共查询到20条相似文献,搜索用时 15 毫秒
1.
Massimo Giulietti 《Combinatorica》2009,29(1):19-25
All sets of lines providing a partition of the set of internal points to a conic C in PG(2,q), q odd, are determined. There exist only three such linesets up to projectivities, namely the set of all non-tangent lines to
C through an external point to C, the set of all non-tangent lines to C through a point in C, and, for square q, the set of all non-tangent lines to C belonging to a Baer subplane PG(2,√q) with √q+1 common points with C. This classification theorem is the analogous of a classical result by Segre and Korchmáros [9] characterizing
the pencil of lines through an internal point to C as the unique set of lines, up to projectivities, which provides a partition
of the set of all non-internal points to C. However, the proof is not analogous, since it does not rely on the famous Lemma
of Tangents of Segre which was the main ingredient in [9]. The main tools in the present paper are certain partitions in conics
of the set of all internal points to C, together with some recent combinatorial characterizations of blocking sets of non-secant
lines, see [2], and of blocking sets of external lines, see [1]. 相似文献
2.
The concept of a tight set of points of a generalised quadrangle was introduced by S. E. Payne in 1987, and that of an m-ovoid of a generalised quadrangle was introduced by J. A. Thas in 1989, and we unify these two concepts by defining intriguing sets of points. We prove that every intriguing set of points in a generalised quadrangle is an m-ovoid or a tight set, and we state an intersection result concerning these objects. In the classical generalised quadrangles,
we construct new m-ovoids and tight sets. In particular, we construct m-ovoids of W(3,q), q odd, for all even m; we construct (q+1)/2-ovoids of W(3,q) for q odd; and we give a lower bound on m for m-ovoids of H(4,q
2). 相似文献
3.
We derive some formulas for the Carlitz q-Fibonacci polynomials Fn(t) which reduce to the finite version of the Rogers-Ramanujan identities obtained by I. Schur for t = 1. Our starting point is a representation of the q-Fibonacci polynomials as the weight of certain lattice paths in
contained in a strip along the x-axis. We give an elementary combinatorial proof by using only the principle of inclusion-exclusion and some standard facts from q-analysis. 相似文献
4.
Li Fenggao 《高校应用数学学报(英文版)》2003,18(2):223-229
Let AG(n, F
q) be the n-dimensional affine space over F
q, where F
q is a finite field with q elements. Denote by Γ
(m) the graph induced by m-flats of AG(n, F
q). For any two adjacent vertices E and F of
is studied. In particular, sizes of maximal cliques in Γ
(m) are determined and it is shown that Γ
(m) is not edge-regular when m<n−1.
Supported by the National Natural Science Foundation of China (19571024) and Hunan Provincial Department of Education (02C512). 相似文献
5.
We investigate R-bounded representations
, where X is a Banach space and G is a lca group. Observing that Ψ induces a (strongly continuous) group homomorphism
, we are then able to analyze certain classical homomorphisms U (e.g. translations in Lp (G)) from the viewpoint of R-boundedness and the theory of scalar-type spectral operators.
Dedicated to the memory of H. H. Schaefer 相似文献
6.
We determine all point-sets of minimum size in PG(2,q), q odd that meet every external line to a conic in PG(2,q). The proof uses a result on the linear system of polynomials vanishing at every internal point to the conic and a corollary
to the classification theorem of all subgroups of PGL(2,q).
* Research supported by the Italian Ministry MURST, Strutture geometriche, combinatoria e loro applicazioni and by the Hungarian-Italian
Intergovernemental project “Algebraic and Geometric Structures”. 相似文献
7.
Given
, a compact abelian group G and a function
, we identify the maximal (i.e. optimal) domain of the convolution
operator
(as an operator from Lp(G) to itself). This is the
largest Banach function space (with order continuous norm) into which Lp(G)
is embedded and to which
has a continuous extension, still with values
in Lp(G). Of course, the optimal domain depends on p and g. Whereas
is compact, this is not always so for the extension of
to its optimal domain.
Several characterizations of precisely when this is the case are presented. 相似文献
8.
Rémi Arcangéli María Cruz López de Silanes Juan José Torrens 《Numerische Mathematik》2007,107(2):181-211
Given a function f on a bounded open subset Ω of with a Lipschitz-continuous boundary, we obtain a Sobolev bound involving the values of f at finitely many points of . This result improves previous ones due to Narcowich et al. (Math Comp 74, 743–763, 2005), and Wendland and Rieger (Numer
Math 101, 643–662, 2005). We then apply the Sobolev bound to derive error estimates for interpolating and smoothing (m, s)-splines. In the case of smoothing, noisy data as well as exact data are considered. 相似文献
9.
Consider the set of all proper edge-colourings of a graph G with n colours. Among all such colourings, the minimum length of a longest two-coloured cycle is denoted L(n, G). The problem of understanding L(n, G) was posed by Häggkvist in 1978 and, specifically, L(n, K n,n ) has received recent attention. Here we construct, for each prime power q ≥ 8, an edge-colouring of K n,n with n colours having all two-coloured cycles of length ≤ 2q 2, for integers n in a set of density 1 ? 3/(q ? 1). One consequence is that L(n, K n,n ) is bounded above by a polylogarithmic function of n, whereas the best known general upper bound was previously 2n ? 4. 相似文献
10.
Anna de Mier 《Combinatorica》2007,27(6):699-720
We give a correspondence between graphs with a given degree sequence and fillings of Ferrers diagrams by nonnegative integers
with prescribed row and column sums. In this setting, k-crossings and k-nestings of the graph become occurrences of the identity and the antiidentity matrices in the filling. We use this to show
the equality of the numbers of k-noncrossing and k-nonnesting graphs with a given degree sequence. This generalizes the analogous result for matchings and partition graphs
of Chen, Deng, Du, Stanley, and Yan, and extends results of Klazar to k > 2. Moreover, this correspondence reinforces the links recently discovered by Krattenthaler between fillings of diagrams
and the results of Chen et al. 相似文献
11.
A weighted norm inequality for the Marcinkiewicz integral operator
is proved when belongs to
. We also give the weighted
Lp-boundedness for a class of Marcinkiewicz integral operators with rough
kernels
and
related to the Littlewood-Paley
-function and the
area integral S, respectively. 相似文献
12.
We introduce the concept of Lp-maximal regularity for second order Cauchy problems. We prove Lp-maximal regularity for an abstract model problem and we apply the abstract results to prove existence, uniqueness and regularity
of solutions for nonlinear wave equations.
The author acknowledges with thanks the support provided by the Department ofApplied Analysis, University of Ulm, and the
travel grants provided by NBMH India and MSF Delhi, India. 相似文献
13.
In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an
(x(q + 1), x; 2, q)-minihyper, with x ≤ q
2 − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q
2 − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers. 相似文献
14.
We prove that for a fixed integer s2 every K
s,s
-free graph of average degree at least r contains a K
p
minor where
. A well-known conjecture on the existence of dense K
s,s
-free graphs would imply that the value of the exponent is best possible. Our result implies Hadwigers conjecture for K
s,s
-free graphs whose chromatic number is sufficiently large compared with s. 相似文献
15.
16.
Ding Shifeng 《高校应用数学学报(英文版)》2003,18(3):343-351
Let G be a block-primitive automorphism group of a 2-(v,k,1) design. If G is isomorphic to PSL (3,q) where q is odd, then G is also point-primitive.
Supported by the National Natural Science Foundation of China (10171089). 相似文献
17.
A geometrical interpretation of the G-structures associated to elastic material bodies is given. In addition, characterizations of their integrability are obtained. Since the lack of integrability is a geometrical measure of the lack of homogeneity, the corresponding inhomogeneity conditions are obtained. 相似文献
18.
We show that any pointwise multiplier for BMO(ℝn) generates a function p from the class (ℝn) of those functions for which the Hardy-Littlewood maximal operator is bounded on the variable Lp space. In particular, this gives a positive answer to Diening's conjecture saying that there are discontinuous functions
which nevertheless belong to (ℝn). 相似文献
19.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
20.
In this paper we show that if X is an s-distance set in
m
and X is on
p concentric spheres then
Moreover if
X is antipodal, then
. 相似文献