共查询到20条相似文献,搜索用时 15 毫秒
1.
Let S⊂ℝ
k+m
be a compact semi-algebraic set defined by P
1≥0,…,P
ℓ
≥0, where P
i
∈ℝ[X
1,…,X
k
,Y
1,…,Y
m
], and deg (P
i
)≤2, 1≤i≤ℓ. Let π denote the standard projection from ℝ
k+m
onto ℝ
m
. We prove that for any q>0, the sum of the first q Betti numbers of π(S) is bounded by (k+m)
O(q
ℓ). We also present an algorithm for computing the first q Betti numbers of π(S), whose complexity is
. For fixed q and ℓ, both the bounds are polynomial in k+m.
The author was supported in part by an NSF Career Award 0133597 and a Sloan Foundation Fellowship. 相似文献
2.
Haruko Okamura 《Graphs and Combinatorics》2005,21(4):503-514
Let k≥2 be an integer and G = (V(G), E(G)) be a k-edge-connected graph. For X⊆V(G), e(X) denotes the number of edges between X and V(G) − X. Let {si, ti}⊆Xi⊆V(G) (i=1,2) and X1∩X2=∅. We here prove that if k is even and e(Xi)≤2k−1 (i=1,2), then there exist paths P1 and P2 such that Pi joins si and ti, V(Pi)⊆Xi (i=1,2) and G − E(P1∪P2) is (k−2)-edge-connected (for odd k, if e(X1)≤2k−2 and e(X2)≤2k−1, then the same result holds [10]), and we give a generalization of this result and some other results about paths not containing
given edges. 相似文献
3.
Let X(t) be an N parameter generalized Lévy sheet taking values in ℝd with a lower index α, ℜ = {(s, t] = ∏
i=1
N
(s
i, t
i], s
i < t
i}, E(x, Q) = {t ∈ Q: X(t) = x}, Q ∈ ℜ be the level set of X at x and X(Q) = {x: ∃t ∈ Q such that X(t) = x} be the image of X on Q. In this paper, the problems of the existence and increment size of the local times for X(t) are studied. In addition, the Hausdorff dimension of E(x, Q) and the upper bound of a uniform dimension for X(Q) are also established. 相似文献
4.
Cecilia Salgado 《Bulletin of the Brazilian Mathematical Society》2012,43(1):7-16
Let X be an elliptic K3 surface endowed with two distinct Jacobian elliptic fibrations π
i
, i = 1, 2, defined over a number field k. We prove that there is an elliptic curve C ⊂ X such that the generic rank over k of X after a base extension by C is strictly larger than the generic rank of X. Moreover, if the generic rank of π
j
is positive then there are infinitely many fibers of π
i
(j ≠ i) with rank at least the generic rank of π
i
plus one. 相似文献
5.
Let X be a smooth complex projective variety with Neron–Severi group isomorphic to ℤ, and D an irreducible divisor with normal crossing singularities. Assume 1<r≤ 3. We prove that if π1(X) doesn't have irreducible PU(r) representations, then π1(X- D) doesn't have irreducible U(r) representations. The proof uses the non-existence of certain stable parabolic bundles. We also obtain a similar result for
GL(2) when D is smooth.
Received: 20 December 1999 / Revised version: 7 May 2000 相似文献
6.
Marco Antei 《Israel Journal of Mathematics》2011,186(1):427-446
Let S be a connected Dedekind scheme and X an S-scheme provided with a section x. We prove that the morphism between fundamental group schemes π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) induced by the canonical morphism from X to its Albanese scheme Alb
X/S
(when the latter exists) fits in an exact sequence of group schemes 0 → (NS
X/S
τ
)⋎ → π
1(X, x)
ab
→ π
1(Alb
X/S
, 0AlbX/S{0_{{\rm{Al}}{{\rm{b}}_{X/S}}}}) → 0, where the kernel is a finite and flat S-group scheme. Furthermore, we prove that any finite and commutative quotient pointed torsor over the generic fiber X
η
of X can be extended to a finite and commutative pointed torsor over X. 相似文献
7.
A. K. Katsaras 《P-Adic Numbers, Ultrametric Analysis, and Applications》2009,1(3):190-203
LetX be a Hausdorff zero-dimensional topological space,K(X) the algebra of all clopen subsets of X, E a Hausdorff locally convex space over a non-Archimedean valued field and C
b
(X) the space of all bounded continuous -valued functions on X. The space M(K(X),E), of all bounded finitely-additive measures m: K(X) → E, is investigated. If we equip C
b
(X) with the topologies β
o
, β, β
u
, τ
b
or β
ob
, it is shown that, for E (compete, the corresponding spaces of continuous linear operators from C
b
(X) to E (are algebraically isomorphic to certain subspaces of M(K(X),E).
The text was submitted by the author in English. 相似文献
8.
Yehoram Gordon 《Israel Journal of Mathematics》1969,7(2):151-163
Given 1≦p<∞ and a real Banach spaceX, we define thep-absolutely summing constantμ
p(X) as inf{Σ
i
=1/m
|x*(x
i)|p
p Σ
i
=1/m
‖x
i‖p
p]1
p}, where the supremum ranges over {x*∈X*; ‖x*‖≤1} and the infimum is taken over all sets {x
1,x
2, …,x
m} ⊂X such that Σ
i
=1/m
‖x
i‖>0. It follows immediately from [2] thatμ
p(X)>0 if and only ifX is finite dimensional. In this paper we find the exact values ofμ
p(X) for various spaces, and obtain some asymptotic estimates ofμ
p(X) for general finite dimensional Banach spaces.
This is a part of the author’s Ph.D. Thesis prepared at the Hebrew University of Jerusalem, under the supervision of Prof.
A. Dvoretzky and Prof. J. Lindenstrauss. 相似文献
9.
We prove a removal lemma for systems of linear equations over finite fields: let X
1, …, X
m
be subsets of the finite field F
q
and let A be a (k × m) matrix with coefficients in F
q
; if the linear system Ax = b has o(q
m−k
) solutions with x
i
∈ X
i
, then we can eliminate all these solutions by deleting o(q) elements from each X
i
. This extends a result of Green [Geometric and Functional Analysis 15 (2) (2005), 340–376] for a single linear equation in abelian groups to systems of linear equations. In particular, we also
obtain an analogous result for systems of equations over integers, a result conjectured by Green. Our proof uses the colored
version of the hypergraph Removal Lemma. 相似文献
10.
Yossi Moshe 《Journal d'Analyse Mathématique》2006,99(1):267-294
Let λ be the upper Lyapunov exponent corresponding to a product of i.i.d. randomm×m matrices (X
i)
i
0/∞
over ℂ. Assume that theX
i's are chosen from a finite set {D
0,D
1...,D
t-1(ℂ), withP(X
i=Dj)>0, and that the monoid generated byD
0, D1,…, Dq−1 contains a matrix of rank 1. We obtain an explicit formula for λ as a sum of a convergent series. We also consider the case
where theX
i's are chosen according to a Markov process and thus generalize a result of Lima and Rahibe [22].
Our results on λ enable us to provide an approximation for the numberN
≠0(F(x)n,r) of nonzero coefficients inF(x)
n.(modr), whereF(x) ∈ ℤ[x] andr≥2. We prove the existence of and supply a formula for a constant α (<1) such thatN
≠0(F(x)n,r) ≈n
α for “almost” everyn.
Supported in part by FWF Project P16004-N05 相似文献
11.
Let (X, Y) be an
d ×
-valued random vector and let (X1, Y1),…,(XN, YN) be a random sample drawn from its distribution. Divide the data sequence into disjoint blocks of length l1, …, ln, find the nearest neighbor to X in each block and call the corresponding couple (Xi*, Yi*). It is shown that the estimate mn(X) = Σi = 1n wniYi*/Σi = 1n wni of m(X) = E{Y|X} satisfies E{|mn(X) − m(X)|p}
0 (p ≥ 1) whenever E{|Y|p} < ∞, ln
∞, and the triangular array of positive weights {wni} satisfies supi ≤ nwni/Σi = 1n wni
0. No other restrictions are put on the distribution of (X, Y). Also, some distribution-free results for the strong convergence of E{|mn(X) − m(X)|p|X1, Y1,…, XN, YN} to zero are included. Finally, an application to the discrimination problem is considered, and a discrimination rule is exhibited and shown to be strongly Bayes risk consistent for all distributions. 相似文献
12.
Siddhartha Bhattacharya 《Israel Journal of Mathematics》2003,137(1):211-221
Let Γ be a discrete group and fori=1,2; letα
i be an action of Γ on a compact abelian groupX
i by continuous automorphisms ofX
i. We study measurable equivariant mapsf: (X
1,α
1)→(X
2,α
2), and prove a rigidity result under certain assumption on the order of mixing of the underlying actions. 相似文献
13.
Strongly Closed Subgraphs in a Distance-Regular Graph with <Emphasis Type="Italic">c</Emphasis><Subscript>2</Subscript> > 1 总被引:1,自引:1,他引:0
Akira Hiraki 《Graphs and Combinatorics》2008,24(6):537-550
Let Γ be a distance-regular graph of diameter d ≥ 3 with c
2 > 1. Let m be an integer with 1 ≤ m ≤ d − 1. We consider the following conditions:
Suppose that the condition (SC)
m
holds. Then it has been known that the condition (BB)
i
holds for all i with 1 ≤ i ≤ m. Similarly we can show that the condition (CA)
i
holds for all i with 1 ≤ i ≤ m. In this paper we prove that if the conditions (BB)
i
and (CA)
i
hold for all i with 1 ≤ i ≤ m, then the condition (SC)
m
holds. Applying this result we give a sufficient condition for the existence of a dual polar graph as a strongly closed subgraph
in Γ. 相似文献
(SC) m : For any pair of vertices at distance m there exists a strongly closed subgraph of diameter m containing them. | |
(BB) m : Let (x, y, z) be a triple of vertices with ∂ Γ (x, y) = 1 and ∂ Γ (x, z) = ∂ Γ (y, z) = m. Then B(x, z) = B(y, z). | |
(CA) m : Let (x, y, z) be a triple of vertices with ∂ Γ (x, y) = 2, ∂ Γ (x, z) = ∂ Γ (y, z) = m and |C(z, x) ∩ C(z, y)| ≥ 2. Then C(x, z) ∪ A(x, z) = C(y, z) ∪ A(y, z). |
14.
Let X
i
, i∈N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a mapping B→R. Under a central limit theorem assumption, an asymptotic evaluation of Z
n
= E (exp (n
Φ (∑
i
=1
n
X
i
/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [1]. In this paper, we show that the same asymptotic evaluation can be gotten without
the central limit theorem assumption.
Received: 19 September 1997 / Revised version:22 April 1999 相似文献
15.
Michal Sadowski 《Central European Journal of Mathematics》2004,2(2):332-338
Let E
Aff(Γ,G, m) be the set of affine equivalence classes of m-dimensional complete flat manifolds with a fixed fundamental group Γ and a fixed holonomy group G. Let n be the dimension of a closed flat manifold whose fundamental group is isomorphic to Γ. We describe E
Aff(Γ,G, m) in terms of equivalence classes of pairs (ε, ρ), consisting of epimorphisms of Γ onto G and representations of G in ℝ
m-n
. As an application we give some estimates of card E
Aff(Γ,G, m). 相似文献
16.
Oleg Pushin 《K-Theory》2004,31(4):307-321
In this short paper we investigate the relation between higher Chern classes and reduced power operations in motivic cohomology.
More precisely, we translate the well-known arguments [5] into the context of motivic cohomology and define higher Chern classes
cp,q : K p(X) → H2q-p (X,Z(q)) → H2q-p(X, Z/l(q)), where X is a smooth scheme over the base field k, l is a prime number and char(k) ≠ l. The same approach produces the classes for K-theory with coefficients as well. Let further Pi : Hm(X, Z/l(n)) → Hm+2i(l-1) (X, Z/l(n + i(l - 1))) denote the ith reduced power operation in motivic cohomology, constructed in [2]. The main result of the paper looks as follows. 相似文献
17.
Let X be a normed lattice and Y be the norm completion of X with a natural embedding π : X → Y . By the Kawai- Luxemburg theorem, X is embedded as an order dense set and π preserves all suprema and infima iff X satisfies the condition (Ao ) (i.e., the norm has pseudo σ-Lebesgue property). Let Xo be the largest ideal in X having the condition (Ao); let Y(o) be the band in Y generated by πXo and Y(1) be the complementary band to Y(o). The structure of Y and, in particular, of the bands Y(o) and Y(1) are studied. The conditions for Y(o) to be a projection band and πXo to be topologically dense in Y(o) are obtained. 相似文献
18.
Akira Hiraki 《Graphs and Combinatorics》2009,25(1):65-79
Let Γ be a distance-regular graph of diameter d ≥ 3 with c
2 > 1. Let m be an integer with 1 ≤ m ≤ d − 1. We consider the following conditions:
In [12] we have shown that the condition (SC)
m
holds if and only if both of the conditions (BB)
i
and (CA)
i
hold for i = 1,...,m. In this paper we show that if a
1 = 0 < a
2 and the condition (BB)
i
holds for i = 1,...,m, then the condition (CA)
i
holds for i = 1,...,m. In particular, the condition (SC)
m
holds. Applying this result we prove that a distance-regular graph with classical parameters (d, b, α, β) such that c
2 > 1 and a
1 = 0 < a
2 satisfies the condition (SC)
i
for i = 1,...,d − 1. In particular, either (b, α, β) = (− 2, −3, −1 − (−2)
d
) or holds. 相似文献
(SC) m : For any pair of vertices at distance m there exists a strongly closed subgraph of diameter m containing them. | |
(BB) m : Let (x, y, z) be a triple of vertices with ∂Γ(x, y) = 1 and ∂Γ(x, z) = ∂Γ(y, z) = m. Then B(x, z) = B(y, z). | |
(CA) m : Let (x, y, z) be a triple of vertices with and |C(z, x) ∩ C(z, y)| ≥ 2. Then C(x, z) ∪ A(x, z) = C(y, z) ∪ A(y, z). |
19.
A. K. Aleškevičienė 《Lithuanian Mathematical Journal》2006,46(2):129-145
Let X,X
1,X
2, … be independent identically distributed random variables, F(x) = P{X < x}, S
0 = 0, and S
n
=Σ
i=1
n
X
i
. We consider the random variables, ladder heights Z
+ and Z
− that are respectively the first positive sum and the first negative sum in the random walk {S
n
}, n = 0, 1, 2, …. We calculate the first three (four in the case EX = 0) moments of random variables Z
+ and Z
− in the qualitatively different cases EX > 0, EX < 0, and EX = 0.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 46, No. 2, pp. 159–179, April–June, 2006. 相似文献
20.
G. Baikunth Nath 《Annals of the Institute of Statistical Mathematics》1977,29(1):259-273
Summary Let (X, Y) be bivariate normally distributed with means (μ
1,μ
2), variances (σ
1
2
,σ
2
2
) and correlation betweenX andY equal to ρ. Let (X
i
,Y
i
) be independent observations on (X,Y) fori=1,2,...,n. Because of practical considerations onlyZ
i
=min (X
i
,Y
i) is observed. In this paper, as in certain routine applications, assuming the means and the variances to be known in advance,
an unbiased consistent estimator of the unknown distribution parameter ρ is proposed. A comparison between the traditional
maximum likelihood estimator and the unbiased estimator is made. Finally, the problem is extended to multivariate normal populations
with common mean, common variance and common non-negative correlation coefficient. 相似文献