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1.
Guohui Tian 《K-Theory》2000,19(2):185-193
Let A be a complex Banach algebra. In this paper, we prove a periodicity theorem that K(S
2
A, G, )K(A, G,), where (A,G,) is a finite covariant system and K(A,G,) is an Abelian group associated with (A,G,). 相似文献
2.
S. Bagh 《Journal of Theoretical Probability》1998,11(4):857-868
Let {gk}be a sequence of normally distributed independent random variables with mathematical expectation zero and variance unity. Let
k
(t ) (k = 0, 1, 2,...) be the normalized Jacobi polynomials orthogonal with respect to the interval [ – 1, 1 ]. Then it is proved that the average number of real roots of the random equations,
k=0
n
gkk(1)=C where Cis a constant, is asymptotically equal to n/in the same interval when nis large and even for C as long as C=O (n
2). 相似文献
3.
Let W be a non-negative random variable with EW=1, and let {W
i
} be a family of independent copies of W, indexed by all the finite sequences i=i
1i
n
of positive integers. For fixed r and n the random multiplicative measure
n
r
has, on each r-adic interval
at nth level, the density
with respect to the Lebesgue measure on [0,1]. If EW log Wr, the sequence {
n
r
}
n
converges a.s. weakly to the Mandelbrot measure
r
. For each fixed 1n, we study asymptotic properties for the sequence of random measures {
n
r
}
r
as r. We prove uniform laws of large numbers, functional central limit theorems, a functional law of iterated logarithm, and large deviation principles. The function-indexed processes
is a natural extension to a tree-indexed process at nth level of the usual smoothed partial-sum process corresponding to n=1. The results extend the classical ones for {
1
r
}
r
, and the recent ones for the masses of {
r
}
r
established in Ref. 23. 相似文献
4.
Maria Specovius-Neugebauer 《Acta Appl Math》1994,37(1-2):195-203
For n2 we consider the Stokes problem in n, -u + p=f, -divu=g, in weighted Soboiev spaces H
6
m,r
, where the weights are proportional to (1+|x|). We prove the existence of weak solutions for any K, whereK is a discrete set of critical values. Furthermore, we characterize the solutions of the homogeneous problem.This research was supported by the DFG research group Equations of Hydrodynamics, Universities of Bayreuth and Paderborn. 相似文献
5.
Z. A. Chanturiya 《Mathematical Notes》1978,23(2):123-127
Let (n) be a system, close to the orthonormal complete system (x
n). An estimate is obtained for the deviation of the system {fn}, obtained from {n} by Schmidt's method, from the system {xn}. This estimate is used to show that, in any LP(–1,1), withp (1,4/3] [4,), and for any >e¦4 = i,13..., there exists an orthogonal algebraic system (P
n
(x))
n=0
, forming a basis in LP and such that n = degP
n
(x) n for n>no(p,).Translated from Matematicheskie Zametki, Vol. 23, No. 2, pp. 223–230, February, 1978. 相似文献
6.
J. A. Morrison 《Queueing Systems》1993,14(1-2):215-237
In this paper the steady-state behavior of many symmetric queues, under the head of the line processor-sharing discipline, is investigated. The arrival process to each of n queues is Poisson, with rateA, and each queue hasr waiting spaces. A job arriving at a full queue is lost. The queues are served by a single exponential server, which has a mean raten, and splits its capacity equally amongst the jobs at the head of each nonempty queue. The normal traffic casep=/< 1 is considered, and it is assumed thatn1 andr= 0(1). A 2-term asymptotic approximation to the loss probabilityL is derived, and it is found thatL = 0(n
–r
), for fixedp. If6=(1–p)/p 1, then the approximation is valid if n2 1 and (r+ 1)2n, and in this caseL r!/(n)r. Numerical values ofL are obtained forr = 1,2,3,4 and 5,n = 1000,500 and 200, and various values ofp< 1. Very small loss probabilities may be obtained with appropriate values of these parameters. 相似文献
7.
Let
, the parameter space, be an open subset ofR
k
,k1. For each
, let the r.v.'sX
n
,n=1, 2,... be defined on the probability space (X, P
) and take values in (S,S,L) whereS is a Borel subset of a Euclidean space andL is the -field of Borel subsets ofS. ForhR
k
and a sequence of p.d. normalizing matrices
n
=
n
k × k
(0 set
n
*
= * = 0 +
n
h, where 0 is the true value of , such that *,
. Let
n
(*, *)( be the log-likelihood ratio of the probability measure
with respect to the probability measure
, whereP
n
is the restriction ofP
over
n
= (X
1,X
2,...,X
n
. In this paper we, under a very general dependence setup obtain a rate of convergence of the normalized log-likelihood ratio statistic to Standard Normal Variable. Two examples are taken into account. 相似文献
8.
Let be the triangulation generated by a uniform three direction mesh of the plane. Let
6 be the Powell-Sabin subtriangulation obtained by subdividing each triangleT by connecting each vertex to the midpoint of the opposite side.Given a smooth functionu, we construct a piecewise polynomial function C
r
(2) of degreen=2r (resp. 2r+1) forr odd (resp. even) in each triangle of
6, interpolating derivatives ofu up to orderr at the vertices of. 相似文献
9.
Henry Berbee 《Probability Theory and Related Fields》1981,56(4):531-536
Summary Let S
n
=
1+...+
n
, n1, be the partial sums of stationary, dependent random variables in
m
. The probability space can be partitioned into I
t
I
r
, where I
t
= {S
n} and I
r
={each S
n
is limit point of (S
n)n1}. This result follows from the inclusion{S
n
> for n>0}I
t
a.s., which is obtained by using Kac's inequality. 相似文献
10.
Masahiro Ohno 《Geometriae Dedicata》1992,44(3):335-347
Let : X Y be a morphism of smooth projective varieties over an algebraically closed field k of characteristic not equal to 2 whose closed fibres are all isomorphic to
r
P1 and let ': X
r
P1 be a surjective morphism. This article gives a sufficient condition concerning ' and Y under which X is isomorphic to Y×
r
P1. 相似文献
11.
Joseph C. Dunn 《Applied Mathematics and Optimization》1982,9(1):303-335
Extremals for constrained minimization problems, min
F, are classified according to the growth properties of the linear functionalF() restricted to . Various singular and nonsingular extremal types are investigated in detail for the special case where = {measurableu(·): [0, 1] U},U = a bounded polyhedral convex set in
m
, andF is understood in Fréchet's sense relative to anL
p
norm withp [1, ). The analysis yields newL
p
minimization corollaries of recently developed general convergence rate theories for conditional and projected gradient methods, and a Newton method for constrained minimization. These results help to explain trends in the behavior of computational procedures for certain large scale structured nonlinear programs in
k
ask increases to , with particular application to a large class of optimal control problems with linearly constrained inputs; control problems with bang-bang solutions are considered at some length.Investigation supported by NSF Research Grants ECS-8005958 and ENG 78-03385. 相似文献
12.
B. T. Polyak 《Set-Valued Analysis》2001,9(1-2):159-168
Let f: XY be a nonlinear differentiable map, X,Y are Hilbert spaces, B(a,r) is a ball in X with a center a and radius r. Suppose f
(x) is Lipschitz in B(a,r) with Lipschitz constant L and f
(a) is a surjection: f
(a)X=Y; this implies the existence of >0 such that f
(a)*
yy, yY. Then, if r,/(2L), the image F=f(B(a,)) of the ball B(a,) is convex. This result has numerous applications in optimization and control. First, duality theory holds for nonconvex mathematical programming problems with extra constraint x–a. Special effective algorithms for such optimization problems can be constructed as well. Second, the reachability set for small power control is convex. This leads to various results in optimal control. 相似文献
13.
E. P. Fadeeva 《Journal of Mathematical Sciences》1991,53(1):87-94
We present an explicit solution of the problem of optimal linear filtering: the recovery of the useful signal(s) at the instantt+, (>0,<0, or=0) from known values of the received signal(s)=(s)+(s) in the past, i.e., at the instantt–s, s0. In doing so we assume the random processes(s) and /gr(s) are stationary and jointly stationary, while the stationary process of noise (s) with zero mean is assumed to be mutually correlated and jointly stationary with the process(s) under the assumption that there exists a common spectral densityf() for these processes.Translated fromTeoriya Sluchaínykh Protsessov, Vol. 14, pp. 83–91, 1986. 相似文献
14.
Angelo Barone-Netto Gianluca Gorni Gaetano Zampieri 《NoDEA : Nonlinear Differential Equations and Applications》1996,3(3):287-303
We give a complete answer to the problem of the finite decidability of the local extremality character of a real analytic function at a given point, a problem that found partial answers in some works by Severi and ojasiewicz. Consider a real analytic functionf defined in a neighbourhood of a pointx
0R
n
. Restrictf to the spherical surface centered inx
0 and with radiusr0 and take its infimumm(r) and its supremumM(r). We establish some properties ofm(r) andM(r) for smallr>0. In particular, we prove that they have asymptotic expansions of the formf(x
0)+c·(r
+o(r
)) asr0 for a realc and a rational 1 (of course the parameters will usually be different form andM).This work was supported by the Brazilian Fundação Carlos Chagas and by the Italian Consiglio Nazionale delle Ricerche. 相似文献
15.
A. K. Guts 《Mathematical Notes》1973,13(5):411-415
Let n be n-dimensional Lobachevskii space, and {lx:x n} be a family of lines, parallel to a linel
0, 0n (in a given direction). Let {cx:Xn} be a family of circular cones in n of opening with axes lX and vertex X. Then, iff:nn(n>2) is a bijective mapping andf(Cx)=C
f(x), it follows thatf is a motion in the space n.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 687–694, May, 1973. 相似文献
16.
Many global optimization problems can be formulated in the form min{c(x, y): x X, y Y, (x, y) Z, y G} where X, Y are polytopes in
p
,
n
, respectively, Z is a closed convex set in p+n, while G is the complement of an open convex set in
n
. The function c:
p+n
is assumed to be linear. Using the fact that the nonconvex constraints depend only upon they-variables, we modify and combine basic global optimization techniques such that some new decomposition methods result which involve global optimization procedures only in
n
. Computational experiments show that the resulting algorithms work well for problems with smalln. 相似文献
17.
V. B. Semenyuk 《Ukrainian Mathematical Journal》1994,46(9):1345-1355
For unbounded domains with external power-type peaks, we propose a method for the approximation of functionsf(x)
w
p
r
() by polynomial splines in the metricw
p
r
(), 1pq, and present the corresponding estimates.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1224–1233, September, 1994. 相似文献
18.
We consider in Hilbert spaces linear ill-posed problems Ax = y with noisy data y
satisfying y
–y. Regularized approximations x
r
to the minimum-norm solution x
of Ax = y are constructed by continuous regularization methods or by iterative methods. For the choice of the regularization parameter r (the stopping index n in iterative methods) the following monotone error rule (ME rule) is used: we choose r = r
ME (n = n
ME) as the largest r-value with the guaranteed monotonical decrease of the error x
r
– x
for r [0, r
ME] (x
n
– x
<#60; x
n–1
– x
for n = 1, 2, ..., n
ME). Main attention is paid to iterative methods of gradient type and to nonstationary implicit iteration methods. As shown, the ME rule leads for many methods to order optimal error bounds. Comparisons with other rules for the choice of the stopping index are made and numerical examples are given.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
19.
Let {W(s)}
s
0 be a standard Wiener process. The supremum of the squared Euclidian norm Y (t)2, of the R2-valued process Y(t)=(1/t
W(t), {12/t
3 int0
t
s dW (s)– {3/t} W(t)), t [, 1], is the asymptotic, large sample distribution, of a test statistic for a change point detection problem, of appearance of linear trend. We determine the asymptotic behavior P {sup
t
[, 1] Y(t)2 > u as u , of this statistic, for a fixed (0,1), and for a moving = (u) 0 at a suitable rate as u . The statistical interest of our results lie in their use as approximate test levels. 相似文献
20.
We show that the system {e
–z
/(1 + z
2) : > 0} is complete in a class of functions analytic in an angle. 相似文献