed using Homma's method. The present paper gives a proof of this result for the case of the elementary manifolds (cells and spheres), thus preserving the validity of two recently proved results whose proof were based on Homma's theorem. The method of proof used in this paper differs from Homma's method and is close to Connell's proof for approximation of stable homeomorphisms (Ann. of Math. (2) 78 (1963), 326-338; MR 27 #4238). Bibliography: 19 items

The paper is a continuation of the author's paper [5] (Math. USSR Sbornik 6 (1968), 97-114). §1 concerns the iterations of a polynomial of degree on a singular set . It is assumed that the critical points of lie either in the domains of attraction of finite attracting cycles or at infinity. The theorems of [5] (Theorem 1 concerning the topological isomorphism of the transformation and of a shift on the space of one-sided -ary sequences with a finite number of identifications; Theorem 2: ) are generalized for the case of a disconnected . In §2 the author investigates the iterations of on the entire plane . He shows (Theorem 3) that the dynamical systems and are topologically isomorphic for sufficiently small in the case of polynomials satisfying one of the hypotheses of §1 and a certain "coarse" condition of "nonconjugacy" of the iterations of distinct critical points. Hypothesis: the set of structurally stable mappings investigated in the paper is everywhere dense in the space of coefficients. Nine figures; bibliography of eight titles.

In this work we construct an open set V in the space of coefficients A_n of the equations dw/dz = P_n(z, w)/Q_n(z, w) such that on the solutions of an arbitrary equation α∊V there exist a countable number of homotopically distinct limit cycles. Also, for each natural number N we construct an open set V_N⊂A_n such that an arbitrary equation α∊V_N has a Petrovskiĭ-Landis genus which exceeds N. Bibliography: 9 items.

I. M. Gel'fand and G. E. Šilov have investigated the action of differential operators of infinite order in spaces of type S. These differential operators were entire functions of a differential operator with constant coefficients, and on the basis of this they constructed an operational method in the problem of uniqueness of the solution of the Cauchy problem. The present work is devoted to the same problem for the case when the coefficients of the differential operator are variable and belong to the set of multiplicators of spaces of type S. Bibliography: 9 titles.

It is known that there do not exist algebraic homomorphisms of the multiplicative group of a field into the additive group . However, if the field has a nontrivial differentiation , then the logarithmic derivative gives a homomorphism , . Ju. I. Manin observed that for abelian varieties over a field with a nontrivial differentiation it is possible to construct homothetic homomorphisms of the group of points into . The study of such homomorphisms (in particular, the computation of the intersection of their kernels) for varieties over function fields permitted Manin to prove the function field analog of Mordell's conjecture. In this paper we introduce and systematically study a class of functions (-functions) encountered in the definition of Manin's map . We study the map in the case of varieties over a field of formal power series. Bibliography: 10 items.

In this paper it is proved that if the rank of the equation over the field does not exceed unity, and if is not divisible by any fourth power and is relatively prime to the discriminant, then, provided that is sufficiently large relative to , the equation does not have more than three positive integer solutions. Bibliography 10 items.