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1.
We find a class V of sequences such that the condition V is necessary and sufficient for convergence of weak greedy algorithm with weakness sequence for each f and all Hilbert spaces H and dictionaries D. We denote by V the class of sequences x={x
k
k=1
, x
k
0, k=1,2,..., with the following property: there exists a sequence 0=q
0<q
1< such that
s=1
2
s
/q
s
)< and
s=1
2–s
k=1
q
s
x
k
2<, where q
s
:=q
s
–q
s–1. 相似文献
2.
Weak L
2
-solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L
2
, are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in
(N 2): Let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the Schrödinger operator
. Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in
. Then u is 1-positive for - < < 1 (i.e., u c 1 with c const > 0) and 1-negative for 1 < < 1 + (i.e., u –c1 with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f. 相似文献
3.
We describe dual spaces of classes of the Hardy–Sobolev type
of functions holomorphic in a polydisk for 0 < p 1 and q (0, ) and for p (1, ) and q = 1. 相似文献
4.
5.
Let (t)t>0 be a convolution semigroup of probability measures on a measurable group (G, ). In this paper, we provide precise information about the asymptotic behavior of t{q>s, whereq is a measurable seminorm and (t)t>0 isq-continuous. 相似文献
6.
In this paper we study initial value problems likeu
t–R¦u¦m+uq=0 in n× +, u(·,0+)=uo(·) in N, whereR > 0, 0 <q < 1,m 1, andu
o is a positive uniformly continuous function verifying –R¦u
o¦m+u
0
q
0 in
N
. We show the existence of the minimum nonnegative continuous viscosity solutionu, as well as the existence of the function t(·) defined byu(x, t) > 0 if 0<t<t
(x) andu(x, t)=0 ift t
(x). Regularity, extinction rate, and asymptotic behavior of t(x) are also studied. Moreover, form=1 we obtain the representation formulau(x, t)=max{([(u
o(x – t))1–q
–(1–q)t]+)1/(1–q): ¦¦R}, (x, t)
+
N+1
.Partially supported by the DGICYT No. 86/0405 project. 相似文献
7.
We consider the (q, ) numeration system, with basis q2 and the set of digits {, +1,,q+–1} where –(q–1)0. We study properties of numbers where some digits do not occur. This is analogous to the Cantor set {0.a1a2ai{0,2}}. We compute an asymptotic equivalent of the nth moment of the Cantor (q, D)-distribution which can be described as the numbers 0. w1w2 with wiD{,,q+–1}, and each such letter can occur with the same probability 1/CardD. Furthermore, we consider n random strings according to the distribution and the expected minimum of them. We find a recursion which we solve asymptotically.This author was supported by the CNRS/NRF-project no 10959. Part of this work was done during the first authors visit to the John Knopfmacher Centre for Applicable Analysis and Number Theory at the University of the Witwatersrand, Johannesburg, South Africa.This author was supported by the CNRS/NRF-project no 10959. 相似文献
8.
Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r
q
, whereq depends on the properties of the norm. We specify it in the case ofL
spaces, >1. 相似文献
9.
Consider the stochastic partial differential equationdu
(t,x) = (t)u
(t, x)dt + dW
Q(t,x), 0 t T
where = 2/x
2, and is a class of positive valued functions. We obtain an estimator for the linear multiplier (t) and establish the consistency, rate of convergence and asymptotic normality of this estimator as 0. 相似文献
10.
The difference sequence spaces (), c(), and c
0() were studied by Kzmaz. The main purpose of the present paper is to introduce the space bv
p consisting of all sequences whose differences are in the space
p
, and to fill up the gap in the existing literature. Moreover, it is proved that the space bv
p is the BK-space including the space
p
. We also show that the spaces bv
p and
p
are linearly isomorphic for 1 p . Furthermore, the basis and the -, -, and -duals of the space bv
p are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv
p : ), (bv :
p
), and (bv
p : 1), and the characterizations of some other matrix classes are obtained by means of a suitable relation. 相似文献
11.
Moser-type estimates for functions whose gradient is in the Lorentz space L(n, q), 1q, are given. Similar results are obtained for solutions uH
inf0
sup1
of Au=(f
i
)
x
i
, where A is a linear elliptic second order differential operator and |f|L(n, q), 2q.Work partially supported by MURST (40%). 相似文献
12.
Summary Let be a probability measure on a separable locally convex Fréchet space E and let s
denote the topology on E of the convergence in . Then (E, s
) is nuclear iff ((E', s
))=1. 相似文献
13.
Let be a projective space. By H() we denote the graph whose vertices are the non-incident point-hyperplane pairs of , two vertices (p,H) and (q,I) being adjacent if and only if p I and q H. In this paper we give a characterization of the graph H() (as well as of some related graphs) by its local structure. We apply this result by two characterizations of groups G with PSL
n
(
)GPGL
n
(
), by properties of centralizers of some (generalized) reflections. Here
is the (skew) field of coordinates of . 相似文献
14.
A general minimax theorem 总被引:2,自引:0,他引:2
Prof. Dr. A. Irle 《Mathematical Methods of Operations Research》1985,29(7):229-247
This paper is concerned with minimax theorems for two-person zero-sum games (X, Y, f) with payofff and as main result the minimax equality inf supf (x, y)=sup inff (x, y) is obtained under a new condition onf. This condition is based on the concept of averaging functions, i.e. real-valued functions defined on some subset of the plane with min {x, y}< (x, y)x, y} forx y and (x, x)=x. After establishing some simple facts on averaging functions, we prove a minimax theorem for payoffsf with the following property: Forf there exist averaging functions and such that for any x1, x2 X, > 0 there exists x0 X withf (x0, y) >
f (x1,y),f (x2,y))– for ally Y, and for any y1, y2 Y, > 0 there exists y0 Y withf (x, y0) (f (x, y1),f (x, y2))+. This result contains as a special case the Fan-König result for concave-convex-like payoffs in a general version, when we take linear averaging with (x, y)=x+(1–)y, (x, y)=x+(1–)y, 0 <, < 1.Then a class of hide-and-seek games is introduced, and we derive conditions for applying the minimax result of this paper.
Zusammenfassung In dieser Arbeit werden Minimaxsätze für Zwei-Personen-Nullsummenspiele (X, Y,f) mit Auszahlungsfunktionf behandelt, und als Hauptresultat wird die Gültigkeit der Minimaxgleichung inf supf (x, y)=sup inff (x, y) unter einer neuen Bedingung an f nachgewiesen. Diese Bedingung basiert auf dem Konzept mittelnder Funktionen, d.h. reellwertiger Funktionen, welche auf einer Teilmenge der Ebene definiert sind und dort der Eigenschaft min {x, y} < < (x, y)相似文献x, y} fürx y, (x, x)=x, genügen. Nach der Herleitung einiger einfacher Aussagen über mittelnde Funktionen beweisen wir einen Minimaxsatz für Auszahlungsfunktionenf mit folgender Eigenschaft: Zuf existieren mittelnde Funktionen und, so daß zu beliebigen x1, x2 X, > 0 mindestens ein x0 X existiert mitf (x0,y) (f (x 1,y),f (x2,y)) – für alley Y und zu beliebigen y1, y2 Y, > 0 mindestens ein y0 Y existiert mitf (x, y0) (f (x, y1),f (x, y 2))+ für allex X. Dieses Resultat enthält als Spezialfall den Fan-König'schen Minimaxsatz für konkav-konvev-ähnliche Auszahlungsfunktionen in einer allgemeinen Version, wenn wir lineare Mittelung mit (x, y)=x+(1–)y, (x, y)= x+(1–)y, 0 <, < 1, betrachten.Es wird eine Klasse von Suchspielen eingeführt, welche mit dem vorstehenden Resultat behandelt werden können.
15.
Pham Dinh Tao 《Numerische Mathematik》1984,45(3):377-401
Résumé Certaines méthodes directes et indirectes pour le calcul de Max {x
t
Ax,
(x)1} sont étudiées.Les méthodes directes sont basées sur les propriétés particulières des normes
1,
2 et
. Ces méthodes sont très simples mais ne s'appliquent qu'à certaines familles de matrices.La méthode indirecte est la méthode autoduale introduite dans [25, 26] avec =
1. Dans ce cas, le choix du vecteur initial pour qu'il y ait convergence vers une solution optimale est largement discuté.
Some methods for computing the maximum of quadratic from on the unit ball of the maximum norm
Summary Some direct and indirect methods are studied for computing Max {x t Ax, (x)1} whereA is symmetric definite positive.Direct methods are constructed using particular properties of 1, 2, norms. These methods are very simple, but uniquely suitable to certains families of matrices.The indirect method is the autodual method, introduced in [25, 26, 29] with = 1. In this case the problem of choosing an initial vector so that convergence of the iterative sequence occurs to an optimal solution is largely discussed.相似文献
16.
Philip Calabrese 《Aequationes Mathematicae》1978,18(1-2):187-205
The notion of a random semi-metric space provides an alternate approach to the study of probabilistic metric spaces from the standpoint of random variables instead of distribution functions and permits a new investigation of the triangle inequality. Starting with a probability space (, , P) and an abstract setS, each pair of points,p, q, inS is assigned a random variableX
pq
with the interpretation thatX
pq
() is the distance betweenp andq at the instant . The probability of the eventJ
pqr
= { :X
pr
()X
pq
()+X
qr
()} is studied under distribution function conditions imposed by Menger Spaces (K. Menger, Statistical Metrics, Proc. Nat. Acad. Sci., U.S.A., 28 (1942), 535–537; B. Schweizer and A. Sklar, Statistical Metric Spaces, Pacific J. Math.10 (1960), 313–334). It turns out that for > 0 there are 3 non-negative, identically-distributed random variablesX, Y andZ for whichP(X < Y + Z) < . This and other results show that distribution function triangle inequalities are very weak. Conditional probabilities are introduced to give necessary and sufficient conditions forP(J
pqr
) = 1. 相似文献
17.
V. N. Konovalov 《Ukrainian Mathematical Journal》2004,56(7):1074-1101
Let s 0 and let
+
s
be the set of functions x defined on a finite interval I and such that, for all collections of s
+ 1 pairwise different points t
0,..., t
s
I, the corresponding divided differences [x; t
0,...,t
s
] of order s are nonnegative. Let
+
s
B
p
+
s
B
p, 1 p where B
p is a unit ball in the space L
p, and let
+
s
L
q
+
s
L
q, 1 q . For every s 3 and 1 q p , we determine the exact orders of the shape-preserving Kolmogorov widths {x - y} \right\ L_q , $$]]> , where M
n is the collection of all affine linear manifolds M
n in L
q such that dim M
n n and M
n
+
s
L
q .Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 901–926, July, 2004. 相似文献
18.
Marilyn Breen 《Monatshefte für Mathematik》1996,122(1):1-7
LetS be a finite union of boxes inR
d
. Forx inS, defineA
x
={yx is clearly visible fromy via staircase paths inS}, and let KerS denote the staircase kernel ofS. Then KerS={A
x
x is a point of local nonconvexity ofS}. A similar result holds with clearly visible replaced by visible and points of local nonconvexity ofS replaced by boundary points ofS.Supported in part by NSF grant DMS-9207019. 相似文献
19.
Tassilo Küpper 《Numerische Mathematik》1976,25(2):201-214
Summary For differential operatorsM of second order (as defined in (1.1)) we describe a method to prove Range-Domain implications—Mu–u and an algorithm to construct these functions , , , . This method has been especially developed for application to non-inverse-positive differential operators. For example, for non-negativea
2 and for given functions = we require =C
0[0, 1] C
2([0, 1]–T) whereT is some finite set), (M) (t)(t), (t[0, 1]–T) and certain additional conditions for eachtT. Such Range-Domain implications can be used to obtain a numerical error estimation for the solution of a boundary value problemMu=r; further, we use them to guarantee the existence of a solution of nonlinear boundary value problems between the bounds- and . 相似文献
20.
Summary We describe a large class of one-parameter families , {}, , of two-dimensional diffeomorphisms which arestable for <0, exhibit acycle for =0, and thereafter have a bifurcation set of positive but arbitrarily smallrelative measure for in small intervals [0, ]. A main assumption is that the basic sets involved in the cycle havelimit capacities that are not too large.The second author acknowledges hospitality and financial support from IMPA/CNPq during the period this paper was prepared 相似文献