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1.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献
2.
Let R be a prime ring with char R ≠ 2, L a non-central Lie ideal of R, d, g non-zero derivations of R, n ≥ 1 a fixed integer. We prove that if (d(x)x − xg(x))
n
= 0 for all x ∈ L, then either d = g = 0 or R satisfies the standard identity s
4 and d, g are inner derivations, induced respectively by the elements a and b such that a + b ∈ Z(R). 相似文献
3.
W. T. Gowers 《Israel Journal of Mathematics》1990,69(2):129-151
We show that if 0<ε≦1, 1≦p<2 andx
1, …,x
n is a sequence of unit vectors in a normed spaceX such thatE ‖∑
l
n
εi
x
l‖≧n
1/p, then one can find a block basisy
1, …,y
m ofx
1, …,x
n which is (1+ε)-symmetric and has cardinality at leastγn
2/p-1(logn)−1, where γ depends on ε only. Two examples are given which show that this bound is close to being best possible. The first
is a sequencex
1, …,x
n satisfying the above conditions with no 2-symmetric block basis of cardinality exceeding 2n
2/p-1. This sequence is not linearly independent. The second example is a sequence which satisfies a lowerp-estimate but which has no 2-symmetric block basis of cardinality exceedingCn
2/p-1(logn)4/3, whereC is an absolute constant. This applies when 1≦p≦3/2. Finally, we obtain improvements of the lower bound when the spaceX containing the sequence satisfies certain type-condition. These results extend results of Amir and Milman in [1] and [2].
We include an appendix giving a simple counterexample to a question about norm-attaining operators. 相似文献
4.
Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. Denote Dg=-divg?{\Delta_g=-{\rm div}_g\nabla} the Laplace–Beltrami operator. We establish some local gradient estimates for the positive solutions of the Lichnerowicz
equation
Dgu(x)+h(x)u(x)=A(x)up(x)+\fracB(x)uq(x)\Delta_gu(x)+h(x)u(x)=A(x)u^p(x)+\frac{B(x)}{u^q(x)} 相似文献
5.
We consider solutions ψ to equations of the form
in a sector Ω ofR
2. The basic assumptions are that the limitsa
ij(x)→δij,b
i(x)→0,c
i→E at infinity are achieved at certain rates and thatg decays faster than ψ. We then discuss the possible patterns of exponential decay for ψ in Ω.
NSERC University Research Fellow.
Research partially supported by USNEF grant MCS-83-01159. 相似文献
6.
A. Taskaraev 《Mathematical Notes》1998,64(5):658-662
The existence and uniqueness of a surface with given geometric characteristics is one of the important topical problems of
global differential geometry. By stating this problem in terms of analysis, we arrive at second-order elliptic and parabolic
partial differential equations. In the present paper we consider generalized solutions of the Monge-Ampère equation ||z
ij
|| = ϕ(x, z, p) in Λ
n
, wherez = z(x
1,...,z
n
) is a convex function,p = (p
1,...,P
n) = (∂z/∂x
1,...,ϖz/ϖx
n), andz
ij =ϖ
2
z/ϖx
i
ϖx
j. We consider the Cayley-Klein model of the space Λ
n
and use a method based on fixed point principle for Banach spaces.
Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 763–768, November, 1998. 相似文献
7.
Consider the standard non-linear regression model y
i
= g(x
i
, θ
0)+ε
i
, i = 1, ... ,n where g(x, θ) is a continuous function on a bounded closed region X × Θ, θ
0 is the unknown parameter vector in Θ ⊂ R
p
, {x
1, x
2, ... , x
n
} is a deterministic design of experiment and {ε1, ε2, ... , ε
n
} is a
sequence of independent random variables. This paper establishes the existences of M-estimates and the asymptotic uniform linearity of M-scores in a family of non-linear regression models when the errors are independent and identically distributed. This result
is then used to obtain the asymptotic distribution of a class of M-estimators for a large class of non-linear regression models. At the same time, we point out that Theorem 2 of Wang (1995)
(J. of Multivariate Analysis, vol. 54, pp. 227–238, Corrigenda. vol. 55, p. 350) is not correct.
This research was supported by the Natural Science Foundation of China (Grant No. 19831010 and grant No. 39930160) and the
Doctoral Foundation of China 相似文献
8.
G. I. Laptev 《Journal of Mathematical Sciences》2008,150(5):2384-2394
This paper deals with conditions for the existence of solutions of the equations
9.
Let L be the infinitesimal generator of an analytic semigroup on L2 (Rn) with suitable upper bounds on its heat kernels. Assume that L has a bounded holomorphic functional calculus on L2(Rn). In this paper,we define the Littlewood- Paley g function associated with L on Rn × Rn, denoted by GL(f)(x1, x2), and decomposition, we prove that ‖SL(f)‖p ≈‖GL(f)‖p ≈‖f‖p for 1 < p <∞. 相似文献
10.
L
p
approximation capability of radial basis function (RBF) neural networks is investigated. If g: R
+1 → R
1 and ∈ L
loc
p
(R
n
) with 1 ≤ p < ∞, then the RBF neural networks with g as the activation function can approximate any given function in L
p
(K) with any accuracy for any compact set K in R
n
, if and only if g(x) is not an even polynomial.
Partly supported by the National Natural Science Foundation of China (10471017) 相似文献
11.
In this paper we consider the problem of determining whether an unknown arithmetic circuit, for which we have oracle access,
computes the identically zero polynomial. This problem is known as the black-box polynomial identity testing (PIT) problem.
Our focus is on polynomials that can be written in the form f([`(x)]) = ?i = 1k hi ([`(x)]) ·gi ([`(x)])f(\bar x) = \sum\nolimits_{i = 1}^k {h_i (\bar x) \cdot g_i (\bar x)} , where each h
i
is a polynomial that depends on only ρ linear functions, and each g
i
is a product of linear functions (when h
i
= 1, for each i, then we get the class of depth-3 circuits with k multiplication gates, also known as ΣΠΣ(k) circuits, but the general case is much richer). When max
i
(deg(h
i
· g
i
)) = d we say that f is computable by a ΣΠΣ(k; d;ρ) circuit. We obtain the following results.
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