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1.
Limit theorems for the ratio of the empirical distribution function to the true distribution function 总被引:4,自引:0,他引:4
Jon A. Wellner 《Probability Theory and Related Fields》1978,45(1):73-88
Summary We consider almost sure limit theorems for
and
where
n
is the empirical distribution function of a random sample ofn uniform (0, 1) random variables anda
n
0. It is shown that (1) ifna
n
/log2
n then both
and
converge to 1 a.s.; (2) ifna
n
/log2
n=d>0 (d>1) then
has an almost surely finite limit superior which is the solution of a certain transcendental equation; and (3) ifna
n
/log2
n0 then
and
have limit superior + almost surely. Similar results are established for the inverse function
n
–1
.Supported by the National Science Foundation under MCS 77-02255 相似文献
2.
3.
Günter Mayer 《Numerische Mathematik》1985,46(1):69-83
Summary Let
be a real irreduciblen×n interval matrix. Then a necessary and sufficient condition is given for the sequence
of the powers of an interval matrix
to converge to a matrix
which is not the null matrix. In addition a criterion for
is proved to decide whether the limit matrix
satisfies the condition of symmetry
. 相似文献
4.
Prof. Ottmar Loos 《Monatshefte für Mathematik》1978,86(2):107-129
Every Jordan pair
defines an algebraic varietyX containing
as a dense open subset.X is projective (affine) if and only if
is separable (radical). The Picard group ofX is generated by the irreducible factors of the generic norm of
. If
is separable then the automorphism group ofX is the projective group of
. 相似文献
5.
Let
denote the closed subspace of
consisting of analytic functions in the unit disk
. For certain class of subharmonic
, the Hankel operatorH
b on
with symbol
is studied. Criteria for boundedness and compactness of such kind of Hankel operators are presented.R. Rochberg's research was partially supported by a grant from the National Science Foundation. 相似文献
6.
Ivan Singer 《Mathematical Methods of Operations Research》1996,43(1):35-44
By [6], the dualities between
and
, whereX andW are two sets and
(i.e., the mappings
satisfying
for all
and all index setsI), can be represented with the aid of functions
. Here we show that they can be also represented with the aid of functions
, whereR = (–, +). As an application, we show that every duality
is completely determined by a suitable duality between 2
X ×R
and 2
W ×R
(i.e., a mapping 2
X ×R
2
W ×R
satisfying
for all {M
i}
iI
2
X ×R
and all index setsI), applied to the epigraphs of the functions
. 相似文献
7.
Summary Let
denote the extended Weyl algebra,
, the Weyl algebra. It is well known that every element of
of the formA=B
k
*
B
k
is positive. We prove that the converse implication also holds: Every positive elementA in
has a quadratic sum factorization for some finite set of elements (B
k
) in
. The corresponding result is not true for the subalgebra
. We identify states on
which do not extend to states on
. It follows from a result of Powers (and Arveson) that such states on
cannot be completely positive. Our theorem is based on a certain regularity property for the representations which are generated by states on
, and this property is not in general shared by representations generated by states defined only on the subalgebra
.Work supported in part by the NSF 相似文献
8.
Let
and
the foliations by the null geodesics of some lorentzian metricg on the torus
. We analyse how geodesic completeness properties ofg are related to the dynamics of
and
. 相似文献
9.
Oswald Riemenschneider 《manuscripta mathematica》1974,14(1):91-99
Let
be a 1-convex holomorphic mapping between complex spaces
resp.S, and let
be the blowingdown factorization of
over S. We prove in part 1 of the present note: The fiber –1(s0) over a point s0S is the Remmert quotient of
if and only if every holomorphic function on
(defined in a neighborhood of the exceptional subvariety of that fiber) can be extended holomorphically to
. This is true, for instance, in the case:
flat, S reduced at s0 and dim
, =const for all sS. In part 2, we use this result to obtain the following: For any Riemann surface R with genus g2 there exists a 2-dimensional normal complex analytic singularity X such that the minimal resolution
of X contains R as exceptional subvariety, and
has a deformation over the unit disc S={|s|<1} which can not be blown down to a deformation of X. 相似文献
10.
O. P. Filatov 《Mathematical Notes》1999,66(3):348-354
For a continuous almost periodic function
, we show that the function
where the supremum is taken over all solutions of the system of differential inclusion
,
, has the following limit (as μ→+0):
, Thus if the parameter μ is small, then
and the limit of the maximal mean can approximately be determined by solving problems of smaller dimensionality. Moreover,
if the compact sets
and
are nondegenerate, then Ψ
f
is independent of initial data.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 431–438, September, 1999. 相似文献
11.
The one-step prediction problem is studied in the context ofP
n-weakly stationary stochastic processes
, where
is an orthogonal polynomial sequence defining a polynomial hypergroup on
. This kind of stochastic processes appears when estimating the mean of classical weakly stationary processes. In particular, it is investigated whether these processes are asymptoticP
n-deterministic, i.e. the prediction mean-squared error tends to zero. Sufficient conditions on the covariance function or the spectral measure are given for
being asymptoticP
n-deterministic. For Jacobi polynomialsP
n(x) the problem of
being asymptoticP
n-deterministic is completely solved. 相似文献
12.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
13.
Daoxing Xia 《Integral Equations and Operator Theory》1999,33(4):489-506
This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
<, where
. The main tool is a pair of matrices
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. 相似文献
14.
The article discusses phenomenological methods for predicting long-term creep, using stress-, temperature-, and vibro-time analogies. Starting from several previously introduced hypotheses, the article proposes a generalized nonlinear thermo-vibro-rheological relationship in which the complex stress-, temperature-, and vibro-time dependences are reduced separately to a time dependence (with certain basic reference values of
, T0, and
, chosen arbitrarily), and to
dependences; the latter appears only in the change of the time factorsa
(i),a
T(T), and
. The prediction methods have been verified experimentally.Institute for the Mechanics of Polymers, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 420–428, May–June, 1970. 相似文献
15.
Fabio Vlacci 《Journal d'Analyse Mathématique》1998,75(1):51-66
We introduce the notion of pointwise regularity (
) of Colombeau’s generalized functions and give comparison theorems between
regularity,
- andC
∞-regularity. We also define the notion of a pointwise wave front set and establish a theorem concerning the effect of a linear
generalized partial differential operator on such a wave front. 相似文献
16.
Giorgio Busetto 《Annali di Matematica Pura ed Applicata》1985,142(1):91-103
Sunto Siano G e
due gruppi, : GG una proiettività e N un sottogruppo normale di G. Vengono provati alcuni risultati sulle proprietà di immersions in
e G rispettivamente, del gruppi
, la chiusura normale di N in
modulo il nocciolo di N in
, e
.
Supported by a C.N.R. grant. 相似文献
Supported by a C.N.R. grant. 相似文献
17.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献
18.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
19.
Hans Fuchs 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1970,21(1):115-119
Summary Lyon's formula for heat transfer to liquid metals for constant wall heat flux (Nu=7+0.025 ( Pe)0.8) is compared with results of Reichardt and Elser (Nu=5.2+0.025 ( Pe)0.8).The difference is shown to be due to the adopted distribution of radial heat flux—both Reichardt and Elser tacitly assuming constant wall temperature. Their results lend therefore support to the Seban-Shimazaki formula (Nu=5+0.025 Pe0.8). Differences between experimental values and Lyon's formula can possibly be explained by inaccuracies of Nikuradse's velocity profiles for low Re number.
Symbole Temperaturleitfähigkeit - c p Spezifische Wärme - D=2R Rohrdurchmesser - q Wärmestromdichte - r laufender Radius - T Temperatur - mittlere Temperatur - u Geschwindigkeit - mittlere Geschwindigkeit - x Längskoordinate - Wärmeübergangszahl - H , M eddy diffusivity for heat/momentum - Wärmeleitfähigkeit - kinemat. Zähigkeit - =r/R dimensionsloser Radius - Dichte - Schubspannung - Nusselt-Zahl - Pe=Re Pr Péclet-Zahl - Prandtl-Zahl - Reynolds-Zahl - Index Wand 相似文献
Symbole Temperaturleitfähigkeit - c p Spezifische Wärme - D=2R Rohrdurchmesser - q Wärmestromdichte - r laufender Radius - T Temperatur - mittlere Temperatur - u Geschwindigkeit - mittlere Geschwindigkeit - x Längskoordinate - Wärmeübergangszahl - H , M eddy diffusivity for heat/momentum - Wärmeleitfähigkeit - kinemat. Zähigkeit - =r/R dimensionsloser Radius - Dichte - Schubspannung - Nusselt-Zahl - Pe=Re Pr Péclet-Zahl - Prandtl-Zahl - Reynolds-Zahl - Index Wand 相似文献
20.
Takuya Hara 《Integral Equations and Operator Theory》1992,15(4):551-567
Let
be a Hilbert space. A continuous positive operatorT on
uniquely determines a Hilbert space
which is continuously imbedded in
and for which
with the canonical imbedding
. A Kreîn space version of this result, however, is not valid in general. This paper provides a necessary and sufficient condition for that a continuous selfadjoint operatorT uniquely determines a Kreîn space (
) which is continuously imbedded in
and for which
with the canonical imbedding
. 相似文献