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1.
For a mixed hypergraph
, where
and
are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every
meets some class in more than one vertex, and every
has a nonempty intersection with at least two classes. The feasible set of
, denoted
, is the set of integers k such that
admits a coloring with precisely k nonempty color classes. It was proved by Jiang et al. [Graphs and Combinatorics 18 (2002), 309–318] that a set S of natural numbers is the feasible set of some mixed hypergraph if and only if either
or S is an ‘interval’
for some integer k ≥ 1.
In this note we consider r-uniform mixed hypergraphs, i.e. those with |C| = |D| = r for all
and all
, r ≥ 3. We prove that S is the feasible set of some r-uniform mixed hypergraph with at least one edge if and only if either
for some natural number k ≥ r − 1, or S is of the form
where S′′ is any (possibly empty) subset of
and S′ is either the empty set or {r − 1} or an ‘interval’ {k, k + 1, ..., r − 1} for some k, 2 ≤ k ≤ r − 2. We also prove that all these feasible sets
can be obtained under the restriction
, i.e. within the class of ‘bi-hypergraphs’.
Research supported in part by the Hungarian Scientific Research Fund, OTKA grant T-049613. 相似文献
2.
A set of linear maps
, V a finite vector space over a field K, is regular if to each
there corresponds a unique element
such that R(x)=y. In this context, Schur’s lemma implies that
is a field if (and only if) it consists of pairwise commuting elements. We consider when
is locally commutative: at some μ ∈V*, AB(μ)=BA(μ) for all
, and
has been normalized to contain the identity. We show that such locally commutative
are equivalent to commutative semifields, generalizing a result of Ganley, and hence characterizing commutative semifield spreads within the class of translation planes. This enables the determination of the orders |V| for which all locally commutative
on V are (globally) commutative. Similarly, we determine a sharp upperbound for the maximum size of the Schur kernel associated with strictly locally commutative
. We apply our main result to demonstrate the existence of a partial spread of degree 5, with nominated shears axis, that cannot be extend to a commutative semifield spread. Finally, we note that although local commutativity for a regular linear set
implies that the set of Lie products
consists entirely of singular maps, the converse is false. 相似文献
3.
E.M.E.ZAYED 《数学学报(英文版)》2003,19(4):679-694
The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k 1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k 1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. 相似文献
4.
The main result in Cossidente and Siciliano (J. Number Theory, Vol. 99 (2003) pp. 373–382) states that if a Singer subgroup of PGL(3,q) is an automorphism group of a projective, geometric
irreducible, non-singular plane algebraic curve
then either
or
. In the former case
is projectively equivalent to the curve
with equation Xq+1Y+Yq+1+X=0 studied by Pellikaan. Furthermore, the curve
has a very nice property from Finite Geometry point of view: apart from the three distinguished points fixed by the Singer
subgroup, the set of its
-rational points can be partitioned into finite projective planes
. In this paper, the full automorphism group of such curves is determined. It turns out that
is the normalizer of a Singer group in
. 相似文献
5.
Let
be a family of subsets of an n-element set.
is called (p,q)-chain intersecting if it does not contain chains
and
with
. The maximum size of these families is determined in this paper. Similarly to the p = q = 1 special case (intersecting families) this depends on the notion of r-complementing-chain-pair-free families, where r = p + q − 1. A family
is called r-complementing-chain-pair-free if there is no chain
of length r such that the complement of every set in
also belongs to
. The maximum size of such families is also determined here and optimal constructions are characterized.
The first author is a member of the Egerváry Research Group (EGRES). Research is supported by OTKA grants T 037547 and TS
049788, by European MCRTN Adonet, Contract Grant No. 504438 and by the Egerváry Research Group of the Hungarian Academy of
Sciences.
The work of the second author was partially supported by the Hungarian National Foundation for Scientific Research (OTKA),
grant numbers T037846 and NK62321. 相似文献
6.
Hidetoshi Maeda 《Archiv der Mathematik》2007,88(5):419-424
Let
be an ample vector bundle of rank n – 1 on a smooth complex projective variety X of dimension n≥ 3 such that X is a
-bundle over
and that
for any fiber F of the bundle projection
. The pairs
with
= 2 are classified, where
is the curve genus of
. This allows us to improve some previous results.
Received: 13 June 2006 相似文献
7.
Antonio G. García Miguel A. Hernández-Medina 《Mediterranean Journal of Mathematics》2005,2(3):345-356
Let
be a symmetric operator with compact resolvent defined in a Hilbert space
For any fixed
we consider an entire
function Ka which involves the resolvent of
Associated with Ka we obtain, by duality in
a Hilbert space
of entire functions which becomes a De Branges space of entire functions. This property provides a characterization of
regardless of the anti-linear mapping which has
as its range space. There exists also a sampling formula allowing to recover any function in
from its samples at the sequence of eigenvalues of
This work has been supported by the grant BFM2003–01034 from the D.G.I. of the Spanish Ministerio de Ciencia y Tecnología. 相似文献
8.
Evgueni Doubtsov 《Integral Equations and Operator Theory》2009,64(2):177-192
Let Bn denote the unit ball of , n ≥ 2. Given an α > 0, let denote the class of functions defined for by integrating the kernel against a complex-valued measure on the sphere . Let denote the space of holomorphic functions in the ball. A function is called a multiplier of provided that for every . In the present paper, we obtain explicit analytic conditions on which imply that g is a multiplier of . Also, we discuss the sharpness of the results obtained.
This research was supported by RFBR (grant no. 08-01-00358-a), by the Russian Science Support Foundation and by the programme
“Key scientific schools NS 2409.2008.1”. 相似文献
9.
E. M. E. ZAYED 《数学学报(英文版)》2005,21(4):733-752
The trace of the wave kernel μ(t) =∑ω=1^∞ exp(-itEω^1/2), where {Eω}ω^∞=1 are the eigenvalues of the negative Laplacian -△↓2 = -∑k^3=1 (δ/δxk)^2 in the (x^1, x^2, x^3)-space, is studied for a variety of bounded domains, where -∞ 〈 t 〈 ∞ and i= √-1. The dependence of μ (t) on the connectivity of bounded domains and the Dirichlet, Neumann and Robin boundary conditions are analyzed. Particular attention is given for a multi-connected vibrating membrane Ω in Ra surrounded by simply connected bounded domains Ω j with smooth bounding surfaces S j (j = 1,……, n), where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth components Si^* (i = 1 + kj-1,……, kj) of the bounding surfaces S j are considered, such that S j = Ui-1+kj-1^kj Si^*, where k0=0. The basic problem is to extract information on the geometry Ω by using the wave equation approach from a complete knowledge of its eigenvalues. Some geometrical quantities of Ω (e.g. the volume, the surface area, the mean curvuture and the Gaussian curvature) are determined from the asymptotic expansion ofexpansion of μ(t) for small │t│. 相似文献
10.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
11.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
12.
Some Limit Theorems for a Particle System of Single Point Catalytic Branching Random Walks 总被引:2,自引:0,他引:2
Vladimir VATUTIN Jie XIONG 《数学学报(英文版)》2007,23(6):997-1012
We study the scaling limit for a catalytic branching particle system whose particles perform random walks on Z and can branch at 0 only. Varying the initial (finite) number of particles, we get for this system different limiting distributions. To be more specific, suppose that initially there are n^β particles and consider the scaled process Zt^n(·) = Znt(√n·), where Zt is the measure-valued process 1 and to a representing the original particle system. We prove that Ztn converges to 0 when β 〈1/4 and to a nondegenerate discrete distribution when β=1/4.In addition,if 1/4〈β〈1/2 then n-^(2β-1/2)Zt^n converges to a random limit,while if β 〉21then n^-βZtn converges to a deterministic limit. 相似文献
13.
The optimal value function
of the quadratic program
, where
is a given symmetric matrix,
a given matrix,
and
are the linear perturbations, is considered. It is proved that
is directionally differentiable at any point
in its effective domain
. Formulae for computing the directional derivative
of
at
in a direction
are obtained. We also present an example showing that, in general,
is not piecewise linear-quadratic on W. The preceding (unpublished) example of Klatte is also discussed. 相似文献
14.
Vasily A. Prokhorov Edward B. Saff Maxim Yattselev 《Complex Analysis and Operator Theory》2009,3(2):501-524
Let be a bounded simply connected domain with boundary Γ and let be a regular compact set with connected complement. In this paper we investigate asymptotics of the extremal constants:
where is the supremum norm on a compact set K, is the set of all algebraic polynomials of degree at most m, and as . Subsequently, we obtain asymptotic behavior of the Kolmogorov k-widths, , of the unit ball An∞ of restricted to E in C(E), where H∞ is the Hardy space of bounded analytic functions on G and C(E) is the space of continuous functions on E.
Received: April 24, 2008. Accepted: May 15, 2008. 相似文献
15.
Alina Iacob 《Archiv der Mathematik》2005,85(4):335-344
We consider two pairs of complete hereditary cotorsion theories
on the category of left R-modules, such that
We prove that for any left R-modules M, N and for any n ≧ 1, the generalized Tate cohomology modules
can be computed either using a left
of M and a left
of M or using a right
a right
of N.
Received: 17 December 2004 相似文献
16.
B. Klartag 《Geometric And Functional Analysis》2006,16(6):1274-1290
Let
be a convex body and ɛ > 0. We prove the existence of another convex body
, whose Banach–Mazur distance from K is bounded by 1 + ɛ, such that the isotropic constant of K’ is smaller than
, where c > 0 is a universal constant. As an application of our result, we present a slight improvement on the best general upper
bound for the isotropic constant, due to Bourgain.
The author is a Clay Research Fellow, and was also supported by NSF grant #DMS-0456590.
Received: November 2005; Accepted: February 2006 相似文献
17.
We consider Dirichlet spaces (
) in L
2 and more general energy forms
in L
p
,
. For the latter we introduce the notions of an extended ’Dirichlet’ space and a transient form. Under the assumption that
, resp.
, are compactly embedded in L
2, resp. L
p
, we prove a Poincaré inequality for transient (Dirichlet) forms. If both
and its adjoint
are sub-Markovian semigroups, we show that the transience of T
t
is independent of
) and that it is implied by the transience of the energy form
of
and the form
belonging to
. 相似文献
18.
The peak algebra
is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks.
By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of
. We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak
algebra. We use these bases to describe the Jacobson radical of
and to characterize the elements of
in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals
of
, j = 0,...,
, such that
is the linear span of sums of permutations with a common set of interior peaks and
is the peak algebra. We extend the above results to
, generalizing results of Schocker (the case j = 0).
Aguiar supported in part by NSF grant DMS-0302423
Orellana supported in part by the Wilson Foundation 相似文献
19.
Let
be the 2k-uniform hypergraph obtained by letting P1, . . .,Pr be pairwise disjoint sets of size k and taking as edges all sets Pi∪Pj with i ≠ j. This can be thought of as the ‘k-expansion’ of the complete graph Kr: each vertex has been replaced with a set of size k. An example of a hypergraph with vertex set V that does not contain
can be obtained by partitioning V = V1 ∪V2 and taking as edges all sets of size 2k that intersect each of V1 and V2 in an odd number of elements. Let
denote a hypergraph on n vertices obtained by this construction that has as many edges as possible. For n sufficiently large we prove a conjecture of Frankl, which states that any hypergraph on n vertices that contains no
has at most as many edges as
.
Sidorenko has given an upper bound of
for the Tur′an density of
for any r, and a construction establishing a matching lower bound when r is of the form 2p+1. In this paper we also show that when r=2p+1, any
-free hypergraph of density
looks approximately like Sidorenko’s construction. On the other hand, when r is not of this form, we show that corresponding constructions do not exist and improve the upper bound on the Turán density
of
to
, where c(r) is a constant depending only on r.
The backbone of our arguments is a strategy of first proving approximate structure theorems, and then showing that any imperfections
in the structure must lead to a suboptimal configuration. The tools for its realisation draw on extremal graph theory, linear
algebra, the Kruskal–Katona theorem and properties of Krawtchouck polynomials.
* Research supported in part by NSF grants DMS-0355497, DMS-0106589, and by an Alfred P. Sloan fellowship. 相似文献
20.
For real parameters a, b, c, and t, where c is not a nonpositive integer, we determine exactly when the integral operator
is bounded on
where
is the open unit ball in
and dvt (z) = (1 − |z| 2) t dv (z) with dv being volume measure on
The characterization remains the same if we replace (1 − 〈z, w 〉) c in the integral kernel above by its modulus |1 − 〈z, w〉| c. 相似文献