共查询到20条相似文献，搜索用时 15 毫秒
1.
Abstract. Given a set A and a function , we study the set of all functions that are continuous for all topologies for which f continuous.
We prove that in a sense to be made precise in the text, for any essentially infinitary function f , any non-constant such g equals f
n
, for some n∈ N. We also prove a similar result for the clone of n -ary functions from . 相似文献
2.
Abstract. Let be a semidirect product of semitopological semigroups S and T . If S and T act on topological spaces X and Y , respectively, then under suitable conditions there is a natural action of on X × Y . In this paper we characterize the almost periodic and strongly almost periodic compactification of the flow , in terms of related compactifications of (S,X) and (T,Y) . 相似文献
3.
Abstract. We prove that the best way to reduce the volume of the n -dimensional unit cube by a linear transformation that maps each of the main vertices to a point within distance ɛ < from is to shorten all edges by a factor (1-ɛ) . In particular, the minimal volume of such an almost cubic parallelepiped is (1-ɛ)
n
. This problem naturally arises in the construction of lattice-based one-way functions with worst-case / average-case connection. 相似文献
4.
Abstract. This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat
equation (with Dirichlet boundary conditions in the bounded domain D
⊂ R
d
and multiplicative noise):
and for the corresponding backward dual equation:
We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward
equation.
\par 相似文献
5.
Abstract. Weakly left ample semigroups are a class of semigroups that are (2,1) -subalgebras of semigroups of partial transformations, where the unary operation takes a transformation α to the identity map in the domain of α . It is known that there is a class of proper weakly left ample semigroups whose structure is determined by unipotent monoids acting on semilattices or categories. In
this paper we show that for every finite weakly left ample semigroup S , there is a finite proper weakly left ample semigroup and an onto morphism from to S which separates idempotents. In fact, is actually a (2,1) -subalgebra of a symmetric inverse semigroup, that is, it is a left ample semigroup (formerly, left type A). 相似文献
6.
A classical inequality for Euler’s gamma function states that
for all and with . We prove the following extension of this result. Let be the weighted power mean of of order r. The inequality
holds for all and with if and only if
(Received 3 April 2000; in revised form 26 June 2000) 相似文献
7.
Abstract. We show how to maintain the width of a set of n planar points subject to insertions and deletions of points in amortized time per update. Previously, no fully dynamic algorithm with a guaranteed sublinear time bound was known. 相似文献
8.
It is well known that the recurrence relations
are periodic, in the sense that they define periodic sequences for all choices of the initial data, and lead to sequences
with periods 2, 5 and 8, respectively. In this paper we determine all periodic recursions of the form
where are complex numbers, are non-zero and . We find that, apart from the three recursions listed above, only
lead to periodic sequences (with periods 6 and 8). The non-periodicity of (R) when (or and ) depends on the connection between (R) and the recurrence relations
and
We investigate these recursions together with the related
Each of (A), (B), and (C) leads to periodic sequences if k = 1 (with periods 6, 5, and 9, respectively). Also, for k = 2, (B) leads to periodicity with period 8. However, no other cases give rise to periodicity. We also prove that every real
sequence satisfying any of (A), (B), and (C) must be bounded. As a consequence, we find that for an arbitrary k, every rational sequence satisfying any of (A), (B), and (C) must be periodic.
(Received 27 June 2000; in revised form 5 January 2001) 相似文献
9.
For any irrational , let denote the regular continued fraction expansion of x and define f, for all z > 0 by and by J. G ALAMBOS proved that (μ the Gauss measure) In this paper, we first point out that for all , ( has no limit for for almost all , proving more precisely that: For all , one has for almost all 相似文献
10.
One of the classical problem in computational biology is the character compatibility problem or perfect phylogeny problem. A standard formulation of this problem in terms of two closely related questions is the following. Given a data set consisting
of a finite set X and a set
of partitions induced on X by a set of characters. Is
compatible, that is, does there exist an evolutionary tree that represents (in a well-defined sense) the data? If this is the case,
is this tree unique? A fundamental result in phylogenetics states that the answer to the former of the two questions is yes
precisely if the partition intersection graph
associated to
can be made chordal by obeying a certain rule.
The main insight from this paper is that the relation graph
associated to a set
of partitions may provide a key for deciding whether such a chordalization of
exists. To prove our results, we introduce an extension of the concept of the partition intersection graph associated to
using
.
Received August 27, 2004 相似文献
12.
Abstract. We study the existence of a holomorphic generalized solution u of the PDE
where f is a given holomorphic generalized function and .
(Received 4 December 2000; in revised form 9 May 2001) 相似文献
13.
Let and be the von Mangoldt function and M?bius function, respectively, x real and y“small” compared with x. This paper gives, for the first time, a non-trivial estimate of the sum for all whenever . Correspondingly, it is also proved that 相似文献
14.
Abstract. Subdivision with finitely supported masks is an efficient method to create discrete multiscale representations of smooth
surfaces for CAGD applications. Recently a new subdivision scheme for triangular meshes, called - subdivision , has been studied. In comparison to dyadic subdivision, which is based on the dilation matrix 2I , -subdivision is based on a dilation M with det M=3 . This has certain advantages, for example, a slower growth for the number of control points.
This paper concerns the problem of achieving maximal sum rule orders for stationary -subdivision schemes with given mask support, which is important because the sum rule order characterizes the order of the
polynomial reproduction, and provides an upper bound on the Sobolev smoothness of the surface. We study both interpolating
and approximating schemes for a natural family of symmetric mask support sets related to squares of sidelength 2n in Z
2
, and obtain exact formulas for the maximal sum rule order for arbitrary n . For approximating schemes, the solution is simple, and schemes with maximal sum rule order are realized by an explicit
family of schemes based on repeated averaging [15].
In the interpolating case, we use properties of multivariate Lagrange polynomial interpolation to prove the existence of
interpolating schemes with maximal sum rule orders. These can be found by solving a linear system which can be reduced in
size by using symmetries. From this, we construct some new examples of smooth ( C
2
,C
3
) interpolating -subdivision schemes with maximal sum rule order and symmetric masks. The construction of associated dual schemes is also
discussed. 相似文献
15.
Let ? be a class of real valued integrable functions on [0,1). We will call a strictly increasing sequence of natural numbers
an sequence if for every f in ? we have
almost everywhere with respect to Lebesgue measure. Here, for a real number y we have used to denote the fractional part of y. For a finite set A we use to denote its cardinality. In this paper we show that for strictly increasing sequences of natural numbers and , both of which are sequences for all , if there exists such that
then the sequence of products of pairs of elements in a and b once ordered by size is also an sequence.
(Received 2 March 2000; in revised form 3 January 2001) 相似文献
16.
We obtain new exact inequalities of the form for functions defined on the axis R or the semiaxis R
+ in the case where for functions defined on the axis R in the case where and for functions of constant sign on R or R
+ in the case where and in the case where .
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 3, pp. 291–302, March, 2006. 相似文献
17.
We establish a new bound for the exponential sum
where λ is an element of the residue ring modulo a large prime number
and
are arbitrary subsets of the residue ring modulo p − 1 and γ ( n) are any complex numbers with | γ ( n)| ≦ 1.
Received: 15 June 2005 相似文献
18.
For a real number x let be the fractional part of x and for any set M let c
M
be the characteristic function of M. For and a positive integer N let
be the discrepancy of the sequence modulo 1. In this paper we prove that 相似文献
19.
For a real number x let be the fractional part of x and for any set M let c
M
be the characteristic function of M. For and a positive integer N let
be the discrepancy of the sequence modulo 1. In this paper we prove that
(Received 2 May 2000; in revised form 19 June 2000) 相似文献
20.
Abstract. Given an m × n rectangular mesh, its adjacency matrix A , having only integer entries, may be interpreted as a map between vector spaces over an arbitrary field K . We describe the kernel of A : it is a direct sum of two natural subspaces whose dimensions are equal to and , where c = gcd (m+1,n+1) - 1 . We show that there are bases to both vector spaces, with entries equal to 0,1 and -1 . When K = Z/(2), the kernel elements of these subspaces are described by rectangular tilings of a special kind. As a corollary, we count
the number of tilings of a rectangle of integer sides with a specified set of tiles. 相似文献
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