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1.
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
2.
Michael Capalbo 《Combinatorica》2005,25(4):379-391
Here we solve an open problem considered by various researchers by presenting the first explicit constructions of an infinite
family
of bounded-degree ‘unique-neighbor’ concentrators Γ; i.e., there are strictly positive constants α and ε, such that all Γ = (X,Y,E(Γ)) ∈
satisfy the following properties. The output-set Y has cardinality
times that of the input-set X, and for each subset S of X with no more than α|X| vertices, there are at least ε|S| vertices in Y that are adjacent in Γ to exactly one vertex in S. Also, the construction of
is simple to specify, and each
has fewer than
edges. We then modify
to obtain explicit unique-neighbor concentrators of maximum degree 3.
* Supported by NSF grant CCR98210-58 and ARO grant DAAH04-96-1-0013. 相似文献
3.
We show that the hereditary discrepancy of a hypergraph
on n points increases by a factor of at most O(log n) when one adds a new edge to
. 相似文献
4.
Abstract
By
we denote the set of all propositional formulas. Let
be the set of all clauses. Define
. In Sec. 2 of this paper we prove that for normal modal logics
, the notions of
-expansions and
-expansions coincide. In Sec. 3, we prove that if I consists of default clauses then the notions of
-expansions for I and
-expansions for I coincide. To this end, we first show, in Sec. 3, that the notion of
-expansions for I is the same as that of
-expansions for I.
The project is supported by NSFC 相似文献
5.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
6.
Chun-Gil Park 《Bulletin of the Brazilian Mathematical Society》2005,36(1):79-97
It is shown that every almost linear mapping
of a unital Poisson JC*-algebra
to a unital Poisson JC*-algebra
is a Poisson JC*-algebra homomorphism when h(2
n
uy) = h(2
n
u) h(y), h(3
n
u y) = h(3
n
u) h(y) or h(q
n
u y) = h(q
n
u) h(y) for all
, all unitary elements
and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative mapping
is a Poisson JC*-algebra homomorphism when h(2x) = 2h(x), h(3x) = 3h(x) or h(qx) = qh(x) for all
. Here the numbers 2, 3, q depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings.Moreover, we prove the Cauchy–Rassias stability of Poisson JC*-algebra homomorphisms in Poisson JC*-algebras.*This work was supported by grant No. R05-2003-000-10006-0 from the Basic Research Program of the Korea Science & Engineering Foundation. 相似文献
7.
Let n and r be positive integers. Suppose that a family
satisfies F1∩···∩Fr ≠∅ for all F1, . . .,Fr ∈
and
. We prove that there exists ε=ε(r) >0 such that
holds for 1/2≤w≤1/2+ε if r≥13. 相似文献
8.
LinghaiZhang 《应用数学学报(英文版)》2004,20(2):283-308
We establish the exponential stability of fast traveling pulse solutions to nonlinear singularly per-turbed systems of integral differential equations arising from neuronal networks.It has been proved that expo-nential stability of these orbits is equivalent to linear stability.Let (?) be the linear differential operator obtainedby linearizing the nonlinear system about its fast pulse,and let σ((?)) be the spectrum of (?).The linearizedstability criterion says that if max{Reλ:λ∈σ((?)),λ≠0}(?)-D,for some positive constant D,and λ=0 is asimple eigenvalue of (?)(ε),then the stability follows immediately (see [13] and [37]).Therefore,to establish theexponential stability of the fast pulse,it suffices to investigate the spectrum of the operator (?).It is relativelyeasy to find the continuous spectrum,but it is very difficult to find the isolated spectrum.The real part ofthe continuous spectrum has a uniformly negative upper bound,hence it causes no threat to the stability.Itremains to see if the isolated spectrum is safe.Eigenvalue functions (see [14] and [35,36]) have been a powerful tool to study the isolated spectrum of the as-sociated linear differential operators because the zeros of the eigenvalue functions coincide with the eigenvaluesof the operators.There have been some known methods to define eigenvalue functions for nonlinear systems ofreaction diffusion equations and for nonlinear dispersive wave equations.But for integral differential equations,we have to use different ideas to construct eigenvalue functions.We will use the method of variation of param-eters to construct the eigenvalue functions in the complex plane C.By analyzing the eigenvalue functions,wefind that there are no nonzero eigenvalues of (?) in {λ∈C:Reλ(?)-D} for the fast traveling pulse.Moreoverλ=0 is simple.This implies that the exponential stability of the fast orbits is true. 相似文献
9.
Long Miao 《Bulletin of the Brazilian Mathematical Society》2007,38(4):585-594
Let
be a class of groups. A subgroup H of a group G is called
-s-supplemented in G, if there exists a subgroup K of G such that G = HK and K/K ∩ HG belongs to
where HG is the maximal normal subgroup of G which is contained in H. The main purpose of this paper is to study some subgroups of Fitting subgroup and generalized Fitting subgroup
-s-supplemented and some new criterions of p-nilpotency of finite groups are obtained.
*This research is supported by the grant of NSFC and TianYuan Fund of Mathematics of China (Grant #10626047). 相似文献
10.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
11.
In this paper, we first introduce new objects called “translation generalized ovals” and “translation generalized ovoids”,
and make a thorough study of these objects. We then obtain numerous new characterizations of the
of Tits and the classical generalized quadrangle
in even characteristic, including the complete classification of 2-transitive generalized ovals for the even case. Next,
we prove a new strong characterization theorem for the
of Tits. As a corollary, we obtain a purely geometric proof of a theorem of Johnson on semifield flocks.
* The second author is a Postdoctoral Fellow of the Fund for Scientific Research—Flanders (Belgium). 相似文献
12.
A triangle is a family of three sets A,B,C such that A∩B, B∩C, C∩A are each nonempty, and
. Let
be a family of r-element subsets of an n-element set, containing no triangle. Our main result implies that for r ≥ 3 and n ≥ 3r/2, we have
This settles a longstanding conjecture of Erdős [7], by improving on earlier results of Bermond, Chvátal, Frankl, and Füredi.
We also show that equality holds if and only if
consists of all r-element subsets containing a fixed element.
Analogous results are obtained for nonuniform families. 相似文献
13.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
14.
The aim of the present paper is to show some properties of functions belonging to the class (k, n, α)−
. The obtained results extend the results by Silverman [3]. 相似文献
15.
On Well-posed Mutually Nearest and
Mutually Furthest Point Problems in Banach Spaces 总被引:3,自引:0,他引:3
ChongLI RenXingNI 《数学学报(英文版)》2004,20(1):147-156
Let G be a non-empty closed(resp.bounded closed)boundedly relatively weakly compact subset in a strictly convex Kadec Banach space X.Let K(X)denote the space of all non-empty compact convex subsets of X endowed with the Hausdorff distance.Moreover,let KG(X)denote the closure of the set {A∈K(x):A∩G=0}.We prove that the set of all A∈KG(X)(resp.A∈K(X)),such that the minimization (resp.maximization)problem min(A,G)(resp.max(A,G))is well posed,contains a dense Gδ-subset of KG(X)(resp.K(X)).thus extending the recent results due to Blasi,Myjak and Papini and Li. 相似文献
16.
We define the reduced minimum modulus
of a nonzero element a in a unital C
*-algebra
by
. We prove that
. Applying this result to
and its closed two side ideal
, we get that dist
,
and
for any
if RR
= 0, where
and
is the quotient homomorphism and
. These results generalize corresponding results in Hilbert spaces. 相似文献
17.
Mowaffaq Hajja 《Results in Mathematics》2006,49(3-4):237-263
An edge-incentric d-simplex is defined to be a d-simplex S which admits a (d − 1)-sphere that touches all the edges of S internally. The center of such a sphere is called the edge-incenter of S and is denoted by
. Equivalently, S is edge-incentric if and only if its vertices are the centers of d + 1 (d − 1)-spheres in mutual external touch, and for this reason one may call such an S a balloon d-simplex. An orthocentric d-simplex is a d-simplex in which the altitudes are concurrent. The point of concurrence is called the orthocenter and is denoted by
. The spaces of edge-incentric and of orthocentric d-simplices have the same dimension d in the sense that a d-simplex in either space can be parametrized, up to shape, by d numbers. Edge-incentric and orthocentric tetrahedra are the first two of the four special classes of tetrahedra studied in
[1, Chapter IX.B, pp. 294–333].
The degree of regularity implied by the coincidence of two or more centers of a general d-simplex is investigated in [8], where it is shown that the coincidence of the centroid
, the circumcenter
, and the incenter
does not imply much regularity. For an orthocentric d-simplex S, however, it is proved in [9] that if any two of the centers
, and
coincide, then S is regular. In this paper, the same question is addressed for edge-incentric d-simplices. Among other things, it is proved that if any three of the centers
, and
of an edge-incentric d-simplex S coincide, then S is regular, and it is also shown that none of the coincidences
, and
implies regularity (except when d ≤ 3, d ≤ 4, and d ≤ 6, respectively). In contrast with the afore-mentioned results for orthocentric d-simplices, this emphasizes once more the feeling that, regarding many important properties, orthocentric d-simplices are the true generalizations of triangles.
Several open questions are posed.
Received: June 19, 2006. 相似文献
18.
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
19.
Alejandra Maestripieri Francisco Martínez Pería 《Integral Equations and Operator Theory》2007,59(2):207-221
The aim of this work is to generalize the notions of Schur complements and shorted operators to Krein spaces. Given a (bounded)
J-selfadjoint operator A (with the unique factorization property) acting on a Krein space
and a suitable closed subspace
of
, the Schur complement
of A to
is defined. The basic properties of
are developed and different characterizations are given, most of them resembling those of the shorted of (bounded) positive
operators on a Hilbert space.
To the memory of Professor Mischa Cotlar 相似文献
20.
Let G be a split adjoint semisimple group over
and
a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms
on congruence quotients of
. This proves a conjecture of Sarnak for
-split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type of simple trace formula.
Received: April 2005 Revision: June 2006 Accepted: October 2006 相似文献