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1.
We prove that a convex function f C[–1, 1] can be approximated by convex polynomials p
n
of degree n at the rate of 3(f, 1/n). We show this by proving that the error in approximating f by C 2 convex cubic splines with n knots is bounded by 3(f, 1/n) and that such a spline approximant has an L
third derivative which is bounded by n 33(f, 1/n). Also we prove that if f C 2[–1, 1], then it is approximable at the rate of n
–2 ( f, 1/ n) and the two estimates yield the desired result.Communicated by Ronald A. DeVore. 相似文献
2.
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3.
We show that the most of the time, most poles of diagonal multipoint Padé or best rational approximants to functions admitting fast rational approximation, leave the region of meromorphy. Following is a typical result: Let f be single-valued and analytic in C S, where cap( S)=0. Let { n
j
}
j=1
be an increasing sequence of positive integers with n
j+1/ n
j
1 as j. Then there exists an infinite sequence L of positive integers such that as j, jL the total multiplicity of poles of any sequence of type ( n
j
, n
j
) multipoint Padé or best rational approximants to f, is o( n
j
) in any compact K in which f is meromorphic. The sequence L is independent of the particular sequence of multipoint Padé or best approximants, and yields the same behavior for near-best approximants. If the errors of best approximation on some compact set satisfy a weak regularity condition, then we may take L={1,2,3,}.Communicated by Edward B. Saff. 相似文献
4.
If f is a self mapping on a closed convex subset K of a separated quasicomplete locally convex linear topological space E such that (i) E is strictly convex, (ii) f (K) is contained in a compact subset of K and (iii) f satisfies a contraction condition, then it is shown that for each xK, the sequence of { U
n
(x)}
n
=1 of iterates, where U
KK is defined by U
(y)=f(y)+(1-) y, yK, converges to a fixed point of f. 相似文献
5.
Let X and Y be Hausdorff spaces and denote by M (X) and M (Y) the corresponding spaces of finite and non-negative Borel measures, endowed with the weak topology. A Borel map : XY induces the map
: M (X)M (Y). We give necessary and sufficient conditions for
to be open. In case of being a surjection between Suslin spaces,
is open if and only if is. 相似文献
6.
A 2-periodic continuous real function f is said to be periodically monotone if it has the following property: there exist number t
1t
2t
3t
1+2 such that f is nonincreasing for t
1t
2 and nondecreasing in t
2tt
3. For any 2-periodic, integrable real function g with
0
2
| g( t| dt) we define
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7.
Let C be a simply connected domain, 0, and let n, nN, be the set of all polynomials of degree at most n. By n() we denote the subset of polynomials p n with p(0)=0 and p( D), where D stands for the unit disk { z: | z|<1}, and=" by=">1},>we denote the maximal range of these polynomials. Let f be a conformal mapping from D onto , f(0)=0. The main theme of this note is to relate n (or some important aspects of it) to the images f
s
( D), where f
s
(z):=f[(1–s)z], 0 s<1. for=" instance=" we=" prove=" the=" existence=" of=" a=" universal=">1.> c
0 such that, for n2 c
0, 相似文献
8.
QUADRATICESTIMATORSOFQUADRATICFUNCTIONSWITHPARAMETERSINNORMALLINEARMODELS¥WUQIGUANG(吴启光)(InstituteofSystemeScience,theChinese... 相似文献
9.
. 0 pq, 1–1/ p+1/ p0. f( x) — n, [–1,1],
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10.
A pointwise version of the Howard-Bezem notion of hereditary majorization is introduced which has various advantages, and its relation to the usual notion of majorization is discussed. This pointwise majorization of primitive recursive functionals (in the sense of Gödel's T as well as Kleene/Feferman's) is applied to systems of intuitionistic and classical arithmetic ( H and H
c) in all finite types with full induction as well as to the corresponding systems with restricted induction and c. 1) |
H and are closed under a generalized fan-rule. For a restricted class of formulae this also holds forH
c andc.
| 2) |
We give a new and very perspicuous proof that for each one can construct a functional such that
is a modulus of uniform continuity for on {1n(nn)}. Such a modulus can also be obtained by majorizing any modulus of pointwise continuity for .
| 3) |
The type structure of all pointwise majorizable set-theoretical functionals of finite type is used to give a short proof that quantifier-free choice with uniqueness (AC!)1,0-qf. is not provable within classical arithmetic in all finite types plus comprehension [given by the schema (C):y
0x
(yx=0A(x)) for arbitraryA], dependent -choice and bounded choice. Furthermore separates several -operators.
| 相似文献
11.
,
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12.
Let B n be a domain and (y), y B and arbitrary positive, continuous function. If p, s (0, +), denote by H
s,
p
( T
B
) the class of the functions f(z) f(x+iy), holomorphic in the tube domain
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13.
The Navier-Stokes equations for compressible barotropic fluid in 1 D with the mass
force under zero velocity boundary conditions are studied. We prove the uniform upper and
lower bounds for the density as well as the uniform in time L
2()-estimates for
x
and
u
x
( u is the velocity).
Moreover, a collection of the decay rate estimates for -
(with
being the stationary density) and u
in 2()-norm and
H
1()-norm as time
t are
established. The results are given for general state function
p() (but mainly monotone) and
viscosity coefficient
µ() of arbitrarily fast (or slow) growth as well as for the large data. 相似文献
14.
A continued fractal
is a curve which is associated to a real number [0, 1]. Properties of the continued fraction expansion of appear as geometrical properties of Q
. It is shown how number theoretic properties of affect topological and geometric properties of Q
such as existence, continuity, Hausdorff dimension, and embeddedness.Communicated by Michael F. Barnsley. 相似文献
15.
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16.
Given two side-payment games v and w, both defined for the same finite player-set N, the following three welfare criteria are characterized in terms of the data v and w: (A) For every y C(w) there exists x C(v) such that yx; (A) For every xC(v) there exists yC(w) such that yx; and (B) There exist yC(w) and xC(v) such that yx. (Here C(v) denotes the core of v.) Given two non-side-payment games v and w, sufficient conditions for the criteria (A) and (B) are established, by observing that an ordinal convex game has a large core.In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986. 相似文献
17.
We study the large-time behavior and rate of convergence to the invariant measures of the processes d X
( t)= b(X)
( t)) d t + ( X
( t)) d B(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/ 2 , the transition density has a good lower bound and when the process has run for about exp( – )/ 2, it is very close to the invariant measure. Let L
=( 2/2) – U · be a second-order differential operator on d. Under suitable conditions, L
z has the discrete spectrum
- \lambda _2^\varepsilon ...and lim \varepsilon ^2 log \lambda _2^\varepsilon = - \Lambda \hfill \\ \varepsilon \to 0 \hfill \\ \end{gathered} $$
" align="middle" vspace="20%" border="0"> 相似文献
18.
R
n n- , : R nPR n/ o - . —
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19.
If { W(t): 0 t} denotes standard Brownian motion and then with probability one the random sequence
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