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1.
Constructions are given of different kinds of flats in the projective space $PG(9,2)={\mathbb P}(\wedge^{2}V(5,2))$ which are external to the Grassmannian ${\cal G}_{\bf 1,4,2}$ of lines of PG(4,2). In particular it is shown that there exist precisely two GL(5,2)-orbits of external 4-flats, each with stabilizer group ?31:5. (No 5-flat is external.) For each k=1,2,3, two distinct kinds of external k-flats are simply constructed out of certain partial spreads in PG(4,2) of size k+2. A third kind of external plane, with stabilizer ?23:(7:3), is also shown to exist. With the aid of a certain ‘key counting lemma’, it is proved that the foregoing amounts to a complete classification of external flats. 相似文献
2.
Two non desarguesian flag transitive planes of order 34 whose Kernel is GF(3) are constructed. These planes are distinct from the planes of the same order contained in the class constructed by Narayana Rao M. L. (Proceedings of American Mathematical Society 39 (1973) 51–56) and Ebert, G.L. and Baker, R. (Enumeration of two dimensional Flag-Transitive planes, Algebras, Groups and Geometries 3 (1985) 248–257). The Flag Transitive group modulo the scalar collineations of these planes is generated by two elements and is of order 328. 相似文献
3.
Klaus Metsch 《Journal of Geometry》2007,86(1-2):154-164
The following result is well-known for finite projective spaces. The smallest cardinality of a set of points of PG(n, q) with the property that every s-subspace has a point in the set is (q
n+1-s
- 1)/(q - 1). We solve in finite projective spaces PG(n, q) the following problem. Given integers s and b with 0 ≤ s ≤ n - 1 and 1 ≤ b ≤ (q
n+1-s
- 1)/(q - 1), what is the smallest number of s-subspaces that must miss a set of b points. If d is the smallest integer such that b ≤ (q
d+1 - 1)/(q - 1), then we shall see that the smallest number is obtained only when the b points generate a subspace of dimension d. We then also determine the smallest number of s-subspaces that must miss a set of b points of PG(n, q) which do not lie together in a subspace of dimension d. The results are obtained by geometrical and combinatorial arguments that rely on a strong algebraic result for projective
planes by T. Szőnyi and Z. Weiner. 相似文献
4.
Let be a compact hypersurface in bounding a convex set with non-empty interior. In this paper it is proved that there always exist at least n geometrically distinct closed characteristics on if is symmetric with respect to the origin.
Received: 18 May 1999 / Published online: 4 April 2002 相似文献
5.
Let be a mapping in the Sobolev space . We assume that the cofactors of the differential matrix Df(x) belong to . Then, among other things, we prove that the Jacobian determinant detDf lies in the Hardy space .
Received: 20 November 2000 / Revised version: 17 December 2001 / Published online: 5 September 2002
Iwaniec was supported by NSF grant DMS-0070807. This research was done while Onninen was visiting Mathematics Department at
Syracuse University. He wishes to thank SU for the support and hospitality. 相似文献
6.
In this paper we introduce and analyze the notion of self-dual
k-sets of type (m, n).
We show that in a non-square order projective space such sets exist
only if the dimension is odd. We prove that, in a projective space of odd dimension
and order q, self-dual
k-sets of type (m, n), with
, are of elliptic and hyperbolic
type, respectively. As a corollary we obtain a new characterization of the
non-singular elliptic and hyperbolic quadrics. 相似文献
7.
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
8.
Joseph Zaks 《Journal of Geometry》2005,82(1-2):195-203
Benz proved that every mapping
that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping
that preserves the distances 1 and
is an isometry, provided d ≥ 5. 相似文献
9.
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
10.
In this paper we characterize the family of external lines to a hyperbolic quadric of PG
(3, q). 相似文献
11.
Yurii G. Leonov 《Journal of Mathematical Sciences》2011,179(2):290-299
A wreath product of the type
\mathbbZ2 \wr G {\mathbb{Z}_2} \wr G is considered for any finite 2-group G. The monomorphism of such a group in the well-known Kaloujnine group P
2,m
is studied for a suitable natural m. 相似文献
12.
We partition the affine plane of order 7 into a set of M?bius-Kantor configurations 83 plus a set consisting only of one point. 相似文献
13.
Jennie Danielsson 《Journal of Geometry》2008,88(1-2):15-18
A general construction of minimal blocking sets of size 2p – 3, where p is a prime and p ≡ 1 (mod 4), p > 5, and of size 2p – 2, where p is a prime and p ≡ 3 (mod 4), p > 5 in PG(2, p) is presented. These blocking sets are all of Rédei type.
相似文献
14.
In this paper the classification of the (n, 3)-arcs in PG(2, 7) is presented. It has been obtained using
a computer-based exhaustive search that exploits projective equivalence and produces exactly one representative of each equivalence class. For each (n, 3)-arc, the automorphism group and the maximal size of a contained
k-arc have been found. 相似文献
15.
Minerva Cordero 《Journal of Geometry》2005,83(1-2):5-9
In this article we determine the number of non-isomorphic semifield planes of order p4 and kernel GF(p2) for p prime, 3 ≤ p ≤ 11. We show that for each of these values of p, the plane is either desarguesian, p-primitive, or a generalized twisted field plane. We also show that the class of p-primitive planes is the largest. We also discuss the autotopism group of the semifields under study. 相似文献
16.
Saharon Shelah 《Mathematical Logic Quarterly》2011,57(4):341-365
We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of ${\mathbb N}$ such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of ${\mathbb N}$ such that expanding ${\mathbb N}$ by any uncountably many of them suffice. Also we find arithmetically closed ${\mathcal A}$ with no ultrafilter on it with suitable definability demand (related to being Ramsey). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
17.
18.
Given a finite subset
of an additive group
such as
or
, we are interested in efficient covering of
by translates of
, and efficient packing of translates of
in
. A set
provides a covering if the translates
with
cover
(i.e., their union is
), and the covering will be efficient if
has small density in
. On the other hand, a set
will provide a packing if the translated sets
with
are mutually disjoint, and the packing is efficient if
has large density.
In the present part (I) we will derive some facts on these concepts when
, and give estimates for the minimal covering densities and maximal packing densities of finite sets
. In part (II) we will again deal with
, and study the behaviour of such densities under linear transformations. In part (III) we will turn to
.
Authors’ address: Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395,
USA
The first author was partially supported by NSF DMS 0074531. 相似文献
19.
In this paper, the irreducible p, q‐representations of the Lie algebras $\mathcal {G}(0,1)$ and $\mathcal {G}(0,0)$ are discussed. We prove two theorems that classify certain irreducible p, q‐representations of these Lie algebras and construct their one variable models in terms of p, q‐derivative and dilation operators. As an application, we derive a p, q‐special function identity based on one such model. 相似文献
20.
Tatsuya Maruta 《Geometriae Dedicata》1995,54(3):263-266
Existence and uniqueness of pseudo-cyclic [q
2+1,q
2–3, 4]-codes over GF(q) are proved. Elliptic quadrics are characterized as those (q
2+1)-caps in PG(3,q) whose corresponding [q
2+1,q
2–3, 4]-codes are pseudo-cyclic. 相似文献