Some mildly wild circles in Sn arising from algebraic K-Theory

We study wild embeddings of S ¹ in S ⁿ which are tame in a sense introduced by Quinn. We show that if is a finitely presented group with H ₁()=H ₂()=0, then any finiteness obstruction K ₀() can be realized on the complement of such an embedded S ¹. We also realize trivially symmetric K _–1() obstructions on the complements of such embeddings. For trivially symmetric , the embeddings constructed are shown to be isotopy homogeneous.     

The arithmetic of the characteristic Pólya functions

In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup of convex characteristic functions on the semiaxis (0,). Letn ()={:₁¦₁1 or ₁=}, and I_o()={: ₁¦ ₁ N()}. The following results are proved: 1) The semigroup is almost delphic in the sense of R. Davidson. 2) N() is a set of the type G which is dense in (in the topology of uniform convergence on compacta). 3) The class I_o() contains only the function identically equal to one.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 717–725, May, 1977.The author thanks I. V. Ostrovskii for the formulation of the problem and valuable remarks.     

Mappings that preserve cones in Lobachevskii space

Let ⁿ be n-dimensional Lobachevskii space, and {l_x:x ⁿ} be a family of lines, parallel to a linel ₀, 0ⁿ (in a given direction). Let {c_x:Xⁿ} be a family of circular cones in ⁿ of opening with axes l_X and vertex X. Then, iff:ⁿⁿ(n>2) is a bijective mapping andf(C_x)=C _f(x), it follows thatf is a motion in the space ⁿ.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973.     

Almost π-Lattices

In this paper we establish some conditions for an almost -domain to be a -domain. Next -lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for -rings.     

Nielsensche Realisierungssätze für Seifertfaserungen

Let M be a closed aspherical manifold and A a finite subgroup of the outer automorphism group Out ₁M of ₁M. A necessary (and in many cases also sufficient) condition for realising A by the induced action of an isomorphic group of homeomorphisms of M is the existence of an extension 1₁MEA1 to the abstract kernel (A,₁M, AOut ₁M). If the center of ₁M is nontrivial, this condition need not be fulfilled ([14]). We showed in [25] however that one can always find a surjection BA of a finite group B with abelian kernel such that there exists an extension to the abstract kernel (B,₁M,BAOut₁M), and one can try to realize B instead of A. The main result of the present paper is a characterisation of all such groups B (for a given A) which can be realized by a group of homeomorphisms. The class of manifolds considered here consists of certain Seifert fiber spaces in arbitrary dimensions but the main result is purely algebraic and can be applied to other classes of manifolds, for example to flat Riemannian manifolds.     

Nonlinear instability of superposed magnetic fluids in the presence of an oblique magnetic field

The nonlinear evolution of interfacial waves separating two magnetic fluids subjected to an oblique magnetic field is studied in two dimensions, with the use of the method of multiple scales. It is shown that the evolution of the envelope is governed by two partial differential equations. These equations can be combined to yield two alternate Schrödinger equations with cubic nonlinearity; one of them leads to the determination of the cutoff wave number separating stable from unstable deformations while the other Schrödinger equation is used to analyze the stability of the system. The stability of the system is discussed both theoretically and computationally, and the stability diagrams are obtained. It is found in the linear theory that the oblique magnetic field has a stabilizing influence if 0 ₁ + ₂ < /2, or 3/2 < ₁ + ₂ 2 and a destabilizing influence if /2 < ₁ + ₂ < 3/2, where 0 _j , (j=1, 2) and , is the angle between the field and the horizontal axis.In the nonlinear theory, the stability analysis reveals that there exist different regions of stability and instability. It is reported that the oblique magnetic field plays a dual role in the stability criterion and the angles ₁ and ₂ play a distinctive role in this analysis besides the effect of the variation of the magnetic permeabilities.     

227-01227-01227-01-property and normal subgroups

Summary D-property (=set of primes) in finite groups is not in general inherited by subgroups. In this paper, as evidence in favor of the following conjecture (F. Gross): (o) If a finite group G satisfies D then its normal subgroups satisfy D-property as well. the Author shows that if the D and the D-properties (=set of the primes not in ) hold together in a finite group G, then both are inherited by the normal subgroups of G. As a corollary, the characterization of the groups satisfying both the properties D and D is given in terms of the composition factors.     

On π-Solvable and Locally π-Solvable Groups with Factorization

We prove that, in a locally -solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow - and p-subgroups A , A _p and B , B _p , p , of the subgroups A and B, respectively, such that A B is a Sylow -subgroup of the group G and, for an arbitrary nonempty set ,

Generating alternating permutations lexicographically

A permutation _{1 2} ... _n is alternating if ₁<₂>₃<₄ .... We present a constant average-time algorithm for generating all alternating permutations in lexicographic order. Ranking and unranking algorithms are also derived.Research supported by the Natural Sciences and Engineering Research Council of Canada under grant A3379.     

Spatial dynamics of time periodic solutions for the Ginzburg-Landau equation

We consider the dynamics of the Ginzburg-Landau equation in a small neighborhood of a known pulse solution by studying a Poincaré map,P: _{T T} , where _T is a section which is transverse to the pulse. Due to the fact that the Ginzburg-Landau equation possesses both a rotational symmetry and a spatial symmetry, we are able to conduct a detailed analytical study of this map in neighborhoods arbitrarily close to the pulse solution. Thus, we are able to complement the work of Holmes [8], who conducted an analytical study of the Poincaré map in a punctured neighborhood of the pulse. We find that the Poincaré map contains an invariant set _itT, where is not necessarily a Cantor set of points, such thatP: is homeomorphic to a shift map on (at least) two symbols. Furthermore, we find that for eachm 1 the mapP _itm possesses a fixed point. Since is not necessarily a Cantor set, this is not immediately clear. Finally, we find that when the pulse solution is broken, for eachm1 there exist parameter values such that pulses possessingm maxima appear.On leave at the University of Utah during 1993/94. Supported by the DFG, Habilitationsstipendium Ma 1587/1-1.     

Square Integrable Representations,von Neumann Algebras and An Application to Gabor Analysis

Let G be a locally compact group, and let be a lattice in G. Let (, H ) be an irreducible, square integrable unitary representation of G. Then the restriction of to extends to VN(), the von Neumann algebra generated by the regular representation of . We determine the center valued (or extended) von Neumann dimension of H as a VN()-module. This result is extended to representations which are square integrable modulo the center of G. An explicit formula is given when G is a semisimple algebraic group and when G is a nilpotent Lie group. As an application, we study the question of the existence of frames for the discretized windowed Fourier transform.     

Transposition generation of alternating permutations

A permutation _{1 2}... _n is alternating if ₁< ₂> ₃< ₄.... Alternating permutations are counted by the Euler numbers. Here we show that alternating permutations can be listed so that successive permutations differ by a transposition, ifn is odd. Extensions and open problems are mentioned.Research supported by the Natural Sciences and Engineering Research Council of Canada under grant A3379.     

Über gemeinsame Lote Windschiefer geraden in elliptischen Räumen

Let the following motions in a projective elliptic space(K,) be called normal forms:Subspace-reflections, rotations, the product of a rotation and a point-reflection whose center lies on the axis of the rotation and the product of two rotations, whose axes of rotation are conjugated.It is shown that all motions of(K, ) have a normal-form provided any two lines of(K, ) have a common perpendicular. The latter is true if and only if K is Pythagorean and if the polarity can be represented by the unit-matrix.     

Range of the posterior probability of an interval for priors with unimodality preserving contaminations

Range of the posterior probability of an interval over the -contamination class ={=(1–)₀+q:qQ} is derived. Here, ₀ is the elicited prior which is assumed unimodal, is the amount of uncertainty in ₀, andQ is the set of all probability densitiesq for which =(1–)₀+q is unimodal with the same mode as that of ₀. We show that the sup (resp. inf) of the posterior probability of an interval is attained by a prior which is equal to (1–)₀ except in one interval (resp. two disjoint intervals) where it is constant.     

Ein beweis des Grauertschen bildgarbensatzes nach ideen von B. Malgrange

In 1960, H. Grauert proved the following coherence theorem [2]: Let X, Y be complex spaces and : X Y a proper holomorphic map. Then, for every coherent analytic sheaf J on X, all direct image sheaves Rⁿ*J are coherent. We give a new proof of this theorem, based on ideas of B. Malgrange. This proof does not use induction on the dimension of the base space Y and can be generalized to relative-analytic spaces X Y where Y belongs to a bigger category of ringed spaces, which contains in particular all complex spaces and differentiable manifolds.     

Waterman classes and triangular sums of double Fourier series

Let ^a ={nln^a (n+1)}, where a R. The following results are established: For every &fnof ^a BV ((- ]²), the triangular partial sums of its Fourier series are uniformly bounded if a = -1, and converge everywhere if a < -1.For every a>0, there exists &fnof ^a BV ((- ]²) such that the triangular partial sums of its Fourier series are unbounded at the point (0;0).     

Une application de Corps des Normes

Let k be a perfect field of characteristic p > 0, K₀ = Frac(W(k)), a uniformizer in K₀ and _n K ₀ (n N) such that ₀ = and _n+1 ^p = _n. We write K = _nN K₀ (_n), H = Gal (K₀/ K and G = Gal(K₀/ K₀). The main result of this paper is that the functor restriction of the Galois action from the category of crystalline representations of G with Hodge–Tate weights in an interval of length p - 2 to the category of p-adic representations of H is fully faithful and its essential image is stable by sub-object and quotient. The proof uses the comparison between two ways of building mod. p representations of H: one thanks to the norm field of K, the other thanks to some categories of filtered modules with divided powers previously introduced by the author.     

The Number of Isomorphism Classes of Finite Groups with Given Element Orders

Let G be a finite group and _e(G) the set of element orders of G. Denote by h( _e(G)) the number of isomorphism classes of finite groups H satisfying _e(H) = _e(G). We prove that if G has at least three prime graph components, then h( _e (G)){1, }.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20