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1.
A k-uniform linear path of length ?, denoted by ? ? (k) , is a family of k-sets {F 1,...,F ? such that |F i ∩ F i+1|=1 for each i and F i ∩ F bj = \(\not 0\) whenever |i?j|>1. Given a k-uniform hypergraph H and a positive integer n, the k-uniform hypergraph Turán number of H, denoted by ex k (n, H), is the maximum number of edges in a k-uniform hypergraph \(\mathcal{F}\) on n vertices that does not contain H as a subhypergraph. With an intensive use of the delta-system method, we determine ex k (n, P ? (k) exactly for all fixed ? ≥1, k≥4, and sufficiently large n. We show that $ex_k (n,\mathbb{P}_{2t + 1}^{(k)} ) = (_{k - 1}^{n - 1} ) + (_{k - 1}^{n - 2} ) + \cdots + (_{k - 1}^{n - t} )$ . The only extremal family consists of all the k-sets in [n] that meet some fixed set of t vertices. We also show that $ex(n,\mathbb{P}_{2t + 2}^{(k)} ) = (_{k - 1}^{n - 1} ) + (_{k - 1}^{n - 2} ) + \cdots + (_{k - 1}^{n - t} ) + (_{k - 2}^{n - t - 2} )$ , and describe the unique extremal family. Stability results on these bounds and some related results are also established. 相似文献
2.
Tapani Matala-aho 《Constructive Approximation》2011,33(3):289-312
We shall present short proofs for type II (simultaneous) Hermite–Padé approximations of the generalized hypergeometric and
q-hypergeometric series
F(t)=?n=0¥\frac?k=0n-1P(k)?k=0n-1Q(k)tn, Fq(t)=?n=0¥\frac?k=0n-1P(qk)?k=0n-1Q(qk)tn,F(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(k)}{\prod _{k=0}^{n-1}Q(k)}t^n,\qquad F_q(t)=\sum_{n=0}^{\infty}\frac{\prod_{k=0}^{n-1}P(q^k)}{\prod _{k=0}^{n-1}Q(q^k)}t^n, 相似文献
3.
Docent Bengt Rosén 《Probability Theory and Related Fields》1969,13(3-4):256-279
Summary Let {a
s
, s=1, 2, ..., N} be a set of reals and {p
s
, s=1, 2, ..., N} be a set of probabilities, i.e. p
s0 and p
1+p
2+...+p
N
=1. Let I
1
I
2,... be independent random variables, all with the distribution P(I=s)=p
s
, s=1, 2, ..., N. Put U
v
=l if I
v
{I
1, I
2, ..., I
v
–1} and U
v
=0 otherwise, v=1, 2, .... The random variable Z
n
=
is called the bonus sum after ncoupons for a coupon collector in the situation {(p
s
, a
s
), s=1, 2, ..., N}.Consider a sequence {(p
ks
, a
ks
), s=l, 2, ..., N
k
}, k=1, 2, ..., of collector situations, and let {Z
n
(k)
, n=1, 2, ...}, k=1, 2, ..., be the corresponding sequence of bonus sum variables. Let d be an arbitrary natural number and let
, k=1, 2, ..., where 1 n
k
(1)<n
k
(2)<< n
k
(d)
.We assume that N
(k)
t8 and that
.It is shown that the random vector V
(k)
is, under general conditions, asymptotically (as kt8) normally distributed. An asymptotic expression for the covariance matrix of V
(k)
is derived.Research supported in part at Stanford University, Stanford, California under contract N0014-67-A-0112-0015. 相似文献
4.
In this paper we derive a technique for obtaining limit theorems for suprema of Lévy processes from their random walk counterparts. For each a>0, let $\{Y^{(a)}_{n}:n\ge1\}
5.
O. M. Fomenko 《Journal of Mathematical Sciences》2002,110(6):3143-3149
Let Sk(Γ0(N)Ψ) be the space of holomorphic Γ0(N)-cusp forms of integral weight k and of character Ψ(mod n), let f(z) be a newform of the space Sk(Γ0(N),Ψ), and let Lf(s) be the corresponding L-function. The following statements are proved. (1) Let $\mathcal{F}_0 $ be the set of all newforms of Sk(Γ0(p),1), let p be prime, and let k≥2 be a constant even number. Then $\sum\limits_{f \in \mathcal{F}_0 :L_f (k/2) \ne 0} {1 \gg \frac{p}{{\log ^2 p}}} {\text{ (}}p \to \infty ).$ (2) Let $\mathcal{F}_0 $ be the set of all Hecke eigenforms of the space Sk(Γ0(1),1) and let k≡0 (mod 4). Then $\sum\limits_{f \in \mathcal{F}_0 :L_f (k/2) \ne 0} {1 \gg \frac{k}{{\log ^2 p}}} {\text{ (}}k \to \infty ).$ Bibliography: 11 titles. 相似文献
6.
A. I. Aptekarev J. S. Dehesa A. Martínez-Finkelshtein R. Yáñez 《Constructive Approximation》2009,30(1):93-119
Given a nontrivial Borel measure on ℝ, let p
n
be the corresponding orthonormal polynomial of degree n whose zeros are λ
j
(n), j=1,…,n. Then for each j=1,…,n,
7.
M. A. Lifshits 《Journal of Mathematical Sciences》2006,137(1):4541-4545
We consider a series of bilinear sequences
8.
Cao Jiading 《分析论及其应用》1989,5(2):99-109
Let an≥0 and F(u)∈C [0,1], Sikkema constructed polynomials:
, ifα
n
≡0, then Bn (0, F, x) are Bernstein polynomials.
Let
, we constructe new polynomials in this paper:
Q
n
(k)
(α
n
,f(t))=d
k
/dx
k
B
n+k
(α
n
,F
k
(u),x), which are called Sikkema-Kantorovic polynomials of order k. Ifα
n
≡0, k=1, then Qn
(1) (0, f(t), x) are Kantorovič polynomials Pn(f). Ifα
n
=0, k=2, then Qn
(2), (0, f(t), x) are Kantorovič polynomials of second order (see Nagel). The main result is:
Theorem 2. Let 1≤p≤∞, in order that for every f∈LP [0, 1],
, it is sufficient and necessary that
,
§ 1. Let f(t) de a continuous function on [a, b], i. e., f∈C [a, b], we define[1–2],[8–10]:
.
As usual, for the space Lp [a,b](1≤p<∞), we have
and L[a, b]=l1[a, b].
Letα
n
⩾0and F(u)∈C[0,1],Sikkema-Bernstein polynomials
[3] [4].
The author expresses his thanks to Professor M. W. Müller of Dortmund University at West Germany for his supports. 相似文献
9.
Viviane Ribeiro Tomaz da Silva 《Israel Journal of Mathematics》2012,188(1):441-462
Let F be a field of characteristic zero and E be the unitary Grassmann algebra generated over an infinite-dimensional F-vector space L. Denote by \(\mathcal{E} = \mathcal{E}^{(0)} \oplus \mathcal{E}^{(1)}\) an arbitrary ?2-grading of E such that the subspace L is homogeneous. Given a superalgebra A = A (0) ⊕ A (1), define the superalgebra \(A\hat \otimes \mathcal{E}\) by \(A\hat \otimes \mathcal{E} = (A^{(0)} \otimes \mathcal{E}^{(0)} ) \oplus (A^{(1)} \otimes \mathcal{E}^{(1)} )\). Note that when E is the canonical grading of E then \(A\hat \otimes \mathcal{E}\) is the Grassmann envelope of A. In this work we find bases of ?2-graded identities and we describe the ?2-graded codimension and cocharacter sequences for the superalgebras \(UT_2 (F)\hat \otimes \mathcal{E}\), when the algebra UT 2(F) of 2 ×2 upper triangular matrices over F is endowed with its canonical grading. 相似文献
10.
Zheng Yan LIN Sung Chul LEE 《数学学报(英文版)》2006,22(2):535-544
Let {Xn,n ≥ 0} be an AR(1) process. Let Q(n) be the rescaled range statistic, or the R/S statistic for {Xn} which is given by (max1≤k≤n(∑j=1^k(Xj - ^-Xn)) - min 1≤k≤n(∑j=1^k( Xj - ^Xn ))) /(n ^-1∑j=1^n(Xj -^-Xn)^2)^1/2 where ^-Xn = n^-1 ∑j=1^nXj. In this paper we show a law of iterated logarithm for rescaled range statistics Q(n) for AR(1) model. 相似文献
11.
Jürgen Grahl 《Arkiv f?r Matematik》2012,50(1):89-110
We show that a family F\mathcal{F} of analytic functions in the unit disk
\mathbbD{\mathbb{D}} all of whose zeros have multiplicity at least k and which satisfy a condition of the form
|