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1.
Joseph Rosenblatt 《Mathematische Annalen》1977,230(3):245-272
For a mean zero norm one sequence (f
n
)L
2[0, 1], the sequence (f
n
{nx+y}) is an orthonormal sequence inL
2([0, 1]2); so if
, then
converges for a.e. (x, y)[0, 1]2 and has a maximal function inL
2([0, 1]2). But for a mean zerofL
2[0, 1], it is harder to give necessary and sufficient conditions for theL
2-norm convergence or a.e. convergence of
. Ifc
n
0 and
, then this series will not converge inL
2-norm on a denseG
subset of the mean zero functions inL
2[0, 1]. Also, there are mean zerofL[0, 1] such that
never converges and there is a mean zero continuous functionf with
a.e. However, iff is mean zero and of bounded variation or in some Lip() with 1/2<1, and if |c
n
| = 0(n
–) for >1/2, then
converges a.e. and unconditionally inL
2[0, 1]. In addition, for any mean zerof of bounded variation, the series
has its maximal function in allL
p[0, 1] with 1p<. Finally, if (f
n
)L
[0, 1] is a uniformly bounded mean zero sequence, then
is a necessary and sufficient condition for
to converge for a.e.y and a.e. (x
n
)[0, 1]. Moreover, iffL
[0, 1] is mean zero and
, then for a.e. (x
n
)[0, 1],
converges for a.e.y and in allL
p
[0, 1] with 1p<. Some of these theorems can be generalized simply to other compact groups besides [0, 1] under addition modulo one. 相似文献
2.
Paolo Cubiotti 《Set-Valued Analysis》1993,1(1):81-87
In this paper, we deal with the following generalized quasi-variational inequality problem: given a closed convex subsetX
n
, a multifunction :X 2
n
and a multifunction :X 2
X
, find a point (
) X ×
n
such that
We prove an existence theorem in which, in particular, the multifunction is not supposed to be upper semicontinuous. 相似文献
3.
Gikō Ikegami 《Inventiones Mathematicae》1989,95(2):215-246
Summary We define a constraint system
, [0,0), which is a kind of family of vector fields
on a manifold. This is a generalized version of the family of the equations
, [0,0),x
m
,y
n
. Finally, we prove a singular perturbation theorem for the system
, [0,0).Dedicated to Professor Kenichi Shiraiwa on his 60th birthday 相似文献
4.
For
-parabolic dissipative systems and systems with growing coefficients as |x| in the presence of degeneracies in the initial hyperplane, we investigate the fundamental matrix of solutions and the solvability of the Cauchy problem. 相似文献
5.
Andrzej Stachurski 《Mathematical Programming》1981,20(1):196-212
In this paper the so-called Broyden's bounded-class of methods is considered. It contains as a subclass Broyden's restricted-class of methods, in which the updating matrices retain symmetry and positive definiteness. These iteration methods are used for solving unconstrained minimization problems of the following form:
It is assumed that the step-size coefficient
k = 1 in each iteration and the functionalf : R
n R1 satisfies the standard assumptions, viz.f is twice continuously differentiable and the Hessian matrix is uniformly positive definite and bounded (there exist constantsm, M > 0 such that my2 y,
for ally R
n) and satisfies a Lipschitz-like condition at the optimal point
, the gradient vanishes at
Under these assumptions the local convergence of Broyden's methods is proved. Furthermore, the Q-superlinear convergence is shown. 相似文献
6.
Michael Werner 《Journal of Geometry》1984,22(2):189-192
Lie theory renders a concept of curvature for the geometries (,) introduced by W. Benz [1]. Among regular curves in
the chains of (,
) are characterized by =0. 相似文献
7.
M. P. Moklyachuk 《Ukrainian Mathematical Journal》1991,43(2):188-194
We consider the problem of linear mean square optimal estimation of transformation
of a stationary random process (t) in observations of process (t) + n(t) for t < – 0, where (t) is white noise uncorrelated with (t). We find least favorable spectral densities f0()
D and minimax (robust) spectral characteristics of an optimal estimator of transformation A for various classesD of densities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 216–223, February, 1991. 相似文献
8.
Albert Raugi 《Probability Theory and Related Fields》1988,77(4):481-496
Résumé SoitG un groupe moyennable connexe, locallement compact, à base dénombrable. Soit une mesure positive sur les boréliens deG. Nous étudions les fonctions boréliennes positivesh vérifiant: g G,
. Sous de bonnes hypothèses sur , nous obtenons, pour ces fonctions, une représentation intégrale à l'aide d'exponentielles.
Summary LetG be a connected locally compact separable amenable group. Let be a positive measure on the Borel -field ofG. We study the positive Borel functionsh onG which satisfy: g G, . Under smooth assumptions on , we establish an integral representation of these functions in term of exponentials.相似文献
9.
The main result is the following theorem. Let
be a commutative Banach algebra with radical R, where the factor algebra
is isomorphic to the algebra of all continuous functions on a totally disconnected compact space. If rn1 /n 0 as n uniformly for r R, rl, then the algebra
is strongly decomposable, i.e., there exists a closed subalgebra B
isomorphic to
such that
=BR.This is a strengthening of the theorem of A. Ya. Khelemskii, who assumed
. There are 4 references.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 589–592, December, 1967. 相似文献
10.
The notion of the split extension of a commutative kinematic space is extended to the case of a weak K-loop with an incidence fibration (F, +,
). Theorem 1 states conditions under wich the quasi-direct productG F+
Q
with Aut(F, +) can be turned in a fibered incidence group (G,
, o) such that (F, +,
) becomes embeddable inG, and Theorem 2 the additional assumption such that (G,
, o) is even a kinematic space. In section 4, Theorem 3 shows that there are suitable examples of proper K-loops with an incidence fibration (derived from hyperbolic planes) on which one can apply Theorem 2.Dedicated to Erich Ellers on the occasion of his 70th birthdayResearch supported by M.U.R.S.T. 40% and by C.N.R. (G.N.S.A.G.A.) 相似文献
11.
M. P. Moklyachuk 《Ukrainian Mathematical Journal》1993,45(3):414-423
We study the problem of optimal linear estimation of the transformation
of a stationary random process (t) with values in a Hilbert space by observations of the process (t) + (t) fort0. We obtain relations for computing the error and the spectral characteristic of the optimal linear estimate of the transformationA for given spectral densities of the processes (t) and (t). The minimax spectral characteristics and the least favorable spectral densities are obtained for various classes of densities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 389–397, March, 1993. 相似文献
12.
Consider the problem of determining the roots of an equation of the formF() =0 whereF maps the Banach spaceX into itself. Convergence theorems for the iterative solution ofF() =0 are proved for multipoint algorithms of the form
n+1=
n
-
(
n
), 1, where
and 0()=0. The theorems are applied to the solution of two point boundary value problems of the form
=f
(y, t), g(y(0))+h(y(1))=c. A set {A(t),B,C} of matrices is called boundary compatible if the linear two point boundary value problem
=A(t)) y+k (t),B y (0) + C y (1) = d has a unique solution for allk (t) andd. Then, under certain conditions, there are boundary compatible sets such that the problem
=f (y, t),g (y (0) ) +h (y (1)) =c has the equivalent integral representation where and are Green's matrices for the linear problem
=A(t)y +k(t),B y (0) +C y (1) =d. Eq. (i) is viewed as an operator equation of the formF (x) =(I-T) (x) = 0 and convergence conditions for the iterative solution of (i) are deduced from the general theorems. Explicit interpretations of the convergence results are given in terms off, g, h and some illustrative numerical examples are presented.This research has been supported by the National Aeronautics and Space Administration under Grant No. NGR-40-002-015.This research has been supported by the National Science Foundation under Grant No. GK-2788. 相似文献
13.
Ivan Singer 《Annali di Matematica Pura ed Applicata》1987,148(1):289-352
Summary We give some applications of infimal generators of complete lattices, in the sense of Kutateladze and Rubinov [12], to the study of dualities between two complete lattices E and F (i.e., mappings : E F satisfying
for all
and all index sets I, including the empty set I=Ø). We give some additional results for E=(2X,
), F=(2W,
) and E=(¯RX, ), F=(¯RW, ) (where X and W are arbitrary sets), with suitable families of infimal generators. We obtain some lattice- theoretic properties of the relations of [22] between dualities : (2X,
) (2W,
), binary relations
X×W, polarities (): (2X,
) (2W,
), coupling functionals : X×W ¯R and Fenchel-Moreau conjugations c():(¯RX, ) (¯RW,). 相似文献
14.
Let P define a partial order on a set X of cardinalityn. A linear extensionL ofP is a linear order withP G L, and
is the set of all linear extensions ofP.
denotes that subset of
withxLy forx, y X. A linear extension majority (LEM) relationM onX is defined byxMy if
. Similarly,M is defined byxMy if
. An LEM cycle exists if there arex, y, z X withxMyMzMx, and an LEM quasi-cycle exists ifxMyMzMx and the equality part of the definition ofM holds for exactly one pair in the triple. The study shows that no semiorders have LEM cycles or LEM quasi-cycles, and that every interval order has a maximal element under theM relation. LEM cycles and LEM quasi-cycles are also considered for partial orders with specific structures. Simulation is used to determine the relative likelihood with which LEM cycles and LEM quasi-cycles are observed when connected partial orders are generated at random by a specific procedure.Dr. Gehrlein's research was supported through a fellowship from the Center for Advanced Study of the University of Delaware. 相似文献
15.
The notion reflection group (,
) was introduced in order to give group theoretical characterizations of absolute planes. Here we consider reflection groups with midpoints and associate to each of them an incidence structure
. Then
is an incidence space which dimension can assume any value. The motion group together with the set
of all reflections in points of a Euclidean or hyperbolic geometry are examples of reflection groups with midpoints. Furthermore the set
can be turned into a K-loop. The precise results are summarized in the theorems at the end of the paper.Cordially dedicated to Sibylla Prieß on the occasion of her 60th birthdaySupported by the NATO Scientific Affairs Division grant CRG 900103. 相似文献
16.
Rudolf Scharlau 《Geometriae Dedicata》1987,24(1):77-84
Following earlier work of Tits [8], this paper deals with the structure of buildings which are not necessarily thick; that is, possessing panels (faces of codimension 1) which are contained in two chambers, only. To every building , there is canonically associated a thick building
whose Weyl group W(
) can be considered as a reflection subgroup of the Weyl group W() of . One can reconstruct from
together with the embedding W(
) W(). Conversely, if
is any thick building and W any reflection group containing W(
) as a reflection subgroup, there exists a weak building with Weyl group W and associated thick building
. 相似文献
17.
Victor Kaftal 《Integral Equations and Operator Theory》1982,5(1):50-70
LetA be a von Neumann algebra,J be the ideal of compact operators relative toA and letF
+ be the left-Fredholm class ofA. We call almost left-Fredholm the class
= {A A: if P A is a projection and AP J then P J}. Then
and the inclusion is proper unlessA is semifinite and has a non-large center.
satisfies all of the algebraic properties ofF
+ but it is generally not open. IfA is semifinite then A
iff there are central projectionsG
with G = I such that AG F+(AG). Let :A A/J. Then the left almost essential spectrum ofA A,
, coincides with the set of eigenvalues of (A) 相似文献
18.
Ching-Kuang Shene 《Journal of Geometry》1992,44(1-2):171-176
Given a ratio , >>0, and a triangle ABC, on the sides
and
, using ratios , and , three circles of Apollonius are denned. In this paper, we will show that the three centers are collinear, the circles are coaxal and develop a necessary and sufficient condition that these circles intersect. J. A. Hoskins, W. D. Hoskins and R. G. Stanton obtained these results in a recent paper using algebraic computation. Our aim is to establish all these results using only results from elementary Euclidean geometry and thereby uncovering more geometric insights and avoid lengthy calculations. 相似文献
19.
Consider the flow t for the system of differential equations
, x,
n, open. Let K(t) be an expanding polyhedral cone of constant dimension, k be a unit vector in K(0), and x
0. A sufficient condition for
K(t) for t0 is that there exists an l so that Df(t(x0))+lI leaves K(t) invariant for all t0. If in addition (Df(t(x0))+lI)n-1 takes k into the relative interior of K(t) for all t>0 then
is in the relative interior of K(t) for all t>0. The latter condition for strong monotonicity may be cumbersome to check; a graph theoretic condition which can replace it is presented in this paper. Knowledge of the facial structure of K(t) is required. The results contained in this paper are extensions of the Kamke-Müller theorem and Hirsch's theorem for strong monotone flows. Applications from chemical kinetics and epidemiology are considered. 相似文献
20.
Abdelhafed Elkhadiri 《Bulletin of the Brazilian Mathematical Society》2000,31(1):45-71
Let be an open subset of
n
and
be a subalgebra of the algebra of analytic functions on . We suppose that
satisfies some weak conditions of noetherianity such that we can construct a finite stratification for each ideal of
. We also suppose that
satifies global £ojasiewicz's inequalities. We prove the following: Let
andf C
on
flat on ; if for eacha the Taylor's serie off ata, T
a
f, is in the ideal generated byT
a
f
1,...,T
a
f
p
in the ring of formal power series, then there exist
1,...,
p
,C
on
flat on such that
. This result extends the classic Hormander's theorem of division (for a polynomial) or the £ojasiewicz-Malgrange theorem in the local analytic case.Reherches menées dans le cadre du Programme d'Appui à la Recherche Scientifique (PARS MI 33) 相似文献