共查询到20条相似文献,搜索用时 31 毫秒
1.
The (0,α)-geometries fully embedded in a projective space are up to a few open cases classified. For (0,α)-geometries fully embedded in an affine space AG(n,q), less is known. The most important model is the so-called linear representation T n-1* (k) of a set k of type {0,1,α +1} with respect to lines in the hyperplane at infinity. We will give a characterization of this model. We also investigate the case where the (0,α)-geometry, fully embedded in AG(n,q), is the dual of a semipartial geometry. 相似文献
2.
Frank de Clerck Stefaan de Winter Elisabeth Kuijken Cristina Tonesi 《Designs, Codes and Cryptography》2006,38(2):179-194
We introduce distance-regular (0,α)-reguli and show that they give rise to (0,α)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (α,β)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (α,β)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known
semipartial geometry Tn*(B) arising from a Baer subspace PG(n, q) in PG(n, q2).
Research Fellow supported by the Flemish Institute for the Promotion of Scientific and Technological Research in Industry
(IWT), grant no. IWT/SB/13367/Tonesi
Research assistant of the Fund for Scientific Research Flanders (FWO-Vlaanderen). 相似文献
3.
In Part I we obtained results about the embedding of (0, α)-geometries in PG(3, q). Here we determine all (0, α)-geometries with q+1 points on a line, which are embedded in PG(n, q), n>3 and q>2. As a particular case all semi partial geometries with parameters s=q,t,α(>1),μ, which are embeddable in PG(n, q), q≠2, are obtained. We also prove some theorems about the embedding of (0, 2)-geometries in PG(n, 2): we show that without loss of generality we may restrict ourselves to reduced (0, 2)-geometries, we determine all (0, 2)-geometries in PG(4, 2), and we describe an unusual embedding of U2,3(9) in PG(5, 2). 相似文献
4.
We study the relation between distance-regular graphs and (α, β)-geometries in two different ways. We give necessary and sufficient
conditions for the neighbourhood geometry of a distance-regular graph to be an (α, β)-geometry, and describe some (classes
of) examples. On the other hand, properties of certain regular two-graphs allow us to construct (0, α)-geometries on the corresponding
Taylor graphs. 相似文献
5.
The study of the intersection of two Baer subgeometries of PG(n, q), q a square, started in Bose et al. (Utilitas Math 17, 65–77, 1980); Bruen (Arch Math 39(3), 285–288, (1982). Later, in Svéd (Baer subspaces in the n-dimensional projective space. Springer-Verlag) and Jagos et
al. (Acta Sci Math 69(1–2), 419–429, 2003), the structure of the intersection of two Baer subgeometries of PG(n, q) has been completely determined. In this paper, generalizing the previous results, we determine all possible intersection
configurations of any two subgeometries of PG(n, q).
相似文献
6.
Jeroen Schillewaert 《Designs, Codes and Cryptography》2008,47(1-3):165-175
This work is inspired by a paper of Hertel and Pott on maximum non-linear functions (Hertel and Pott, A characterization of
a class of maximum non-linear functions. Preprint, 2006). Geometrically, these functions correspond with quasi-quadrics; objects
introduced in De Clerck et al. (Australas J Combin 22:151–166, 2000). Hertel and Pott obtain a characterization of some binary
quasi-quadrics in affine spaces by their intersection numbers with hyperplanes and spaces of codimension 2. We obtain a similar
characterization for quadrics in projective spaces by intersection numbers with low-dimensional spaces. Ferri and Tallini
(Rend Mat Appl 11(1): 15–21, 1991) characterized the non-singular quadric Q(4,q) by its intersection numbers with planes and solids. We prove a corollary of this theorem for Q(4,q) and then extend this corollary to all quadrics in PG(n,q),n ≥ 4. The only exceptions occur for q even, where we can have an oval or an ovoid as intersection with our point set in the non-singular part.
相似文献
7.
In this paper, a necessary and sufficient condition of A(a)-acceptability for rational approximations to the functionexp(q) and some sufficient conditions to guarantee A(α)-acceptability of Padé approximations[^(R)]mn (q)\hat R_m^n (q) to the functionexp(q) are given, where a ∈(0,π/2), n≤m,m≥2. Furthermore, it is proved that the condition of A(α)-acceptability of rational approximations toexp(q) is equivalent to the nonnegatively of a real polynomial in interval (−∞,0). Finally, we prove that[^(R)]41 (q)\hat R_4^1 (q) is A(π/3)-acceptable. Based on this conclusion, two A(π/3)-stable multiderivative (hybrid) one-step methods are constructed. 相似文献
8.
Let 1<q<∞, n(1−1/q)≤α<∞, 0<p<∞ and ω1,ω2 ɛA
1(R
n
) (the Muckenhoupt class). In this paper, the author introduce the weighted Herz-type Hardy spaces hk
q
α,p
(gw1,ω2) and present their atomic decomposition. Using the atomic decomposition, the author find out their dual spaces, establish
the boundedness on these spaces of the pseudo-differential operators of order zero and show thatD(R
n
), the class of C∞(Rn)-functions with compactly support, is dense inhK
q
α,p
(ω1,ω2) and there is a subsequence, which converges in distrbutional sense to some distribution ofhK
q
α,p
(ω1,ω2), of any bounded sequence inhK
q
α,p
(ω1,ω2). In addition, the author also set up the boundedness of some non-linear quantities in compensated compactness.
Supported by the NECF and the NECF and the NNSF of China. 相似文献
9.
Let Ω and
be a subset of Σ = PG(2n−1,q) and a subset of PG(2n,q) respectively, with Σ ⊂ PG(2n,q) and
. Denote by K the cone of vertex Ω and base
and consider the point set B defined by
in the André, Bruck-Bose representation of PG(2,qn) in PG(2n,q) associated to a regular spread
of PG(2n−1,q). We are interested in finding conditions on
and Ω in order to force the set B to be a minimal blocking set in PG(2,qn) . Our interest is motivated by the following observation. Assume a Property α of the pair (Ω,
) forces B to turn out a minimal blocking set. Then one can try to find new classes of minimal blocking sets working with the list of
all known pairs (Ω,
) with Property α. With this in mind, we deal with the problem in the case Ω is a subspace of PG(2n−1,q) and
a blocking set in a subspace of PG(2n,q); both in a mutually suitable position. We achieve, in this way, new classes and new sizes of minimal blocking sets in PG(2,qn), generalizing the main constructions of [14]. For example, for q = 3h, we get large blocking sets of size qn + 2 + 1 (n≥ 5) and of size greater than qn+2 + qn−6 (n≥ 6). As an application, a characterization of Buekenhout-Metz unitals in PG(2,q2k) is also given. 相似文献
10.
Chun Gil PARK Jin Chuan HOU Sei Qwon OH 《数学学报(英文版)》2005,21(6):1391-1398
It is shown that every almost *-homomorphism h : A→B of a unital JC*-algebra A to a unital JC*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x∈A, and that every almost linear mapping h : A→B is a *-homomorphism when h(2^nu o y) - h(2^nu) o h(y), h(3^nu o y) - h(3^nu) o h(y) or h(q^nu o y) = h(q^nu) o h(y) for all unitaries u ∈A, all y ∈A, and n = 0, 1,.... Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings. We prove that every almost *-homomorphism h : A→B of a unital Lie C*-algebra A to a unital Lie C*-algebra B is a *-homomorphism when h(rx) = rh(x) (r 〉 1) for all x ∈A. 相似文献
11.
An H-design is said to be (1, α)-resolvable, if its block set can be partitioned into α-parallel classes, each of which contains every point of the design exactly α times. When α = 1, a (1, α)-resolvable H-design of type g
n
is simply called a resolvable H-design and denoted by RH(g
n
), for which the general existence problem has been determined leaving mainly the case of g ≡ 0 (mod 12) open. When α = 2, a (1, 2)-RH(1
n
) is usually called a (1, 2)-resolvable Steiner quadruple system of order n, for which the existence problem is far from complete. In this paper, we consider these two outstanding problems. First,
we prove that an RH(12
n
) exists for all n ≥ 4 with a small number of possible exceptions. Next, we give a near complete solution to the existence problem of (1, 2)-resolvable
H-designs with group size 2. As a consequence, we obtain a near complete solution to the above two open problems. 相似文献
12.
M. A. Grechkoseeva 《Siberian Mathematical Journal》2007,48(1):73-75
We prove that the nonisomorphic simple groups B
n
(q) and C
n
(q) have different sets of element orders.
Original Russian Text Copyright ? 2007 Grechkoseeva M. A.
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 1, pp. 89–92, January–February, 2007. 相似文献
13.
Normal Bases and Their Dual-Bases over Finite Fields 总被引:2,自引:0,他引:2
Qun Ying LIAO Qi SUN 《数学学报(英文版)》2006,22(3):845-848
In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2) The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr(α^2) = 1, where α generates N; 3) An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis. 相似文献
14.
V. A. Ustimenko 《Journal of Mathematical Sciences》2007,140(3):461-471
The paper is devoted to the study of a linguistic dynamical system of dimension n ≥ 2 over an arbitrary commutative ring K,
i.e., a family F of nonlinear polynomial maps f
α : K
n
→ K
n
depending on “time” α ∈ {K − 0} such that f
α
−1 = f
−αM, the relation f
α1 (x) = f
α2 (x) for some x ∈ Kn implies α1 = α2, and each map f
α has no invariant points. The neighborhood {f
α (υ)∣α ∈ K − {0}} of an element v determines the graph Γ(F) of the dynamical system on the vertex set Kn. We refer to F as a linguistic dynamical system of rank d ≥ 1 if for each string a = (α1, υ, α2), s ≤ d, where αi + αi+1 is a nonzero divisor for i = 1, υ, d − 1, the vertices υ
a = f
α1 × ⋯ × f
αs
(υ) in the graph are connected by a unique path. For each commutative ring K and each even integer n ≠= 0 mod 3, there is a family of linguistic dynamical systems Ln(K) of rank d ≥ 1/3n. Let L(n, K) be the graph of the dynamical system Ln(q). If K = Fq, the graphs L(n, Fq) form a new family of graphs of large girth. The projective limit L(K) of L(n, K), n → ∞, is well defined for each commutative
ring K; in the case of an integral domain K, the graph L(K) is a forest. If K has zero divisors, then the girth of K drops
to 4. We introduce some other families of graphs of large girth related to the dynamical systems Ln(q) in the case of even q. The dynamical systems and related graphs can be used for the development of symmetric or asymmetric
cryptographic algorithms. These graphs allow us to establish the best known upper bounds on the minimal order of regular graphs
without cycles of length 4n, with odd n ≥ 3. Bibliography: 42 titles.
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 214–234. 相似文献
15.
Complete (n,r)-arcs in PG(k−1,q) and projective (n,k,n−r)
q
-codes that admit no projective extensions are equivalent objects. We show that projective codes of reasonable length admit
only projective extensions. Thus, we are able to prove the maximality of many known linear codes. At the same time our results
sharply limit the possibilities for constructing long non-linear codes. We also show that certain short linear codes are maximal.
The methods here may be just as interesting as the results. They are based on the Bruen–Silverman model of linear codes (see
Alderson TL (2002) PhD. Thesis, University of Western Ontario; Alderson TL (to appear) J Combin Theory Ser A; Bruen AA, Silverman
R (1988) Geom Dedicata 28(1): 31–43; Silverman R (1960) Can J Math 12: 158–176) as well as the theory of Rédei blocking sets
first introduced in Bruen AA, Levinger B (1973) Can J Math 25: 1060–1065.
相似文献
16.
Let q be a power of a prime and n a positive integer. Let P(q) be a parabolic subgroup of the finite general linear group GL
n
(q). We show that the number of P(q)-conjugacy classes in GL
n
(q) is, as a function of q, a polynomial in q with integer coefficients. This answers a question of Alperin in (Commun. Algebra 34(3): 889–891, 2006) 相似文献
17.
We show that the only orthogonal polynomials satisfying a q-difference equation of the form π(x)D
q
P
n
(x) = (α
n
x + β
n
)P
n
(x) + γ
n
P
n−1(x) where π(x) is a polynomial of degree 2, are the Al-Salam Carlitz 1, little and big q-Laguerre, the little and big q-Jacobi, and the q-Bessel polynomials. This is a q-analog of the work carried out in [1].
2000 Mathematics Subject Classification Primary—33C45, 33D45 相似文献
18.
A resolution of the lines of AG(n,q) is a partition of the lines classes (called resolution classes) such that every point of the geometry is on exactly one line of each resolution class. Two resolutions R,R' of AG(n,q) are orthogonal if any resolution class from R has at most one line in common with any class from R'. In this paper, we construct orthogonal resolutions on AG(n,q) for all n=2i+1, i=1,2,…, and all q>2 a prime power. The method involves constructing AG(n,q) from a finite projective plane of order qn-1 and using the structure of the plane to display the orthogonal resolutions. 相似文献
19.
Agarwal and Bressoud (Pacific J. Math.
136(2) (1989) 209–228) defined a class of weighted lattice paths and interpreted several q-series combinatorially. Using the same class of lattice paths, Agarwal (Utilitas Math.
53 (1998) 71–80; ARS Combinatoria
76 (2005) 151–160) provided combinatorial interpretations for several more q-series. In this paper, a new class of weighted lattice paths, which we call associated lattice paths is introduced. It is
shown that these new lattice paths can also be used for giving combinatorial meaning to certain q-series. However, the main advantage of our associated lattice paths is that they provide a graphical representation for partitions
with n + t copies of n introduced and studied by Agarwal (Partitions with n copies of n, Lecture Notes in Math., No. 1234 (Berlin/New York: Springer-Verlag) (1985) 1–4) and Agarwal and Andrews (J. Combin. Theory
A45(1) (1987) 40–49). 相似文献
20.
S. Wehmeier 《Lithuanian Mathematical Journal》2006,46(3):371-383
We show that the Turán-Kubilius inequality holds for additive arithmetical semigroups satisfying the following conditions:
G(n) = q
n
(A+O(1/ln n)) (where A > 0 and q > 1) for the number of elements of degree n and P(n) = O(q
n
/n) for the number of prime elements of degree n. This is an improvement of a result of Zhang. We also give some variants of the inequality under some stronger or weaker
assumptions and applications for the prime divisor function ω and related functions.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 3, pp. 457–471, July–September, 2006. 相似文献