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1.
An intriguing set of points of a generalised quadrangle was introduced in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] as a unification of the pre-existing notions of tight set and m-ovoid. It was shown in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] that every intriguing set of points in a finite generalised quadrangle is a tight set or an m-ovoid (for some m). Moreover, it was shown that an m-ovoid and an i-tight set of a common generalised quadrangle intersect in mi points. These results yielded new proofs of old results, and in this paper, we study the natural analogue of intriguing sets in finite polar spaces of higher rank. In particular, we use the techniques developed in this paper to give an alternative proof of a result of Thas [J.A. Thas, Ovoids and spreads of finite classical polar spaces, Geom. Dedicata 10 (1-4) (1981) 135-143] that there are no ovoids of H(2r,q2), Q−(2r+1,q), and W(2r−1,q) for r>2. We also strengthen a result of Drudge on the non-existence of tight sets in W(2r−1,q), H(2r+1,q2), and Q+(2r+1,q), and we give a new proof of a result of De Winter, Luyckx, and Thas [S. De Winter, J.A. Thas, SPG-reguli satisfying the polar property and a new semipartial geometry, Des. Codes Cryptogr. 32 (1-3) (2004) 153-166; D. Luyckx, m-Systems of finite classical polar spaces, PhD thesis, The University of Ghent, 2002] that an m-system of W(4m+3,q) or Q−(4m+3,q) is a pseudo-ovoid of the ambient projective space. 相似文献
2.
We introduce new classes of sets called Λ
g
-closed sets and Λ
g
-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λ
g
-closed sets and Λ
g
-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.
Dedicated to Professor Maximilian Ganster on the occasion of his 50th birthday 相似文献
3.
We show that every -tight set of a Hermitian polar spaces , , is the union of disjoint generators of the polar space provided that . This was known before only when . This result is a contribution to the conjecture that the smallest -tight set of that is not a union of disjoint generators occurs for and is for sufficiently large an embedded subgeometry. 相似文献
4.
K. T. Arasu Yu Qing Chen J. F. Dillon Xiaoyu Liu Kevin J. Player 《Designs, Codes and Cryptography》2007,44(1-3):307-319
We show that difference sets satisfying the condition n|λ have a product property which can be exploited to construct more difference sets. Many of the newly discovered difference
sets arise in precisely this way.
Dedicated to Dan Hughes on the occasion of his 80th birthday. 相似文献
5.
Jan De Beule Patrick Govaerts Anja Hallez Leo Storme 《Designs, Codes and Cryptography》2009,50(2):187-201
Minihypers are substructures of projective spaces introduced to study linear codes meeting the Griesmer bound. Recently, many
results in finite geometry were obtained by applying characterization results on minihypers (De Beule et al. 16:342–349, 2008;
Govaerts and Storme 4:279–286, 2004; Govaerts et al. 28:659–672, 2002). In this paper, using characterization results on certain
minihypers, we present new results on tight sets in classical finite polar spaces and weighted m-covers, and on weighted m-ovoids of classical finite generalized quadrangles. The link with minihypers gives us characterization results of i-tight sets in terms of generators and Baer subgeometries contained in the Hermitian and symplectic polar spaces, and in terms
of generators for the quadratic polar spaces. We also present extendability results on partial weighted m-ovoids and partial weighted m-covers, having small deficiency, to weighted m-covers and weighted m-ovoids of classical finite generalized quadrangles. As a particular application, we prove in an alternative way the extendability
of 53-, 54-, and 55-caps of PG(5,3), contained in a non-singular elliptic quadric Q−(5,3), to 56-caps contained in this elliptic quadric Q−(5,3).
相似文献
6.
Characterizations of γ-open sets and locally γ-regular sets are given. We generalize some already established results and answer an open question by giving a characterization
to γ-quasi-open sets.
相似文献
7.
Let F be any field. Let p(F) be the characteristic of F if F is not of characteristic zero, and let p(F)=+∞ otherwise. Let A1,…,An be finite nonempty subsets of F, and let with k{1,2,3,…}, a1,…,anF{0} and degg<k. We show that When kn and |Ai|i for i=1,…,n, we also have consequently, if nk then for any finite subset A of F we have In the case n>k, we propose a further conjecture which extends the Erdős–Heilbronn conjecture in a new direction. 相似文献
8.
O. El-Fallah K. Kellay T. Ransford 《Journal of Mathematical Analysis and Applications》2010,372(2):565-573
We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques. 相似文献
9.
R. Sh. Omanadze 《Mathematical Notes》1997,62(3):356-359
The notions of effectively subcreative set and strongly effectively acceleratable set are introduced. It is proved that the
notions of effectively subcreative set, strongly effectively acceleratable set, andsQ-complete recursively enumerable set are equivalent.
Translated fromMatematicheskie Zametki, Vol. 62, No. 3, pp. 425–429, September, 1997.
Translated by V. N. Dubrovsky 相似文献
10.
K. Y. Al-Zoubi 《Acta Mathematica Hungarica》2008,118(1-2):75-83
A space (X, T) is called I-Lindelöf [1] if every cover A of X by regular closed subsets of the space (X, T) contains a countable subfamily A′ such that X = ∪{int (A): A ∈ A′}. In this work we introduce the class of I-Lindelöf sets as a proper subclass of rc-Lindelöf sets [3]. We study various properties of I-Lindelöf sets and investigate the relationship between I-Lindelöf sets and I-Lindelöf subspaces. We give a new characterization of I-Lindelöf spaces in terms of this type of sets. Also, we study spaces (X, T) in which every I-Lindelöf set in (X, T) is closed. 相似文献
11.
Takashi Noiri 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):411-421
We introduce a new set called mng-closedwhich is defined on a set with two families of sets satisfying some minimal conditions. This set enables us to unify
modifications of g-closed sets due to Levine [19].
相似文献
12.
In this paper, we investigate whether consistent mappings can be used as homomorphism mappings between a covering based approximation space and its image with respect to twenty-two pairs of covering upper and lower approximation operators. We also consider the problem of constructing such mappings and minimizing them. In addition, we investigate the problem of reducing the data volume using consistent mappings as well as the maximum amount of their compressibility. We also apply our algorithms against several datasets. 相似文献
13.
Meltem Öztürk 《Annals of Operations Research》2008,163(1):177-196
Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization
has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties
of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval
representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework
generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets
having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that
we call “d-weak orders”, “d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish
some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation. 相似文献
14.
Greg Martin 《Journal of Combinatorial Theory, Series A》2006,113(4):591-607
We give explicit constructions of sets S with the property that for each integer k, there are at most g solutions to k=s1+s2,si∈S; such sets are called Sidon sets if g=2 and generalized Sidon sets if g?3. We extend to generalized Sidon sets the Sidon-set constructions of Singer, Bose, and Ruzsa. We also further optimize Kolountzakis’ idea of interleaving several copies of a Sidon set, extending the improvements of Cilleruelo, Ruzsa and Trujillo, Jia, and Habsieger and Plagne. The resulting constructions yield the largest known generalized Sidon sets in virtually all cases. 相似文献
15.
Lijun Ji 《Designs, Codes and Cryptography》2007,45(1):39-49
Recently, Franek et al. introduced large sets of v − 1 L-intersecting Steiner triple systems of order v (STS(v)) and gave four constructions for them (Des., Codes and Cryptogr., 26 (2002), 243–256). In this paper, we mainly focus on
large sets of v − 1{0, 1}-intersecting STS(v) and large sets of v + 1{1}-intersecting STS(v). For this purpose, we introduce a concept of L-intersecting partitionable candelabra system (L-PCS) of order v with q(v) subsystems and establish a relationship between L-PCS and large set of q(v)L-intersecting STS(v). Some constructions for L-PCSs are also presented by 3-wise balanced designs. These facilitate the production of some new infinite classes of these large
sets.
Research supported by Tianyuan Mathematics Foundation of NSFC Grant 10526032 and Natural Science Foundation of Universities
of Jiangsu Province Grant 05KJB110111. 相似文献
16.
Guobiao Weng Weisheng Qiu Zeying Wang Qing Xiang 《Designs, Codes and Cryptography》2007,44(1-3):49-62
Let (K, + ,*) be an odd order presemifield with commutative multiplication. We show that the set of nonzero squares of (K, *) is a skew Hadamard difference set or a Paley type partial difference set in (K, +) according as q is congruent to 3 modulo 4 or q is congruent to 1 modulo 4. Applying this result to the Coulter–Matthews presemifield and the Ding–Yuan variation of it,
we recover a recent construction of skew Hadamard difference sets by Ding and Yuan [7]. On the other hand, applying this result
to the known presemifields with commutative multiplication and having order q congruent to 1 modulo 4, we construct several families of pseudo-Paley graphs. We compute the p-ranks of these pseudo-Paley graphs when q = 34, 36, 38, 310, 54, and 74. The p-rank results indicate that these graphs seem to be new. Along the way, we also disprove a conjecture of René Peeters [17,
p. 47] which says that the Paley graphs of nonprime order are uniquely determined by their parameters and the minimality of
their relevant p-ranks.
Dedicated to Dan Hughes on the occasion of his 80th birthday. 相似文献
17.
Horst Trinker 《Designs, Codes and Cryptography》2009,50(2):229-234
In (Can J Math 51(2):326–346, 1999), Martin and Stinson provide a generalized MacWilliams identity for linear ordered orthogonal
arrays and linear ordered codes (introduced by Rosenbloom and Tsfasman (Prob Inform Transm 33(1):45–52, 1997) as “codes for
the m-metric”) using association schemes. We give an elementary proof of this generalized MacWilliams identity using group characters
and use it to derive an explicit formula for the dual type distribution of a linear ordered code or orthogonal array.
相似文献
18.
This paper deals with higher-order optimality conditions of set-valued optimization problems. By virtue of the higher-order derivatives introduced in (Aubin and Frankowska, Set-Valued Analysis, Birkhäuser, Boston, [1990]) higher-order necessary and sufficient optimality conditions are obtained for a set-valued optimization problem whose constraint condition is determined by a fixed set. Higher-order Fritz John type necessary and sufficient optimality conditions are also obtained for a set-valued optimization problem whose constraint condition is determined by a set-valued map. 相似文献
19.
Radomír Halaš 《Czechoslovak Mathematical Journal》2000,50(2):415-429
In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of R-polars are studied. Connections between R-polars and prime ideals, especially in distributive sets, are found. 相似文献
20.
Alik M. Najafov 《Central European Journal of Mathematics》2005,3(3):496-507
In this paper the spaces of type Sobolev-Morrey-W
p,a,г,τ
l
(Q,G)-are constructed, the differential properties are studied and it is proved that the functions from these spaces satisfy Holder's
condition, in the case, if the domain G∋R
n
satisfies the flexible λ-horn condition. 相似文献