共查询到20条相似文献,搜索用时 640 毫秒
1.
Peter Frankl 《Combinatorica》1983,3(2):193-199
Letn, k, t be integers,n>k>t≧0, and letm(n, k, t) denote the maximum number of sets, in a family ofk-subsets of ann-set, no two of which intersect in exactlyt elements. The problem of determiningm(n, k, t) was raised by Erdős in 1975. In the present paper we prove that ifk≦2t+1 andk−t is a prime, thenm(n, k, t)≦(
t
n
)(
k
2k-t-1
)/(
t
2k-t-1
). Moreover, equality holds if and only if an (n, 2k−t−1,t)-Steiner system exists. The proof uses a linear algebraic approach. 相似文献
2.
Fort=2,3 andk2t–1 we prove the existence oft–(n,k,) designs with independence numberC
,k
n
(k–t)/(k–1)
(ln n)
1/(k–1)
. This is, up to the constant factor, the best possible.Some other related results are considered.Supported by NSF Grant DMS-9011850 相似文献
3.
J. Mijnheer 《Journal of Mathematical Sciences》1995,76(2):2283-2287
Let {X(t): 0≤t<∞) be a stable subordinator with α∈(0,1). For increasing sequences tk we give normalizing constants ak such thatliminf
k→∞ a
k
−1
X(tk) is a.s constant. We also derive a.s. upper bounds.
Proceedings of the XVI Seminar on Stability Problems for Stochastic Models Part I, Eger, Hungary, 1994. 相似文献
4.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
5.
Asymptotic Upper Bounds for Ramsey Functions 总被引:5,自引:0,他引:5
We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nf
a
+1(d), where f
a
+1(d)=∫0
1(((1−t)1/(
a
+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(K
k
+
l
,K
n
)≤ (l+o(1))n
k
/(logn)
k
−1. In particular, r(K
k
, K
n
)≤(1+o(1))n
k
−1/(log n)
k
−2.
Received: May 11, 1998 Final version received: March 24, 1999 相似文献
6.
Gil Kalai 《Israel Journal of Mathematics》1983,45(4):337-351
Let
(n, k) be the class of all simplicial complexesC over a fixed set ofn vertices (2≦k≦n) such that: (1)C has a complete (k−1)-skeleton, (2)C has precisely (
k
n−1
)k-faces, (3)H
k
(C)=0. We prove that for
,H
k−1(C) is a finite group, and our main result is:
. This formula extends to high dimensions Cayley’s formula for the number of trees onn labelled vertices. Its proof is based on a generalization of the matrix tree theorem. 相似文献
7.
Here we prove the following result.
Theorem 1.1.Let X be an integral projective curve of arithmetic genus g and k≧ ≧4 an integer. Assume the existence of L ∈ Pick
(X) with h
0
(X, L)=2 and L spanned. Fix a rank 1 torsion free sheaf M on X with h
0(X,M)=r+1≧2, h1
(X, M)≧2 and M spanned by its global sections. Set d≔deg(M) and s≔max {n≧0:h
0 (X, M ⊗(L*)⊗n)>0}. Then one of the following cases occur:
We find also other upper bounds onh
0 (X, F).
(a) | M≊L ⊗r; |
(b) | M is the subsheaf of ω X⊗(L*)⊗t, t:=g−d+r−1, spanned by H0(X, ωX⊗(L*)⊗t); |
(c) | there is a rank 1 torsion free sheaf F on X with 1≦h 0(X, F)≦k−2 such that M≊L⊗s⊗F. Moreover, if we fix an integer m with 2≦m≦k−2 and assume r#(s+1)k−(ns+n+1) per every 2≦n≦m, we have h0 (X, F)≦k−m−1. |
Sunto In questo lavoro si dimostra il seguente teorema. Teorem 1.1.Sia X una curva proiettiva ridotta e irriducibile di genere aritmetico g e k≥4 un intero. Si supponga l'esistenza di L ε Pick (X) con h 0 (X, L)=2 e L generato. Si fissi un fascio senza torsione di rango uno M su X con h0 (X, M)=r++1≥2, h1 (X, M) ≧2 e M generato dalle sue sezioni globali. Si ponga d≔deg(M) e s≔max{n≧0:h 0(X, M ⊗(L*)⊗n)>0}. Allora si verifica uno dei casi seguenti:相似文献Si ricavano anche altre maggiorazioni suh 0,(X, F).
(a) M≊L ⊗r; (b) M è il sottofascio di ω X⊗(L*)⊗t, t:=g−d+r−1 generato da H0 (X, ωX⊗(L*)⊗t); (c) esiste un fascio senza torsione di rango un F su X con 1≦h 0 (X, F) <=k−2 tale che M ≊L ⊗8 ⊗ F. Inoltre, se si fissa un intero m con 2≦m≦k−2 e si suppone r#(s+1) k−(ns+n+1) per ogni 2≦n≦m, si ottiene h 0 (X, F)≦k−m−1.
8.
孙乐平 《高校应用数学学报(英文版)》2003,18(4):390-402
§ 1 IntroductionFunctional differential equations have a wide range of applications in science andengineering.The simplestand perhapsmostnatural type of functional differential equationis a“delay differential equation”,that is,differential equation with dependence on the paststate.The simplest type of pastdependence is thatit is carried through the state variablebut not through its derivative.Then the equation can be expressed as delay differentialequations(DDEs) .There are also a number… 相似文献
9.
Gerald Kuba 《Mathematica Slovaca》2009,59(3):349-356
Let ℛ
n
(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛ
n
(t)| of the set ℛ
n
(t) by showing that, as t → ∞, t
2 log t ≪ |ℛ2(t)| ≪ t
2 log t and t
n
≪ |ℛ
n
(t)| ≪ t
n
for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛ
k,n
(t) ⊂ ℛ
n
(t) such that p(X) ∈ ℛ
k,n
(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t
k+1 ≪ |ℛ
k,n
(t)| ≪ t
k+1 and hence |ℛ
n−1,n
(t)| ≫ |ℛ
n
(t)| so that ℛ
n−1,n
(t) is the dominating subclass of ℛ
n
(t) since we can show that |ℛ
n
(t)∖ℛ
n−1,n
(t)| ≪ t
n−1(log t)2.On the contrary, if R
n
s
(t) is the total number of all polynomials in ℛ
n
(t) which split completely into linear factors over ℤ, then t
2(log t)
n−1 ≪ R
n
s
(t) ≪ t
2 (log t)
n−1 (t → ∞) for every fixed n ≥ 2.
相似文献
10.
Riccardo Benedetti Francois Loeser Jean Jacques Risler 《Discrete and Computational Geometry》1991,6(1):191-209
For every polynomial mapf=(f
1,…,f
k): ℝ
n
→ℝ
k
, we consider the number of connected components of its zero set,B(Z
f) and two natural “measures of the complexity off,” that is the triple(n, k, d), d being equal to max(degree off
i), and thek-tuple (Δ1,...,Δ4), Δ
k
being the Newton polyhedron off
i respectively. Our aim is to boundB(Z
f) by recursive functions of these measures of complexity. In particular, with respect to (n, k, d) we shall improve the well-known Milnor-Thom’s bound μ
d
(n)=d(2d−1)
n−1. Considered as a polynomial ind, μ
d
(n) has leading coefficient equal to 2
n−1. We obtain a bound depending onn, d, andk such that ifn is sufficiently larger thank, then it improves μ
d
(n) for everyd. In particular, it is asymptotically equal to 1/2(k+1)n
k−1
dn, ifk is fixed andn tends to infinity. The two bounds are obtained by a similar technique involving a slight modification of Milnor-Thom's argument,
Smith's theory, and information about the sum of Betti numbers of complex complete intersections. 相似文献
11.
Z. Ditzian 《Israel Journal of Mathematics》1985,52(4):341-354
Equivalences between the condition |P
n
(k)
(x)|≦K(n
−1√1−x
2+1/n
2)
k
n
-a, whereP
n(x) is the bestn-th degree polynomial approximation tof(x), and the Peetre interpolation space betweenC[−1,1] and the space (1−x
2)
k
f
(2k)(x)∈C[−1,1] is established. A similar result is shown forE
n(f)=
‖f−P
n‖
C[−1,1]. Rates other thann
-a are also discussed.
Supported by NSERC grant A4816 of Canada. 相似文献
12.
K. Kubilius 《Lithuanian Mathematical Journal》1999,39(3):251-261
The uniform distance between the solution of a nonlinear equation driven by a functionh with boundedp-variation and its Milstein-type approximation is estimated by δ
n
v γ
p
(n) v γ
p
2
(n), where δ
n
=max(t
k
−t
k−1
) is the maximum step size of the approximation on the interval [0,T], γ
p
(n)=max υ
p
1/p
(h;[t
k-1,t
k
]), 1 <p < 2, and υ
p
(h;[t
k-1,t
k
]) is thep-variation of the functionh on [t
k-1,t
k]. In particular, ifh is a Lipschitz function of order α, then the uniform distance has the bound δ
n
α
for δn <1.
Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius; Vilnius Technical University, Saulétekio 11, 2054 Vilnius,
Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 317–330, July–September, 1999. 相似文献
13.
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(
n
n+x
). Here we prove that the order x Veronese embedding ofP
n
is not weakly (k−1)-defective, i.e. for a general S⊃P
n
such that #(S) = k+1 the projective space | I
2S
(x)| of all degree t hypersurfaces ofP
n
singular at each point of S has dimension (
n
/n+x
)−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I
2S
(x)| has an ordinary double point at each P∈ S and Sing (F)=S.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
14.
Bao Yongguang 《分析论及其应用》1995,11(4):15-23
Let ξn −1 < ξn −2 < ξn − 2 < ... < ξ1 be the zeros of the the (n−1)-th Legendre polynomial Pn−1(x) and −1=xn<xn−1<...<x1=1, the zeros of the polynomial
. By the theory of the inverse Pal-Type interpolation, for a function f(x)∈C
[−1,1]
1
, there exists a unique polynomial Rn(x) of degree 2n−2 (if n is even) satisfying conditions Rn(f, ξk) = f (εk) (1 ⩽ k ⩽ n −1); R1
n(f,xk)=f1(xk)(1≤k≤n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation
polynomial {Rn(f, x)} (n is even) and the main result of this paper is that if f∈C
[1,1]
r
, r≥2, n≥r+2, and n is even then |R1
n(f,x)−f1(x)|=0(1)|Wn(x)|h(x)·n3−r·E2n−r−3(f(r)) holds uniformly for all x∈[−1,1], where
. 相似文献
15.
The convexity theory for oriented matroids, first developed by Las Vergnas [17], provides the framework for a new computational
approach to the Steinitz problem [13]. We describe an algorithm which, for a given combinatorial (d − 2)-sphereS withn vertices, determines the setC
d,n(S) of rankd oriented matroids withn points and face latticeS. SinceS is polytopal if and only if there is a realizableM εC
d,n(S), this method together with the coordinatizability test for oriented matroids in [10] yields a decision procedure for the
polytopality of a large class of spheres. As main new result we prove that there exist 431 combinatorial types of neighborly
5-polytopes with 10 vertices by establishing coordinates for 98 “doubted polytopes” in the classification of Altshuler [1].
We show that for alln ≧k + 5 ≧8 there exist simplicialk-spheres withn vertices which are non-polytopal due to the simple fact that they fail to be matroid spheres. On the other hand, we show
that the 3-sphereM
963
9
with 9 vertices in [2] is the smallest non-polytopal matroid sphere, and non-polytopal matroidk-spheres withn vertices exist for alln ≧k + 6 ≧ 9. 相似文献
16.
Jean Bourgain Jeff Kahn Gil Kalai Yitzhak Katznelson Nathan Linial 《Israel Journal of Mathematics》1992,77(1-2):55-64
LetX be a probability space and letf: X
n
→ {0, 1} be a measurable map. Define the influence of thek-th variable onf, denoted byI
f
(k), as follows: Foru=(u
1,u
2,…,u
n−1) ∈X
n−1 consider the setl
k
(u)={(u
1,u
2,...,u
k−1,t,u
k
,…,u
n−1):t ∈X}.
More generally, forS a subset of [n]={1,...,n} let the influence ofS onf, denoted byI
f
(S), be the probability that assigning values to the variables not inS at random, the value off is undetermined.
Theorem 1:There is an absolute constant c
1
so that for every function f: X
n
→ {0, 1},with Pr(f
−1(1))=p≤1/2,there is a variable k so that
Theorem 2:For every f: X
n
→ {0, 1},with Prob(f=1)=1/2, and every ε>0,there is S ⊂ [n], |S|=c
2(ε)n/logn so that I
f
(S)≥1−ε.
These extend previous results by Kahn, Kalai and Linial for Boolean functions, i.e., the caseX={0, 1}.
Work supported in part by grants from the Binational Israel-US Science Foundation and the Israeli Academy of Science. 相似文献
17.
E. I. Pancheva 《Journal of Mathematical Sciences》1998,92(3):3911-3920
Given an extremal process X: [0,∞)→[0,∞)d with lower curve C and associated point process N={(tk, Xk):k≥0}, tk distinct and Xk independent, given a sequence ζ
n
=(τ
n
, ξ
n
), n≥1, of time-space changes (max-automorphisms of [0,∞)d+1), we study the limit behavior of the sequence of extremal processes Yn(t)=ξ
n
-1
○ X ○ τn(t)=Cn(t) V max {ξ
n
-1
○ Xk: tk ≤ τn(t){ ⇒ Y under a regularity condition on the norming sequence ζn and asymptotic negligibility of the max-increments of Yn. The limit class consists of self-similar (with respect to a group ηα=(σα, Lα), α>0, of time-space changes) extremal processes. By self-similarity here we mean the property Lα ○ Y(t)
=
d
Y ○ αα(t) for all α>0. The univariate marginals of Y are max-self-decomposable. If additionally the initial extremal process X is
assumed to have homogeneous max-increments, then the limit process is max-stable with homogeneous max-increments.
Supported by the Bulgarian Ministry of Education and Sciences (grant No. MM 234/1996).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part I. 相似文献
18.
Y. Lacroix 《Israel Journal of Mathematics》2002,132(1):253-263
LetG denote the set of decreasingG: ℝ→ℝ withGэ1 on ]−∞,0], and ƒ
0
∞
G(t)dt⩽1. LetX be a compact metric space, andT: X→X a continuous map. Let μ denone aT-invariant ergodic probability measure onX, and assume (X, T, μ) to be aperiodic. LetU⊂X be such that μ(U)>0. Let τ
U
(x)=inf{k⩾1:T
k
xεU}, and defineG
U
(t)=1/u(U)u({xεU:u(U)τU(x)>t),tεℝ We prove that for μ-a.e.x∈X, there exists a sequence (U
n
)
n≥1
of neighbourhoods ofx such that {x}=∩
n
U
n
, and for anyG ∈G, there exists a subsequence (n
k
)
k≥1
withG
U
n
k
↑U weakly.
We also construct a uniquely ergodic Toeplitz flowO(x
∞,S, μ), the orbit closure of a Toeplitz sequencex
∞, such that the above conclusion still holds, with moreover the requirement that eachU
n
be a cylinder set.
In memory of Anzelm Iwanik 相似文献
19.
Ki Sik Ha 《Semigroup Forum》1989,38(1):215-221
LetZ be a generator of an exponentially boundedC-semigroup {S
t
}
t≥0 in a Banach space and letT
t
=C
−1
S
t
. We show that the spectral mapping theorems such as exp(tσ(Z)) ⊂ σ(T
t
) and exp(tσ
p
(Z)) ⊂ tσ
p
(T
t
) ⊂ exp(tσ
p
(Z)) ⋃ {0} for everyt≥0 hold.
The present studies were supported by the Basic Science Research Institute Program, Ministry of Education, 1987. 相似文献
20.
Alain Haraux 《Journal d'Analyse Mathématique》2005,95(1):297-321
IfA=A
*≥0 on the real Hilbert spaceH=L
2
(Ω, dμ) withKerA=A
−1
({0})∈0, (I+A)−1 compact andf(u)=c|u|
p−1
u withc>0,p>1, the solutions ofu”+u’+Au+f(u)=0 tend to 0 in norm at least liket
−1/(p−1)
ast→∞. Here it is shown that the set of initial data of those solutions tending to 0 exponentially fast has near 0 the structure
of a manifold with codimension dim(Ker A). If, in addition,A=−Δ with Neumann homogeneous boundary conditions, we show that the following alternative holds true: eitheru(t) tends to 0 exponentially fast, or ‖u(t)‖≥γt
−1/(p−1) with γ>0 fort≥1. 相似文献