Limiting Laws for Entrance Times of Critical Mappings of a Circle

A renormalization group transformation R ₁ has a single stable point in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number (the golden mean). Let a homeomorphism T be the C ¹-conjugate of . We let denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any , the sequence has a finite limiting distribution function , which is continuous in , and singular on the interval [0,1]. We also study the sequence for k>1.     

Coloured Permutations Containing and Avoiding Certain Patterns

Let be the set of all coloured permutations on the symbols 1, 2, . . . , n with colours 1, 2, . . . , r, which is the analogous of the symmetric group when r = 1, and the hyperoctahedral group when r = 2. Let be a subset of d colours; we define to be the set of all coloured permutations . We prove that the number of -avoiding coloured permutations in . We then prove that for any , the number of coloured permutations in which avoid all patterns in except for and contain exactly once equals . Finally, for any , this number equals . These results generalize recent results due to Mansour, Mansour and West, and Simion.AMS Subject Classification: 05A05, 05A15.     

Sharp Conditions for the CLT of Linear Processes in a Hilbert Space

In this paper we study the behavior of sums of a linear process associated to a strictly stationary sequence with values in a real separable Hilbert space and are linear operators from H to H. One of the results is that satisfies the CLT provided are i.i.d. centered having finite second moments and . We shall provide an example which shows that the condition on the operators is essentially sharp. Extensions of this result are given for sequences of weak dependent random variables under minimal conditions.     

Sharp Constants in Inequalities for Intermediate Derivatives (the Gabushin Case)

We solve Tikhomirov's problem on the explicit computation of sharp constants in the Kolmogorov type inequalities

Upper Bounds of the Lebesgue Constants for Fourier–Jacobi Series Summation Methods Defined by a Multiplier Function

Let be the Jacobi polynomials and let C[a,b] be the space of continuous functions on [a,b] with the uniform norm. In this paper, we study sequences of Lebesgue constants, i.e., of the norms of linear operators generated by a multiplier matrix defined by the following relations:

Inequalities of Bernstein type for polynomial splines in L2

For 2-periodic polynomial splines of order r, of minimal defect, with nodes at the points k/n, n , there are established the sharp inequalities

The Maximum Size Of Graphs With A Unique<Emphasis Type="Italic">k</Emphasis>- Factor

For suitable positive integers n and k let m(n, k) denote the maximum number of edges in a graph of order n which has a unique k-factor. In 1964, Hetyei and in 1984, Hendry proved for even n and , respectively. Recently, Johann confirmed the following conjectures of Hendry: for and kn even and for n = 2kq, where q is a positive integer. In this paper we prove for and kn even, and we determine m(n, 3).     

A Limit Result for U-Statistics of Binary Variables

Define , where is a symmetric U-type statistic, H _k() is the Hermite polynomial of degree k, and {X, X _n, n1} are independent identically distributed binary random variables with Pr(X{–1, 1}})=1. We show that according as EX=0 or EX0, respectively.     

Limit theorems for diffusion-type processes inR m

For a sequence of stochastic equations of diffusion type, conditions that are close to necessary and sufficient ones are established for the weak convergence of measures ,n=1, ... , associated with the solutions, to the limiting measure . The conditions under which the weak convergence of the solutions of stochastic equations implies their strong convergence are established as well.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 10, pp. 1371–1378, October, 1993.     

Asymptotic behavior of solutions of A 2nth order nonlinear differential equation

In this paper we prove two results. The first is an extension of the result of G. D. Jones [4[:Every nontrivial solution for

Strictly Cyclic Algebra of Operators Acting on Banach Spaces H p(β)

Let be a sequence of positive numbers and 1 p< . We consider the space H ^p() of all power series such that . We investigate strict cyclicity of the weakly closed algebra generated by the operator of multiplication by zacting on H ^p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra . We also give a necessary condition for a composition operator to be bounded on H ^p() when is strictly cyclic.     

On the embedding of core-free projective images of normal subgroups

Sunto Siano G e due gruppi, : GG una proiettività e N un sottogruppo normale di G. Vengono provati alcuni risultati sulle proprietà di immersions in e G rispettivamente, del gruppi , la chiusura normale di N in modulo il nocciolo di N in , e .

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Supported by a C.N.R. grant.     

Strong law of large numbers for functionals of products of random matrices

For the sequence A₁, A₂, ..., A_n, ... of m×m independent random matrices such that for each k there exists a joint density function P_k(X) of the elements _ij ^k, we prove the following theorem: if and for some positive constants ₁ and ₂, then with probability 1,

Das asymptotische Verhalten der Peanokerne einiger interpolatorischer Quadraturverfahren

Summary Interpolatory quadrature formulae consist in replacing by wherep _f denotes the interpolating polynomial off with respect to a certain knot setX. The remainder may in many cases be written as wherem=n resp. (n+1) forn even and odd, respectively. We determine the asymptotic behaviour of the Peano kernelP _X (t) forn for the quadrature formulae of Filippi, Polya and Clenshaw-Curtis.

     

Kolmogorov-type inequalities for mixed derivatives of functions of many variables

Let = (₁,...,_d) be a vector with positive components and let D be the corresponding mixed derivative (of order _j with respect to the jth variable). In the case where d > 1 and 0 < k < r are arbitrary, we prove that

On the closure of reachable sets for control systems

We prove the existence of a dense subsetD of continuous functions such that, forfD, the reachable set for the control system

On Large Deviations of Vector-Valued Additive Functions of a Markov Gaussian Field

We prove a local limit theorem for large deviations of the sums , where , is a Markov Gaussian random field, is a bounded vector-valued function, and . This paper generalizes the paper [13].     

Global convergence result for conjugate gradient methods

Conjugate gradient optimization algorithms depend on the search directions,

Beckman-Quarles type theorems for mappings from $$ \mathbb{R}^n $$ to $$ \mathbb{C}^n $$

Summary. Let We say that preserves the distance d 0 if for each implies Let A _n denote the set of all positive numbers d such that any map that preserves unit distance preserves also distance d. Let D _n denote the set of all positive numbers d with the property: if and then there exists a finite set S _xy with such that any map that preserves unit distance preserves also the distance between x and y. Obviously, We prove: (1) (2) for n 2 D _n is a dense subset of (2) implies that each mapping f from to (n 2) preserving unit distance preserves all distances, if f is continuous with respect to the product topologies on and      

Iterating the Bar Construction

For a 1-connected space X Adams's bar construction B(C*(X)) describes H*(X) only as a graded module and gives no information about the multiplicative structure. Thus it is not possible to iterate the bar construction in order to determine the cohomology of iterated loop spaces ⁱ X. In this paper for an n-connected pointed space X a sequence of A()-algebra structures , is constructed, such that for each there exists an isomorphism of graded algebras