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1.
Summary This paper is concerned with the rate of convergence to zero of theL
pmetrics
np1p, constructed out of differences between distribution functions, for departure from normality for normed sums of independent and identically distributed random variables with zero mean and unit variance. It is shown that the
np are, under broad conditions, asymptotically equivalent in the strong sense that, for 1p, p,
np/np is universally bounded away from zero and infinity asn. 相似文献
2.
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
3.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ...,
n
) = 1(1) + ... +
n
(
n
), where
i
(
i
) are ordinary moduli of continuity that depend on one variable. In the case where
i
(
i
) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L
2 for (1, ...,
n
) = 1(1) + ... +
n
(
n
); (ii) in the integral metric L
p (p 1) for (1, ...,
n
) = c
11 + ... + c
n
n
; (iii) in the integral metric L
(2, ..., 2, 2r) (r = 2, 3, ...) for (1, ...,
n
) = 1(1) + ... +
n – 1(
n – 1) + c
n
n
. 相似文献
4.
Marcel Erné 《Algebra Universalis》1988,25(1):290-321
By a result of Pigozzi and Kogalovskii, every algebraic latticeL having a completely join —irreducible top element can be represented as the lattice L() of equational theories extending some fixed theory . Conversely, strengthening a recent result due to Lampe, we show that such a representationL=L() forcesL to satisfy the following condition: if the top element ofL is the join of a nonempty subsetB ofL then there are elementsb..., B such thata=(... (((b1 a) b2) a) ... bn) a for alla L. In presence of modularity, this equation reduces to the identitya=(a b1) ... (a bn). Motivated by these facts, we study several weak forms of distributive laws in arbitrary lattices and related types of prime elements. The main tool for applications to universal algebra is a generalized version of Lampe's Zipper Lemma.Presented by Ralph Freese. 相似文献
5.
An iterative process for nonlinear lipschitzian and strongly accretive mappings in uniformly convex and uniformly smooth Banach spaces 总被引:2,自引:0,他引:2
Lei Deng 《Acta Appl Math》1993,32(2):183-196
SupposeX is ans-uniformly smooth Banach space (s > 1). LetT: X X be a Lipschitzian and strongly accretive map with constantk (0, 1) and Lipschitz constantL. DefineS: X X bySx=f–Tx+x. For arbitraryx
0
X, the sequence {xn}
n=1
is defined byx
n+1=(1–
n)xn+
nSyn,y
n=(1–
n)xn+
nSxn,n0, where {n}
n=0
, {n}
n=0
are two real sequences satisfying: (i) 0
n
p–1
2–1s(k+k
n–L
2n)(w+h)–1 for eachn, (ii) 0
n
p–1
min{k/L2, sk/(+h)} for eachn, (iii) n n=, wherew=b(1+L)s andb is the constant appearing in a characteristic inequality ofX, h=max{1, s(s-l)/2},p=min {2, s}. Then {xn}
n=1
converges strongly to the unique solution ofTx=f. Moreover, ifp=2,
n=2–1s(k +k–L2)(w+h)–1, and
n= for eachn and some 0 min {k/L2, sk/(w + h)}, then xn + 1–q
n/sx1-q, whereq denotes the solution ofTx=f and=(1 – 4–1s2(k +k – L
2)2(w + h)–1
(0, 1). A related result deals with the iterative approximation of Lipschitz strongly pseudocontractive maps inX. SupposeX ism-uniformly convex Banach spaces (m > 1) andc is the constant appearing in a characteristic inequality ofX, two similar results are showed in the cases of L satisfying (1 – c2)(1 + L)m < 1 + c – cm(l – k) or (1 – c2)Lm < 1 + c – cm(1 – s). 相似文献
6.
Anders Barrlund 《BIT Numerical Mathematics》1991,31(2):358-363
LetA andA+A be Hermitian positive definite matrices. Suppose thatA=LDL
H and (A+A)=(L+L)(D+D)(L+L)H are theLDL
H decompositons ofA andA+A, respectively. In this paper upper bounds on |D|
F
and |L|
F
are presented. Moreover, perturbation bounds are given for theLU decomposition of a complexn ×n matrix. 相似文献
7.
A. G. Areshkina 《Mathematical Notes》1998,64(2):154-158
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have
; this measure defines an indefinite integral over the measure onL
2
(T, ,). We prove that if {
n
(t)}
n
=1/
is an orthonormal basis inL
2 and
n
(e)=e
n
(t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL
2 is uniquely expandable in a series(e)=
n
=1/
n
n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies
n
=1/
n
/2
<. In the caseL
2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L
2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998. 相似文献
8.
L. I. Bausov 《Mathematical Notes》1968,4(2):612-617
Let Cn (, ) be the upper bound for deviations of periodic functions which form the Zygmund class Z,0 0<<2 from a class of positive linear operators. A study is made of the conditions under which there exists a limit
nCn(, )=C(, ). An explicit expression is given for the functions C(,).Translated from Matematicheskie Zametki, Vol. 4, No. 2, pp. 201–210, August, 1968. 相似文献
9.
S. R. Treil' 《Journal of Mathematical Sciences》1989,44(6):868-869
It is proved that for every sequence of points n from the unit circle, n1, and for an arbitrary sequence of positive numbers An, An, there exists a continuous real function u, such that for the Toeplitz operator T (acting in the Hardy space H2) with the symbol =e
iu
we have the estimates (T–nI)–1>An, n.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 157, pp. 175–177, 1987. 相似文献
10.
A. M. Sedletskii 《Mathematical Notes》1977,22(6):941-947
Conditions on the closeness of real sequences {n} and {n} are studied which imply the equality of the excesses of the systems {exp(inx)} and {exp(inx)} in the space L2(–a, a). A theorem is formulated in terms of the difference of the sequences {n} and {n} enumerating the functions. In the corollaries of the theorem, conditions are given in terms of the behavior of the difference n–n0. An example is constructed showing that the condition n–n0 alone is not sufficient for equality of the excesses.Translated from Matematicheskie Zametki, Vol. 22, No. 6, pp. 803–814, December, 1977. 相似文献
11.
D. Leladze 《Georgian Mathematical Journal》1994,1(3):287-302
We have obtained an estimate, in terms of partial and mixed moduli, of the continuity of deviation of the Cesáro (C, ) means ( = (1,...,n),i , 1 > –1,
) of the sequence of rectangular partial sums ofn-multiple (n>1) conjugate trigonometric series from then-multiple truncated conjugate function. This estimate implies the result on them
-convergence (1) of (C, ) means (1 > 0,
) provided that the essential conditions are imposed on the partial moduli of continuity. Finally, it is shown that them
-convergence cannot be replaced by ordinary convergence. 相似文献
12.
Li Fuan 《数学学报(英文版)》1989,5(2):146-158
LetA andR be commutative rings, andm andn be integers3. It is proved that, if :St
m (A)St
n (R) is an isomorphism, thenm=n. Whenn4, we have: (1) Every isomorphism :St
n(A)St
n(R) induces an isomorphism:E
n (A)E
n (R), and is uniquely determined by; (2) IfSt
n (A) St
n (R) thenK
2.n
(A)K
2.n
(R); (3) Every isomorphismE
n (A) E
n (R) can be lifted to an isomorphismSt
n(A)St
n(R); (4)St
n(A) St
n(R) if and only ifAR. For the casen=3, ifSt
3(A) andSt
3(R) are respectively central extensions ofE
3(A) andE
3 (R), then the above (1) and (2) hold.The Project supported by National Natural Science Foundation of China 相似文献
13.
Dr. Hermann Rost 《Probability Theory and Related Fields》1970,15(1):19-28
Summary Given a stochastic matrixP on the state spaceI an ordering for measures inI can be defined in the following way: iff(f)(f) for allf in a sufficiently rich subcone of the cone of positiveP-subharmonic functions. It is shown that, if, are probability measures with , then in theP-process (X
n)n0 having as initial distribution there exists a stopping time such thatX
is distributed according to. In addition, can be chosen in such a way, that for every positive subharmonicf with(f)< the submartingale (f(X
n))n0 is uniformly integrable. 相似文献
14.
Consider a classical cusp eigenform f=
n=1
a
n
(f)q
n
of weight k2 for 0(N) with a Dirichlet character mod N, and let L
f
(s,)=
n=1
(n)a
n
(f)n
-s
denote the L-function of f twisted with an arbitrary Dirichlet character . For a prime number p5, consider a family of cusp eigenforms f
(k) of weight k
, k
{f
(k)=
n=1
a
n
(f
(k))q
n
} containing f=f
(k), such that the Fourier coefficients a
n
(f
(k)) are given by certain p-adic analytic functions k
a
n
(f
(k)). The purpose of this paper is to construct a two variable p-adic L function attached to Colemans family {f
(k)} of cusp eigenforms of a fixed positive slope =v
p
(
p
)>0 where
p
=
p
(k
) is an eigenvalue (which depends on k
) of the Atkin operator U=U
p
. Our p-adic L-function interpolates the special values L
f(k)(s,) at points (s,k
) with s=1,2,...,k
-1. We give a construction using the Rankin-Selberg method and the theory of p-adic integration on a profinite group Y with values in an affinoid K-algebra A, where K is a fixed finite extension of Q
p
.
Our p-adic L-functions are p-adic Mellin transforms of certain A-valued measures. In their turn, such measures come from Eisenstein distributions with values in certain Banach A-modules M
=M
(N;A) of families of overconvergent forms over A. To Robert Alexander Rankin in memoriam 相似文献
15.
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
16.
Gerold Alsmeyer 《Mathematical Methods of Operations Research》1986,30(3):A111-A134
Let
1, 2, ... be a sequence of i.i.d. random variables with positive mean
and finite variance
and letr(b), b0, be real numbers tending to 0 asb . Definings
n=1+...+n andS
n=Sn(b)=sn+r(b)n, the stopping time =(b)=inf {n>/1:Sn >b} whereb=b(b) , will be considered with special regard to the excess over the boundaryR
b=s+r(b)–b. It turns out that the limiting distribution ofR
b is the same as in the caser(b)0 for allb. Proving this, Blackwell's renewal theorem and its integral version have to be established first in the above stated situation. Finally, an expansion ofE to vanishing terms asb will be provided and applied to some examples arising in economics.
Zusammenfassung Seien 1, 2, ... unabhängige identisch verteilte Zufallsgrößen mit positivem Erwartungswert und endlicher Varianz sowier(b), b0, reelle Zahlen mitr(b)0 für b. Sei ferners 1, s2, ... der zugehörige Summenprozeß,S n= Sn(b)=sn+r(b)n fürn1 und =(b)=inf {n1: Sn>b, wobeib=b(b) fürb . Es wird gezeigt, daß die asymptotische Verteilung des ExzessesR b=s +r(b) –b mit der im Fallr(·)0 übereinstimmt. Dazu werden sowohl das Blackwellsche Erneuerungstheorem als auch seine Integralversion in der vorher beschriebenen parameterabhängigen Situation geeignet formuliert und bewiesen. Als Folgerung ergibt sich dann eine asymptotische Entwicklung vonE(b) fürb bis zu Termen o(1). Anh- and einiger Beispiele aus dem ökonomischen Bereich wird schließlich noch aufgezeigt, wo Approximationen fürE(b) von Interesse sein können.相似文献
17.
A well-known simple heuristic algorithm for solving the all-nearest-neighbors problem in thek-dimensional Euclidean spaceE
k
,k>1, projects the given point setS onto thex-axis. For each pointq S a nearest neighbor inS under anyL
p
-metric (1 p ) is found by sweeping fromq into two opposite directions along thex-axis. If
q
denotes the distance betweenq and its nearest neighbor inS the sweep process stops after all points in a vertical 2
q
-slice centered aroundq have been examined. We show that this algorithm solves the all-nearest-neighbors problem forn independent and uniformly distributed points in the unit cube [0,1]
k
in (n
2–1/k
) expected time, while its worst-case performance is (n
2). 相似文献
18.
G. Ramharter 《Acta Mathematica Hungarica》2000,88(4):331-340
Given any (non-degenerate) n-dimensional lattice L, let (L) denote the supremum of the numbers such that there exists a lattice packing Q + L of density where Q is some o-symmetric parallelepiped with faces parallel to the coordinate axes. Many efforts have been made to determine or estimate the minimal such density
n
taken over all n-dimensional lattices. It is known that
0$$
" align="middle" border="0">
. Here we investigate a sequence of lattices L
n
which are known to minimize the function (L) in dimensions n 3 and are likely to provide the minima
n
= (L
n
) in certain higher dimensions. We establish the inequality (L
n
) n
–n/2 which supports the conjecture that lim sup
n (
n
)1/(n log n) is positive. 相似文献
19.
Mercedes H. Rosas 《Journal of Algebraic Combinatorics》2001,14(2):153-173
The Kronecker product of two Schur functions s
and s
, denoted by s
* s
, is the Frobenius characteristic of the tensor product of the irreducible representations of the symmetric group corresponding to the partitions and . The coefficient of s
in this product is denoted by
, and corresponds to the multiplicity of the irreducible character in .We use Sergeev's Formula for a Schur function of a difference of two alphabets and the comultiplication expansion for s
[XY] to find closed formulas for the Kronecker coefficients
when is an arbitrary shape and and are hook shapes or two-row shapes.Remmel (J.B. Remmel, J. Algebra
120 (1989), 100–118; Discrete Math.
99 (1992), 265–287) and Remmel and Whitehead (J.B. Remmel and T. Whitehead, Bull. Belg. Math. Soc. Simon Stiven
1 (1994), 649–683) derived some closed formulas for the Kronecker product of Schur functions indexed by two-row shapes or hook shapes using a different approach. We believe that the approach of this paper is more natural. The formulas obtained are simpler and reflect the symmetry of the Kronecker product. 相似文献
20.
Michael Sand 《Integral Equations and Operator Theory》1996,26(2):210-221
If is a complex, separable Hilbert space, letL
2 () denote theL
2-space of functions defined on the unit circle and having values in . The bilateral shift onL
2() is the operator (U
f)()=f(). A Hilbert spaceH iscontractively contained in the Hilbert spaceK ifHK and the inclusion mapH–K is a contraction. We describe the structure of those Hilbert spaces, contractively contained inL
2(), that are carried into themselves contractively byU
. We also do this for the subcase of those spaces which are carried into themselves unitarily byU
. 相似文献