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.     

Points cônes du mouvement brownien plan,le cas critique

Summary LetB=(B _t,t0) be a planar Brownian motion and let >0. For anyt0, the pointz=B _t is called a one-sided cone point with angle if there exist >0 and a wedgeW(,z) with vertexz and angle such thatB _sW(,z) for everys[t, t+]. Burdzy and Shimura have shown independently that one-sided cone points with angle exist when >/2 but not when      

Kollineationen und Schliessungssätze für Ebene Faserungen

Every affine central collineation of a translation plane induces a special collineation of the projective space spanned by the spreadF belonging to . Here the relations between these special collineations of and certain incidence propositions inF are investigated; so new proofs are given for some characterisations of (A,B)-regular spreads included in [7].     

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.     

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.     

Finite presentability of Steinberg groups over group rings

LetA be a finitely generated commutative -algebra with Krull dimensiond, and let be an arbitrary finite group. It is proved that the Steinberg groupSt _n (A) is finitely presented whenevern4. If, in addition,nd+3, andK ₁ (A) andK ₂ (A) are finitely generated, thenE _n (A) andGL _n (A) are finitely presented.The Project supported by National Natural Science Foundation of China.     

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, }.     

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.     

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.     

Some <Emphasis Type="Italic">L</Emphasis>-Function of a Regular Covering of a Graph

Let ₁:KH, ₂:HG and ₂₁:KG be three finite regular coverings of graphs, and let be a representation of the covering transformation group of ₁. We show that the (Bartholdi type) L-function of G associated to the representation of the covering transformation group of ₂₁ induced from is equal to that of H associated to by means of ordinary voltage assignments.Acknowledgments. We would like to thank the referee for many valuable comments and suggestions. This is partially supported by Grant-in-Aid for Science Research (C).Final version received: February 16, 2004     

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.     

Über Gruppen von Homöomorphismen Seifertscher Faserräume und Flacher Mannigfaltigkeiten

Let M be a compact manifold and A a finite subgroup of the outer automorphism group Out ₁(M) of ₁(M). A necessary condition for realising A by an isomorphic group of homeomorphisms of M is the existence of an extension to the abstract kernel (A, ₁(M), : AOut ₁(M)). If the center of ₁(M) is nontrivial this condition need not be fulfilled. We show however, that we can find a finite group B with a normal abelian subgroup C with B/CA, and such that there exists an extension to the abstract kernel (B, ₁(M), : BAOut ₁(M)). In the case of Seifert fiber spaces or flat Riemannian manifolds B can be ralized by an isomorphic group of homeomorphisms of M.     

Criterion for π-supersolvability for finite groups

It is proved that the class of finite -supersolvable groups is precisely the class of all finite -solvable groups with the following property: For each maximal subgroup M of a -solvable group G with index p for some p , there exists a cyclic subgroup S of order p ( ) such that G = MS and S commutes with each element of the Sylow system _M of the subgroup M.Translated from Matematicheskie Zametki, vol. 52, No. 1, pp. 57–61, July, 1992.     

On the properties of ε(≥0) optimal policies in discounted unbounded return model

This paper investigates the properties of (0) optimal policies in the model of [2]. It is shown that, if * = ( ₀ ^* , ₁ ^* ,..., _n ^* , _n ^+1/* , ...) is a-discounted optimal policy, then ( ₀ ^* , ₁ ^* , ..., _n ^* ) for alln0 is also a-discounted optimal policy. Under some condition we prove that stochastic stationary policy _n ^* corresponding to the decision rule _n ^* is also optimal for the same discounting factor. We have also shown that for each-optimal stochastic stationary policy ₀ ^* , ₀ ^* can be decomposed into several decision rules to which the corresponding stationary policies are also-optimal separately; and conversely, a proper convex combination of these decision rules is identified with the former ₀ ^* . We have further proved that for any (,)-optimal policy, say *=( ₀ ^* , ₁ ^* , ..., _n ^* , _n ^+1/* , ...), _n–1 ^* ) is ((1– ⁿ )^–1 e, ) optimal forn>0. At the end of this paper we mention that the results about convex combinations and decompositions of optimal policies of § 4 in [1] can be extended to our case.Project supported by the Science Fund of the Chinese Academy of Sciences.     

Bildgarben und Fasercohomologie für Relativ Analytische Räume

Let : XY be a relative analytic space and an _X module. The object of this paper is to collect some results on the connection between the fibre cohomology groups Hⁱ(X(y),(y)) and the direct image sheaves Rⁱ _*. This generalizes results of Kodaira-Spencer and Grauert-Riemen-schneider giving a unified approach based on the methods of [9].     

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.     

A generalization of a theorem of M. Riesz to the case of functions of several variables

The following theorem was proved by M. Riesz: Iff(x) L(–,),f(x) 0 and the conjugate functionf (x) is also integrable on [-, ], thenf(x) L log⁺L. The analog of this theorem for functions of several variables is established.Translated from Matematicheskie Zametki, Vol. 4, No. 3, pp. 269–280, November, 1968.     

The Parametric Buffer Phenomenon for a Singularly Perturbed Telegraph Equation with a Pendulum Nonlinearity

We consider the boundary-value problem u _tt + u _t + (1 + cos2)sin u =² u _xx, u _x|_x=0=u_x|_x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number.     

Character coordinates and annihilators of cyclotomic numbers

The object of this paper is a representation theoretical approach to the problem of determining allQ-linear relations between conjugate numbers in a cyclotomic field. We apply our method to relations between the numbers cot^(m)(k/n), tan^(m)(k/n), cosec^(m)(2k/n), sec^(m)(2k/n), respectively, where m is0 and (k,n)=1. Thereby we complete previous work of Chowla, Hasse, Jager-Lenstra, and others.