共查询到20条相似文献,搜索用时 78 毫秒
1.
Suppose thatX andY are real Banach spaces,U ⊂X is an open bounded set star-shaped with respect to some point,n, k ∈ ℕ,k <n, andMn, k (U,Y) is the sharp constant in the Markov type inequality for derivatives of polynomial mappings. It is proved that for anyM ≥M
n,k
(U, Y) there exists a constantB > 0 such that for any functionf ∈C
n
(U, Y) the following inequality holds:
The constantM =M
n−1,k
(U, Y) is best possible in the sense thatM
n−1,k
(U, Y) = infM, where inf is taken over allM such that for someB > 0 the estimate holds for allf ∈C
n
(U, Y).
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 332–342, March, 1998.
This research was partially supported by the International Science Foundation under grant No. U92000. and by the State Committee
of the Ukraine for Science and Technology. 相似文献
2.
If a setX ⊂E
n has non-emptyk-dimensional interior, or if some point isk-dimensional surrounded, then the classic theorem of E. Steinitz may be extended. For example ifX ⊂E
n has int
k
X ≠ 0, (0 ≦k≦n) and ifp ɛ int conX, thenp ɛ int conY for someY ⊂X with cardY≦2n−k+1. 相似文献
3.
LetX be a 1-connected space with Moore loop space ΩX. By a well-known theorem of J. W. Milnor and J. C. Moore [7] the Hurewicz homomorphism induces an isomorphism of Hopf algebrasU(π*(ΩX) ⊗Q)→H
*(ΩX;Q). HereU(−) denotes the universal enveloping algebra and the Lie bracket on π*(ΩX) ⊗Q is given by the Samelson product.
Assume now thatX is the geometric realization of anr-reduced simplicial set,r≥3. LetL
X
be a differential graded free Lie algebra over ℤ describing the tame homotopy type ofX according to the theory of [4]. Then the main result of the present paper is the construction of a sequence of morphisms
of differential graded algebras betwenU(L
X
) and the algebraC U
*(ΩX)z of normalized cubical chains on ΩX such that the induced morphisms on homology with coefficientsR
k
are isomorphismsH
r-1+l
(U(L
x
);R
k
) ≅H
r-1+l
C U
*(ΩX);R
k
) forl≤k; hereR
0⊆R
1⊆… is a tame ring system, i. e.R
k
)⊑Q and each primep with 2p−3≤k is invertible inR
k
.
However, it is no longer true that the Pontrjagin algebraH
≤r−1+k
(ΩX; R
k
) of ΩX in degrees ≤r−1+k is determined by π*(ΩX) or by a cofibrant (-fibrant) modelM of π*(ΩX) as will be shown by an example. But there is a filtration onH
≤r−1+k
(ΩX; R
k
) such that the associated graded algebra is isomorphic toH
≤r−1+k
(U(M); R
k
).This will be proved by using a filtered Lie algebra model ofX constructed from a bigraded model of π*(ΩX).
Supported by a CNRS grant and PROCOPE
Supported by PROCOPE 相似文献
4.
David Mejzler 《Israel Journal of Mathematics》1987,57(1):1-27
LetX
1, ...,X
n be independent random variables, letF
i be the distribution function ofX
i (1≦i≦n) and letX
1n
≦... ≦X
nn be the corresponding order statistics. We consider the statisticsX
kn, wherek=k(n),k/n → 1 andn−k → ∞. Under some additional restrictions concerning the behaviour of the sequences {a
n>0,b
n,k(n),F
n} we characterize the class of all distribution functionsH such that Prob{(X
kn
−b
n
)/a
n
<x)}→H.
Dedicated to the Memory of N. V. Smirnov (1900–1966) 相似文献
5.
LetK be a field, charK=0 andM
n
(K) the algebra ofn×n matrices overK. If λ=(λ1,…,λ
m
) andμ=(μ
1,…,μ
m
) are partitions ofn
2 let
wherex
1,…,x
n
2,y
1,…,y
n
2 are noncommuting indeterminates andS
n
2 is the symmetric group of degreen
2.
The polynomialsF
λ, μ
, when evaluated inM
n
(K), take central values and we study the problem of classifying those partitions λ,μ for whichF
λ, μ
is a central polynomial (not a polynomial identity) forM
n
(K).
We give a formula that allows us to evaluateF
λ, μ
inM(K) in general and we prove that if λ andμ are not both derived in a suitable way from the partition δ=(1, 3,…, 2n−3, 2n−1), thenF
λ, μ
is a polynomial identity forM
n
(K). As an application, we exhibit a new class of central polynomials forM
n
(K).
In memory of Shimshon Amitsur
Research supported by a grant from MURST of Italy. 相似文献
6.
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
7.
Richard Resco 《Israel Journal of Mathematics》1980,35(3):215-221
LetD be a division algebra over a fieldk, letn be an arbitrary positive integer, and letk(x
1,...,x
n) denote the rational function field inn variables overk. In this note we complete previous work by proving that the following three conditions are equivalent: (i) there exists an
integerj such that the matrix ringM
j(D) contains a commutative subfield which has transcendence degreen overk; (ii) K dim (D⊗k
k(x
1,...,x
n
)) =n; (iii) gl. dim (D⊗k
k(x
1,...,x
n
)) =n. The crucial tool in the proof of this theorem is the Nullstellensatz forD[x
1,...,x
n] which was obtained by Amitsur and Small. 相似文献
8.
J. Dippon 《Mathematical Methods of Statistics》2008,17(2):138-145
Assume that the function values f(x) of an unknown regression function f: ℝ → ℝ can be observed with some random error V. To estimate the zero ϑ of f, Robbins and Monro suggested to run the recursion X
n+1 = X
n
− a/n
Y
n
with Y
n
= f(X
n
) − V
n
. Under regularity assumptions, the normalized Robbins-Monro process, given by (X
n+1 − ϑ)/√Var(X
n+1, is asymptotically standard normal. In this paper Edgeworth expansions are presented which provide approximations of the
distribution function up to an error of order o(1/√n) or even o(1/n). As corollaries asymptotic confidence intervals for the unknown parameter ϑ are obtained with coverage probability errors of order O(1/n). Further results concern Cornish-Fisher expansions of the quantile function, an Edgeworth correction of the distribution
function and a stochastic expansion in terms of a bivariate polynomial in 1/√n and a standard normal random variable. The proofs of this paper heavily rely on recently published results on Edgeworth expansions
for approximations of the Robbins-Monro process.
相似文献
9.
M. Rudelson 《Israel Journal of Mathematics》1995,89(1-3):189-204
We prove a variant of a theorem of N. Alon and V. D. Milman. Using it we construct for everyn-dimensional Banach spacesX andY a measure space Ω and two operator-valued functionsT: Ω→L(X, Y),S: Ω→L(Y, X) so that ∫Ω
S(ω)oT(ω)dω is the identity operator inX and ∫Ω||S(ω)||·||T(ω)||dω=O(n
α
) for some absolute constantα<1.
We prove also that any subset of the unitn-cube which is convex, symmetric with respect to the origin and has a sufficiently large volume possesses a section of big
dimension isomorphic to ak-cube.
Research supported in part by a grant of the Israel Academy of Sciences. 相似文献
10.
Hans-Joachim Baues 《Inventiones Mathematicae》1998,132(3):467-489
11.
A. Arias 《Israel Journal of Mathematics》1988,63(2):139-148
We show that for 1 ≦p < ∞,p ≠ 2, ifɛ > 0 is small enough andX ≦L
p is the span ofn independent Rademacher functions orn independent Gaussian random variables, then any superspaceY ofX satisfyingd(Y,L
p
m
) ≦ 1 +ɛ has dimension larger thanr
n, wherer =r(ɛ, p) > 1.
This forms part of the author’s doctoral dissertation prepared at Texas A&M University under the direction of Professor W.
B. Johnson.
Supported in part by NSF DMS-85 00764. 相似文献
12.
Sam Gutmann 《Journal of multivariate analysis》1978,8(4):573-578
Let (X1, X2,…, Xk, Y1, Y2,…, Yk) be multivariate normal and define a matrix C by Cij = cov(Xi, Yj). If (i)
(X1,…, Xk) =
(Y1,…, Yk) and (ii) C is symmetric positive definite, then 0 < varf(X1,…, Xk) < ∞ corr(f(X1,…, Xk),f(Y1,…, Yk)) > 0. Condition (i) is necessary for the conclusion. The sufficiency of (i) and (ii) follows from an infinite-dimensional version, which can also be applied to a pair of jointly normal Brownian motions. 相似文献
13.
Central limit theorem for integrated square error of kernel estimators of spherical density 总被引:1,自引:0,他引:1
LetX
1,…,X
n
be iid observations of a random variableX with probability density functionf(x) on the q-dimensional unit sphere Ωq in Rq+1,q ⩾ 1. Let
be a kernel estimator off(x). In this paper we establish a central limit theorem for integrated square error off
n
under some mild conditions. 相似文献
14.
Let K
0(Var
k
) be the Grothendieck ring of algebraic varieties over a field k. Let X, Y be two algebraic varieties over k which are piecewise isomorphic (i.e. X and Y admit finite partitions X
1, ..., X
n
, Y
1, ..., Y
n
into locally closed subvarieties such that X
i
is isomorphic to Y
i
for all i ≤ n), then [X] = [Y] in K
0(Var
k
). Larsen and Lunts ask whether the converse is true. For characteristic zero and algebraically closed field k, we answer positively this question when dim X ≤ 1 or X is a smooth connected projective surface or if X contains only finitely many rational curves. 相似文献
15.
Let {Xn, n1} be a sequence of independent random variables (r.v.'s) with a common distribution function (d.f.) F. Define the moving maxima Yk(n)=max(Xn−k(n)+1,Xn−k(n)+2,…,Xn), where {k(n), n1} is a sequence of positive integers. Let Yk(n)1 and Yk(n)2 be two independent copies of Yk(n). Under certain conditions on F and k(n), the set of almost sure limit points of the vector consisting of properly normalised Yk(n)1 and Yk(n)2 is obtained. 相似文献
16.
Copositive approximation of periodic functions 总被引:1,自引:0,他引:1
Let f be a real continuous 2π-periodic function changing its sign in the fixed distinct points y
i
∈ Y:= {y
i
}
i∈ℤ such that for x ∈ [y
i
, y
i−1], f(x) ≧ 0 if i is odd and f(x) ≦ 0 if i is even. Then for each n ≧ N(Y) we construct a trigonometric polynomial P
n
of order ≦ n, changing its sign at the same points y
i
∈ Y as f, and
where N(Y) is a constant depending only on Y, c(s) is a constant depending only on s, ω
3(f, t) is the third modulus of smoothness of f and ∥ · ∥ is the max-norm.
This work was done while the first author was visiting CPT-CNRS, Luminy, France, in June 2006. 相似文献
17.
It is shown that for real,m x n matricesA andB the system of matrix equationsAX=B, BY=A is solvable forX andY doubly stochastic if and only ifA=BP for some permutation matrixP. This result is then used to derive other equations and to characterize the Green’s relations on the semigroup Ω
n
of alln x n doubly stochastic matrices. The regular matrices in Ω
n
are characterized in several ways by use of the Moore-Penrose generalized inverse. It is shown that a regular matrix in Ω
n
is orthostochastic and that it is unitarily similar to a diagnonal matrix if and only if it belongs to a subgroup of Ω
n
. The paper is concluded with extensions of some of these results to the convex setS
n of alln x n nonnegative matrices having row and column sums at most one.
His research was supported by the N. S. F. Grant GP-15943. 相似文献
18.
Anders Grimvall 《Stochastic Processes and their Applications》1973,1(4):335-368
Starting from a real-valued Markov chain X0,X1,…,Xn with stationary transition probabilities, a random element {Y(t);t[0, 1]} of the function space D[0, 1] is constructed by letting Y(k/n)=Xk, k= 0,1,…,n, and assuming Y (t) constant in between. Sample tightness criteria for sequences {Y(t);t[0,1]};n of such random elements in D[0, 1] are then given in terms of the one-step transition probabilities of the underlying Markov chains. Applications are made to Galton-Watson branching processes. 相似文献
19.
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
20.
S. P. Zhou 《Israel Journal of Mathematics》1992,78(1):75-83
The present paper gives a converse result by showing that there exists a functionf ∈C
[−1,1], which satisfies that sgn(x)f(x) ≥ 0 forx ∈ [−1, 1], such that {fx75-1} whereE
n
(0)
(f, 1) is the best approximation of degreen tof by polynomials which are copositive with it, that is, polynomialsP withP(x(f(x) ≥ 0 for allx ∈ [−1, 1],E
n(f) is the ordinary best polynomial approximation off of degreen. 相似文献