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1.
Let T be a fixed tournament on k vertices. Let D(n,T ) denote the maximum number of orientations of an n-vertex graph that have no copy of T. We prove that
for all sufficiently (very) large n, where tk−1(n) is the maximum possible number of edges of a graphon n vertices with no Kk, (determined by Turán’s Theorem). The proof is based on a directed version of Szemerédi’s regularity lemma together with
some additional ideas and tools from Extremal Graph Theory, and provides an example of a precise result proved by applying
this lemma. For the two possible tournaments with three vertices we obtain separate proofs that avoid the use of the regularity
lemma and therefore show that in these cases
already holds for (relatively) small values of n.
* Research supported in part by a USA Israeli BSF grant, by a grant from the Israel Science Foundation and by the Hermann
Minkowski Minerva Center for Geometry at Tel Aviv University. 相似文献
2.
Let X be a locally compact topological space and (X, E, Xω) be any triple consisting of a hyperfinite set X in a sufficiently saturated nonstandard universe, a monadic equivalence relation E on X, and an E-closed galactic set Xω ⊆ X, such that all internal subsets of Xω are relatively compact in the induced topology and X is homeomorphic to the quotient Xω/E. We will show that each regular complex Borel measure on X can be obtained by pushing down the Loeb measure induced by some internal function
. The construction gives rise to an isometric isomorphism of the Banach space M(X) of all regular complex Borel measures on X, normed by total variation, and the quotient
, for certain external subspaces
of the hyperfinite dimensional Banach space
, with the norm ‖f‖1 = ∑x ∈ X |f(x)|. If additionally X = G is a hyperfinite group, Xω = Gω is a galactic subgroup of G, E is the equivalence corresponding to a normal monadic subgroup G0 of Gω, and G is isomorphic to the locally compact group Gω/G0, then the above Banach space isomorphism preserves the convolution, as well, i.e., M(G) and
are isometrically isomorphic as Banach algebras.
Research of both authors supported by a grant by VEGA – Scientific Grant Agency of Slovak Republic. 相似文献
3.
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
4.
Let Ω and Π be two finitely connected hyperbolic domains in the complex plane
and let R(z, Ω) denote the hyperbolic radius of Ω at z and R(w, Π) the hyperbolic radius of Π at w. We consider functions f that are analytic in Ω and such that all values f(z) lie in the domain Π. This set of analytic functions is denoted by A(Ω, Π). We prove among other things that the quantities
are finite for all
if and only if ∂Ω and ∂Π do not contain isolated points.
This work was supported by a grant of the Deutsche Forschungsgemeinschaft for F. G. Avkhadiev. 相似文献
5.
Zhijian Qiu 《Integral Equations and Operator Theory》2007,59(2):223-244
Let K be a compact subset in the complex plane and let A(K) be the uniform closure of the functions continuous on K and analytic on K°. Let μ be a positive finite measure with its support contained in K. For 1 ≤ q < ∞, let Aq(K, μ) denote the closure of A(K) in Lq(μ). The aim of this work is to study the structure of the space Aq(K, μ). We seek a necessary and sufficient condition on K so that a Thomson-type structure theorem for Aq(K, μ) can be established. Our theorem deduces J. Thomson’s structure theorem for Pq(μ), the closure of polynomials in Lq(μ), as the special case when K is a closed disk containing the support of μ. 相似文献
6.
Let C be a simply connected domain, 0, and let n,nN, be the set of all polynomials of degree at mostn. By n() we denote the subset of polynomials p n withp(0)=0 andp(D), whereD stands for the unit disk {z: |z|<1}, and=" by=">1},>we denote the maximal range of these polynomials. Letf be a conformal mapping fromD onto ,f(0)=0. The main theme of this note is to relate n (or some important aspects of it) to the imagesf
s
(D), wheref
s
(z):=f[(1–s)z], 0s<1. for=" instance=" we=" prove=" the=" existence=" of=" a=" universal=">1.>c
0 such that, forn2c
0, 相似文献
7.
Tuoc Van Phan 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2012,4(1):395-400
Let Ω be an open, bounded domain in
\mathbbRn (n ? \mathbbN){\mathbb{R}^n\;(n \in \mathbb{N})} with smooth boundary ∂Ω. Let p, q, r, d
1, τ be positive real numbers and s be a non-negative number which satisfies
0 < \fracp-1r < \fracqs+1{0 < \frac{p-1}{r} < \frac{q}{s+1}}. We consider the shadow system of the well-known Gierer–Meinhardt system:
$ \left \{ {l@{\quad}l} \displaystyle{u_t = d_1\Delta u - u + \frac{u^p}{\xi^q}}, & \quad {\rm in}\;\Omega \times (0,T), \\ \displaystyle{\tau \xi_t = -\xi + \frac{1}{|\Omega|} \int\nolimits_\Omega\frac{u^r}{\xi^s} {\rm d}x}, & \quad {\rm in}\;(0,T), \\ \displaystyle{\frac{\partial u}{\partial \nu} =0}, & \quad {\rm on}\;\partial \Omega \times (0,T), \\ \displaystyle{\xi(0) = \xi_0 >0 , \quad u(\cdot,0) = u_0(\cdot)} \geq 0 & \quad {\rm in}\;\Omega. \right. $ \left \{ \begin{array}{l@{\quad}l} \displaystyle{u_t = d_1\Delta u - u + \frac{u^p}{\xi^q}}, & \quad {\rm in}\;\Omega \times (0,T), \\ \displaystyle{\tau \xi_t = -\xi + \frac{1}{|\Omega|} \int\nolimits_\Omega\frac{u^r}{\xi^s} {\rm d}x}, & \quad {\rm in}\;(0,T), \\ \displaystyle{\frac{\partial u}{\partial \nu} =0}, & \quad {\rm on}\;\partial \Omega \times (0,T), \\ \displaystyle{\xi(0) = \xi_0 >0 , \quad u(\cdot,0) = u_0(\cdot)} \geq 0 & \quad {\rm in}\;\Omega. \end{array} \right. 相似文献
8.
We build a version of a thermodynamic formalism for maps
of the form f(z) = ∑
j = 0
p + q
a
j
e
(j−p)z
where p, q > 0 and
. We show in particular the existence and uniqueness of (t,α)-conformal measures and that the Hausdorff dimension HD(J
f
r
) = h is the unique zero of the pressure function t ↦ P(t) for t > 1, where the set J
f
r
is the radial Julia set.
Partially supported by NSF Grant DMS 0100078.
Partially supported by Warsaw University of Technology Grant No. 504G11200023000, Polish KBN Grant No. 2PO3A03425 and Chilean
FONDECYT Grant No. 11060280. 相似文献
9.
Let Q be an alphabet with q elements. For any code C over Q of length n and for any two codewords a = (a 1, . . . , a n ) and b = (b 1, . . . , b n ) in C, let ${D({\bf a, b}) = \{(x_1, . . . , x_n) \in {Q^n} : {x_i} \in \{a_i, b_i\}\,{\rm for}\,1 \leq i \leq n\}}
10.
Frederic Palesi 《Geometriae Dedicata》2011,151(1):107-140
Let M be a non-orientable surface with Euler characteristic χ(M) ≤ −2. We consider the moduli space of flat SU(2)-connections, or equivalently the space of conjugacy classes of representations
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