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1.
In this paper, we continue our investigation on “Extremal problems under dimension constraints” introduced [1]. The general problem we deal with in this paper can be formulated as follows. Let
be an affine plane of dimension k in
. Given
determine or estimate
.Here we consider and solve the problem in the special case where
is a hyperplane in
and the “forbidden set”
. The same problem is considered for the case, where
is a hyperplane passing through the origin, which surprisingly turns out to be more difficult. For this case we have only partial results.AMS Classification: 05C35, 05B30, 52C99 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.
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
4.
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
5.
In this paper we fix a set * of positive elements of the free group
(e. g. the set of finite words occurring in a Markov subshift) as well as n partial isometries on a Hilbert space H. Based on these we define a map S :
which we prove to be a partial representation of
on H under certain conditions studied by Matsumoto.*Supported by Capes. 相似文献
6.
For a class of stable planes we define a notion of isotopy equivalence with
respect to that class and prove that any two planes of a certain class of
-planes comprising all affine
-planes are isotopy equivalent. Furthermore we obtain that all affine
-planes are isotopy equivalent in the class of affine
-planes. Finally we give an example which shows that this approach cannot be easily generalized
to 2-dimensional projective planes, and we outline a different way for a
possible generalization.Received: 27 April 2001 相似文献
7.
Jorge L. Arocha Javier Bracho Chaim Goodman-Strauss Luis Montejano 《Archiv der Mathematik》2006,86(2):185-192
We prove that affine configurations of 4 lines in
are topologically and combinatorially homeomorphic to affine configurations of 6 points in
Received: 14 July 2004; revised: 18 February 2005 相似文献
8.
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
9.
Let F be either or . Consider the standard embedding and the action of GLn(F) on GLn+1(F) by conjugation. We show that any GLn(F)-invariant distribution on GLn+1(F) is invariant with respect to transposition. We prove that this implies that for any irreducible admissible smooth Fréchet
representations π of GLn+1(F) and of GLn(F),
. For p-adic fields those results were proven in [AGRS].
相似文献
10.
11.
Gioconda Moscariello Carlo Sbordone 《Journal of Fixed Point Theory and Applications》2007,1(2):337-350
Let
be a sequence of Borel measurable functions satisfying, for a function
the inequalities
and suppose
Then there exists a sequence of increasing homeomorphisms
converging to a homeomorphism
weakly in
and locally uniformly, such that
Dedicated to the memory of Jean Leray 相似文献
13.
B. Bouchard 《Journal of Theoretical Probability》2005,18(2):439-467
Motivated by applications in financial mathematics, Ref. 3 showed that, although
fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of
: if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extended by Ref. 1 in the multidimensional case, replacing
by a closed convex cone K of [0, )d, and by Ref. 12 who provided a conditional version in the unidimensional case. In this paper, we show that the conditional bipolar theorem of Ref. 12 can be extended to the multidimensional case. Using a decomposition result obtained in Ref. 3 and Ref. 1, we also remove the boundedness assumption of Ref. 12 in the one dimensional case and provide less restrictive assumptions in the multidimensional case. These assumptions are completely removed in the case of polyhedral cones K. 相似文献
14.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
15.
Violeta Petkova 《Archiv der Mathematik》2005,84(4):311-324
Let
be a weighted space with weight . In this paper we show that for every Wiener-Hopf operator T on
and for every a I, there exists a function
such that
for all
Here (g)a denotes the function x g(x)eax for
and
where R+ is the spectral radius of the shift S : f(x) f(x–1) on
while
is the spectral radius of the backward shift S–1 : f(x) (P+f)(x+1) on
Moreover, there exists a constant C, depending on , such that
for every a I. If R– < R+, we prove that there exists a bounded holomorphic function v on
such that for
the function va is the restriction of v on the line
Received: 18 May 2004 相似文献
16.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献
17.
George M. Bergman 《Algebra Universalis》2005,53(2-3):357-395
Properties of several sorts of lattices of convex subsets of
are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of
and the lattice of all convex subsets of
The lattices of arbitrary, of open bounded, and of compact convex sets in
all satisfy the same identities, but the last of these is join-semidistributive, while for n > 1 the first two are not. The lattice of relatively convex subsets of a fixed set
satisfies some, but in general not all of the identities of the lattice of “genuine” convex subsets of
To the memory of Ivan RivalReceived April 22, 2003; accepted in final form February 16, 2005.This revised version was published online in August 2005 with a corrected cover date. 相似文献
18.
Hans Cuypers 《Designs, Codes and Cryptography》2005,34(2-3):333-337
In this note we prove the uniqueness of the tight spherical 7-design in
consisting of 4600 vectors and with automorphism group 2 × Co2 as well as the uniqueness of the tight spherical 5-design in
on 112 vectors and with automorphism group 2 × Sp6(2).To the memory of Jaap Seidel 相似文献
19.
T. R. Riley 《Geometriae Dedicata》2005,113(1):215-229
We give a nondeterministic algorithm that expresses elements of
, for N ≥ 3, as words in a finite set of generators, with the length of these words at most a constant times the word metric. We show that the nondeterministic time-complexity of the subtractive version of Euclid’s algorithm for finding the greatest common divisor of N ≥ 3 integers a1, ..., aN is at most a constant times
. This leads to an elementary proof that for N ≥ 3 the word metric in
is biLipschitz equivalent to the logarithm of the matrix norm – an instance of a theorem of Mozes, Lubotzky and Raghunathan. And we show constructively that there exists K>0 such that for all N ≥ 3 and primes p, the diameter of the Cayley graph of
with respect to the generating set
is at most
.Mathematics Subject Classification: 20F05 相似文献
20.
A finite group whose irreducible complex characters are rational is called a
-group. In this paper we will find the structure of Frobenius
-groups.Received: 14 April 2003 相似文献