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1.
J. E. Marcos 《Czechoslovak Mathematical Journal》2003,53(3):689-706
We define various ring sequential convergences on
and
. We describe their properties and properties of their convergence completions. In particular, we define a convergence
on
by means of a nonprincipal ultrafilter on the positive prime numbers such that the underlying set of the completion is the ultraproduct of the prime finite fields
Further, we show that
is sequentially precompact but fails to be strongly sequentially precompact; this solves a problem posed by D. Dikranjan. 相似文献
2.
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
相似文献
3.
We consider type II codes over finite rings
. It is well-known that their gth complete weight enumerator polynomials are invariant under the action of a certain finite subgroup of
, which we denote Hk,g. We show that the invariant ring with respect to Hk,g is generated by such polynomials. This is carried out by using some closely related results concerning theta series and Siegel modular forms with respect to
. 相似文献
4.
We study self-dual codes over the rings
and
. We define various weights and weight enumerators over these rings and describe the groups of invariants for each weight enumerator over the rings. We examine the torsion codes over these rings to describe the structure of self-dual codes. Finally we classify self-dual codes of small lengths over
. 相似文献
5.
We show that for a
-action Ψ being the Kronecker sum of a symbolic strictly ergodic
-actionT and a Chacon
-actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a
-action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a
-action with rankr and spectral multiplicitym. 相似文献
6.
We study two questions posed by Johnson, Lindenstrauss, Preiss, and
Schechtman, concerning the structure of level sets of uniform and Lipschitz
quotient mappings from
. We show that if
, is a uniform quotient mapping then for every
has
a bounded number of components, each component of
separates
and the upper bound of the number of components depends
only on
and the moduli of co-uniform and uniform continuity of
.Next we prove that all level sets of any co-Lipschitz uniformly
continuous mapping from
to
are locally connected, and we show
that for every pair of a constant
and a function
with
, there exists a natural number
, so that
for every co-Lipschitz uniformly continuous map
with a
co-Lipschitz constant
and a modulus of uniform continuity
, there
exists a natural number
and a finite set
with
card
so that for all
has exactly
components,
has exactly
components and
each component of
is homeomorphic with the real line and
separates the plane into exactly 2 components. The number and form
of components of
for
are also described - they have a
finite tree structure. 相似文献
7.
With the help of some new results about weight enumerators of self-dual codes over
we investigate a class of double circulant codes over
, one of which leads to an extremal even unimodular 40–dimensional lattice. It is conjectured that there should be Nine more constructions of the Leech lattice 相似文献
8.
Let
be realhomogeneous functions in
ofdegree
and let bethe Borel measure on
given by
where dx denotes theLebesgue measure on
and > 0. Let T
be the convolution operator
and let
Assume that, for x 0, the followingtwo conditions hold:
vanishes only at h = 0 and
. In this paper we show that if
then E
is the empty set and if
then E
is the closed segment withendpoints
and
. Also, we give some examples. 相似文献
9.
We characterize weakly self-dual bases of the field extension
over
, examine the existence of weakly self-dual polynomial bases, and use duality to analyze normal basis multiplication. 相似文献
10.
P. C. Craighero R. Gattazzo M. C. Ronconi 《Annali di Matematica Pura ed Applicata》1981,129(1):81-130
Summary In this paper we classify the algebraic cubic surfaces of the affine space
is the complex field, whose algebraic curves are set-theoretic complete intersections of ; in other words surfaces such that every prime ideal of height 1in the coordinate ring [] of is the radical of a principal ideal; if is non singular in codimension 1this means that [] is semifactorial. We give the equations of such surfaces within linear isomorphisms of
providing also methods by which one can construct the equations of the surfaces cutting on its curves as set-theoretic complete intersections. Moreover for each of these surfaces we determine the minimum positive number such that every algebraic curve of with multiplicity of intersection , is complete intersection of itself with another surface
§ 8where the results are summarized). We tackle also the problem of such a classification over algebraically closed fields k different from .
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
Lavoro eseguito nell'ambito del G.N.S.A.G.A. del C.N.R. 相似文献
11.
We present new results on the exponential dichotomy on the entire axis of linear differential equations in
. 相似文献
12.
Gonzalo Perera 《Journal of Theoretical Probability》1997,10(3):581-603
We study the asymptotic distribution of
where A is a subset of
, A
N
= A[–N, N]
d
, v(A) = lim
N
card(A
N) (2N+1)
–d
(0, 1) and X is a stationary weakly dependent random field. We show that the geometry of A has a relevant influence on the problem. More specifically, S
N(A, X) is asymptotically normal for each X that satisfies certain mixting hypotheses if and only if
has a limit F(n; A) as N for each
. We also study the class of sets A that satisfy this condition. 相似文献
13.
Milan Kučera 《Czechoslovak Mathematical Journal》2000,50(2):225-244
A bifurcation problem for variational inequalities
,
is studied, where K is a closed convex cone in
, 3, B
is a × matrix, G is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case. 相似文献
14.
The generating line of the first single shift plane (cf. [11, p. 435]) is a 2-surface of
4 which we call the the affine part
of Knarr's surface. We compute all affinities leaving
invariant. After embedding
4 into PG(4,
) we calculate the uniquely determined projective closure
Kn
of
. Using a suitable projection we transform questions on Knarr's surface to questions on Cayley's surface in PG(3,
). In this way we determine all planes carrying 1-dimensional algebraic varieties of
Kn
. We exhibit all automorphic collineations of
Kn
. 相似文献
15.
We show that ifP
, |P|=d+k,dk1 andO int convP, then there exists a simplexS of dimension
with vertices inP, satisfyingO rel intS, the bound being sharp. We give an upper bound for the minimal number of vertices of facets of a (j-1)-neighbourly convex polytope in
withv vertices.Research (partially) supported by Hung. Nat. Found. for Sci. Research, grant no. 1817Research (partially) supported by Hung. Nat. Found. for Sci. Research, grant no. 326-0213 相似文献
16.
In this paper, we characterize the dynamic of every Abelian subgroups
of
,
or
. We show that there exists a
-invariant, dense open set U in
saturated by minimal orbits with
a union of at most n
-invariant vector subspaces of
of dimension n−1 or n−2 over
. As a consequence,
has height at most n and in particular it admits a minimal set in
.
This work is supported by the research unit: systèmes dynamiques et combinatoire: 99UR15-15 相似文献
17.
Richard Urzúa Luz 《Bulletin of the Brazilian Mathematical Society》2003,34(2):287-302
Let a minimal affine
-action on the torus
T
q
,
p 2 and
q 1. The cohomology of
(see definition below) depends on both the algebraic properties
of the induced action on H
1(T
q
,
) and the arithmetical
properties of the translation cocycle. We give a Diophantine
condition that characterizes those affine actions whose first
cohomology group is finite dimensional. In this case it is
necessarily isomorphic to
. Thus the
-action
F
obtained by suspension of is parameter
rigid, i.e., any other
-action with the same
orbit foliation is smoothly conjugate to a reparametrization of
F
by
an automorphism of
.*Partially supported by CNPq fellowship by Fondecyt Grant
1000047 and DGICT-UCN and fundación Andes, Chile. 相似文献
18.
D. M. Smirnov 《Algebra and Logic》2005,44(2):109-116
Let be the set of all primes,
the field of all algebraic numbers, and Z the set of square-free natural numbers. We consider partially ordered sets of interpretability types such as
, and
, where AD is a variety of -divisible Abelian groups with unique taking of the pth root p(x) for every p ,
is a variety of
-modules over a normal field
, contained in
, and Gn is a variety of n-groupoids defined by a cyclic permutation (12 ...n). We prove that
, and
are distributive lattices, with
and
where
ub and
ubf are lattices (w.r.t. inclusion) of all subsets of the set and of finite subsets of , respectively.Deceased.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 198–210, March–April, 2005. 相似文献
19.
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]. 相似文献
20.
Damjan Kobal 《K-Theory》1999,17(2):113-140
The goal of this paper is to present a new view on the link between the well known K-theory of finitely generated projective modules and much less understood K-theory of Hermitian forms on finitely generated projective modules.For a given Hermitian ring (R, , ), we obtain the K-theory space KR equipped with an involution and the Hermitian K-theory space KHerm(R, , ). The fixed subspace
2 is homotopy equivalent to the Hermitian K-theory space KHerm(R,, , ). We construct the Karoubi Tower diagram, which is obtained by iterating Karoubi's construction of the homotopy fibers of the forgetful and hyperbolic maps. Using an interesting factorization of these maps, we prove various homotopy properties of the Karoubi Tower. The homotopy inverse limit of the Karoubi Tower is homotopy equivalent to the homotopy fibre of the inclusion of the fixed set
2 into the homotopy fixed set
h
2. Considering Karoubi's fundamental periodicity theorem, the Karoubi Tower generalizes the low dimensional connections between Hermitian K-theory and K-theory groups. Illustrative examples of the Karoubi Tower are given by the finite field case and the classical Hermitian rings over
,
and
. Considering topological K-theory for these cases, the Karoubi Tower comprises the classical Bott periodicity.Another important application of the Karoubi Tower is an elegant and comprehensive generalization of the classical invariants of quadratic forms. 相似文献