共查询到20条相似文献,搜索用时 31 毫秒
1.
A Mendelsohn triple system of order ν, MTS(ν) for short, is a pair ( X, B) where X is a
ν-set (of points) and B is a collection of cyclic triples on X such that every ordered pair of distinct
points from X appears in exactly one cyclic triple of B. The cyclic triple ( a, b, c) contains the ordered
pairs ( a, b), ( b, c) and ( c, a). An MTS(ν) corresponds to an idempotent semisymmetric Latin square
(quasigroup) of order ν. An MTS(ν) is called frame self-orthogonal, FSOMTS for short, if its associated
semisymmetric Latin square is frame self-orthogonal. It is known that an FSOMTS(1
n
) exists for all
n≡1 (mod 3) except n=10 and for all n≥15, n≡0 (mod 3) with possible exception that n=18. In
this paper, it is shown that (i) an FSOMTS(2
n
) exists if and only if n≡0,1 (mod 3) and n>5 with
possible exceptions n∈{9, 27, 33, 39}; (ii) an FSOMTS(3
n
) exists if and only if n≥4, with possible
exceptions that n∈{6, 14, 18, 19}.
*Research supported by NSFC 10371002
*Partially supported by National Science Foundation under Grant CCR-0098093 相似文献
2.
We improve the existence results for holey self-orthogonal Latin squares with symmetric orthogonal mates (HSOLSSOMs) and show
that the necessary conditions for the existence of a HSOLSSOM of type h
n
are also sufficient with at most 28 pairs ( h, n) of possible exceptions.
Research supported in part by NSERC Grant A-5320 for the first author, NSF Grants CCR-9504205 and CCR-9357851 for the second
author, and NSFC Grant 19231060-2 for the third author. 相似文献
3.
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2 nu1 (HSOLSSOM(2 nu1)). For u2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n3 u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n9 and n3 u/2+1 or (2) n263 and n2( u-2). In this paper we show that in (1) the condition n9 can be extended to n30 and that in (2), the condition n263 can be improved to n4, except possibly for 19 pairs ( n, u), the largest of which is (53,28). 相似文献
4.
In this paper, two new direct construction methods are given for holey self‐orthogonal Latin squares with a symmetric orthogonal mate (HSOLSSOMs). Some new HSOLSSOMs using already known methods are also given. The known existence results for HSOLSSOMs of types 1 m u1 and hn are improved; for type 1 m u1 there remain just four possible exceptions with u odd and 3 ≤ u ≤ 15; for type hn, there are just two possible exceptions remaining, for ( h, n) = (6, 12) and (6, 18). As a byproduct, the known existence results for three holey mutually orthogonal Latin squares (3 HMOLS) are also improved. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 435–444, 2001 相似文献
6.
We consider a pair of MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning It is shown that a pair of MOLS with n holes of size h exist for h 2 if and only if n 4 For SOLS (self-orthogonal Latin squares) with holes, we have the same result, with two possible exceptions SOLS with 7 or 13 holes of size 6 相似文献
7.
We show that the fixed elements for the natural GL m-action on the universal division algebra UD( m, n) of m generic n× n-matrices form a division subalgebra of degree n, assuming n3 and 2 mn2−2. This allows us to describe the asymptotic behavior of the dimension of the space of SL m-invariant homogeneous central polynomials p( X1,…, Xm) for n× n-matrices. Here the base field is assumed to be of characteristic zero. 相似文献
8.
In this paper we introduce and study the square mean and the geometric mean in Riesz spaces. We prove that every geometric mean closed Riesz space is square mean closed and give a counterexample to the converse. We define for positive a, b in a square mean closed Riesz space E an addition via the formula ab=sup {(cos x) a + (sin x) b: 0 x 2π},which goes back to a formula by de Schipper. In case that E is geometric mean closed this turns the mldeflying set of the positive cone of E into a lattice ordered semigroup, which in turn is the positive cone ofa Riesz space E□. We prove, under the additional condition that E is geometric mean closed, that E□ is Riesz isomorphic to the square of E as introduced earlier by Buskes and van Rooij. 相似文献
9.
We develop a general context for the computation of the determinant of a Hankel matrix Hn = ( αi+j)0i,jn, assuming some suitable conditions for the exponential (or ordinary) generating function of the sequence ( αn) n0. Several well-known particular cases are thus derived in a unified way. 相似文献
10.
Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix.Recently we showed that if G has no 4-cycle, then μ2- μn-1, with equality if and only if G is the friendship graph.Here we prove that if m9 and G has no 4-cycle, then μ2m, with equality if G is a star. For 4 m8 this assertion fails. 相似文献
11.
It is proven that any set E consisting of finitely many intervals can be approximated with order 1/ n by polynomial inverse images of [-1,1]. This leads to a new proof of the fact that the n-th Chebyshev constant is Kcap( E) n with some K independent of n. The proof uses properties of monotone systems, in particular, the statement in the so-called inheritance problem. 相似文献
12.
In this paper we consider the classical Erdős–Rényi model of random graphs Gn,p. We show that for p= p( n) n−3/4−δ, for any fixed δ>0, the chromatic number χ( Gn,p) is a.a.s. ℓ, ℓ+1, or ℓ+2, where ℓ is the maximum integer satisfying 2( ℓ−1)log( ℓ−1) p( n−1). 相似文献
13.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following: 1. , for 1a5, a≠2. 2. A8. 3. PSL(3,4)e, for 1e10. 4. A5×PSL(3,4)e, for 1e10. Based on this result, we virtually show that if G is an ah-group with π( G) 2,3,5,7 , then F( G)≠1, or equivalently, that G has an abelian normal subgroup.In addition, we show that if G is an ah-group of minimal size which is not isomorphic to S3, then the non-abelian socle of G is either trivial or isomorphic to one of the following: 1. , for 3a5. 2. PSL(3,4)e, for 1e10. Our research lead us to interesting results related to transitivity and homogeneousity in permutation groups, and to subgroups of wreath products of form Z2Sn. These results are of independent interest and are located in appendices for greater autonomy. 相似文献
14.
We discuss the existence of a diffeomorphism such that | where are closed differential forms and 2kn. Our main results (the case k=n having been handled by Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] and Dacorogna and Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) are that- – when n is even and k=2, under some natural non-degeneracy condition, we can prove the existence of such diffeomorphism satisfying Dirichlet data on the boundary of a bounded open set and the natural Hölder regularity; at the same time we get Darboux theorem with optimal regularity;
- – we are also able to handle the degenerate cases when k=2 (in particular when n is odd), k=n−1 and some cases where 3kn−2.
Résumé
Nous montrons l'existence d'un difféomorphisme
satisfaisant
où
sont des formes différentielles fermées et 2
kn. Nos résultats principaux (le cas
k=
n a été discuté notamment dans Moser [J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965) 286–294] et Dacorogna et Moser [B. Dacorogna, J. Moser, On a partial differential equation involving the Jacobian determinant, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (1990) 1–26]) sont les suivants.
- – Si n est pair, k=2 et sous des conditions naturelles de non dégénérescence, nous montrons l'existence et la régularité dans les espaces de Hölder d'un tel difféomorphisme satisfaisant de plus une condition de Dirichlet. On obtient aussi le théorème de Darboux avec la régularité optimale.
- – Par ailleurs quand k=2 et n est impair ou k=n−1, ainsi que quelques cas particuliers où 3kn−2, nous montrons l'existence locale d'un tel difféomorphisme satisfaisant, en outre, des conditions de Cauchy.
Keywords: Darboux theorem; Symplectic forms; Pullback; Hölder regularity
相似文献
15.
There are basic equivalent assertions known for operator monotone functions and operator convex functions in two papers by Hansen and Pedersen. In this note we consider their results as correlation problem between two sequences of matrix
n-monotone functions and matrix
n-convex functions, and we focus the following three assertions at each label
n among them:
- (i) f(0)0 and f is n-convex in [0,α),
- (ii) For each matrix a with its spectrum in [0,α) and a contraction c in the matrix algebra Mn,
- (iii) The function is n-monotone in (0,α).
We show that for any
nN two conditions (ii) and (iii) are equivalent. The assertion that
f is
n-convex with
f(0)0 implies that
g(
t) is (
n-1)-monotone holds. The implication from (iii) to (i) does not hold even for
n=1. We also show in a limited case that the condition (i) implies (ii).
相似文献
16.
Consider the Hardy-type operator
T :
Lp(
a,
b)→
Lp(
a,
b),-∞
a<
b∞, which is defined by
It is shown that
where
ρn(
T) stands for any of the following: the Kolmogorov
n-width, the Gel’fand
n-width, the Bernstein
n-width or the
nth approximation number of
T.
相似文献
17.
New pointwise inversion formulae are obtained for the
d-dimensional totally geodesic Radon transform on the
n-dimensional real hyperbolic space, 1
dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms.
相似文献
18.
Suppose
μ and
ν are integer partitions of
n, and
N>
n. It is well known that the Ferrers boards associated to
μ and
ν are rook-equivalent iff the multisets [
μi+
i:1
iN] and [
νi+
i:1
iN] are equal. We use the Garsia–Milne involution principle to produce a bijective proof of this theorem in which non-attacking rook placements for
μ are explicitly matched with corresponding placements for
ν. One byproduct is a direct combinatorial proof that the matrix of Stirling numbers of the first kind is the inverse of the matrix of Stirling numbers of the second kind. We also prove
q-analogues and
p,
q-analogues of these results. We also use the Garsia–Milne involution principle to show that for any two rook boards
B and
B′, if
B and
B′ are bijectively rook-equivalent, then
B and
B′ are bijectively hit-equivalent.
相似文献
19.
A graph
G is (
m,
n)-
linked if for any two disjoint subsets
R,
BV(
G) with |
R|
m and |
B|
n,
G has two disjoint connected subgraphs containing
R and
B, respectively. We shall prove that a planar graph with at least six vertices is (3,3)-linked if and only if
G is 4-connected and maximal.
相似文献
20.
We extend the direct algorithm for computing the derivatives of the compactly supported Daubechies
N-vanishing-moment basis functions. The method yields exact values at dyadic rationals for the
nth derivative (0
n N − 1) of the basis functions, when it exists. Example results are shown for the first derivatives of the basis functions from the Daubechies
N-vanishing-moment extremal phase orthonormal family (for
N = 3, 4, and 5), and the CDF(2,
N) spline-based biorthogonal family (for
N = 6, 8, and 10).
相似文献