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1.
Nous donnons une caractérisation des domaines DX pour lesquels la fonction extrémale relative *(,E,D) a la propriété de stabilité pour tout ED, i.e. lim
k*(,E,D
k
)=*(,E,D), ED. Ensuite, nous étudions la relation entre cette propriété et les enveloppes pluripolaires. Nous concluons par quelques remarques sur la propriété de stabilité lim
k*(,E
k
,D)=*(,E,D). 相似文献
2.
S. A. Kruglyak V. I. Rabanovich Yu. S. Samoilenko 《Functional Analysis and Its Applications》2002,36(3):182-195
In the paper, for all n, we describe the set n of all real numbers admitting a collection of projections P
1,...,P
n on a Hilbert space H such that k=1
n
P
k= I (I is the identity operator on H) and study the problem to find all collections of this kind for a given
n
. 相似文献
3.
Tatsuya Maruta 《Geometriae Dedicata》1999,74(3):305-311
Any {f,r- 2+s; r,q}-minihyper includes a hyperplane in PG(r, q) if fr-1 + s 1 + q – 1 for 1 s q – 1, q 3, r 4, where i = (qi + 1 – 1)/ (q – 1 ). A lower bound on f for which an {f, r – 2 + 1; r, q}-minihyper with q 3, r 4 exists is also given. As an application to coding theory, we show the nonexistence of [ n, k, n + 1 – qk – 2 ]q codes for k 5, q 3 for qk – 1 – 2q – 1 < n qk – 1 – q – 1 when k > q –
q - \sqrt q + 2$$
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and for
when
, which is a generalization of [18, Them. 2.4]. 相似文献
4.
Manfred Stoll 《Potential Analysis》2002,16(3):205-220
Let B denote the unit ball in C
n
, n1, and let ,
, and denote the volume measure, gradient, and Laplacian respectively, with respect to the Bergman metric on B. For R and 0<p<, we denote by L
p
the set of real, or complex-valued measurable functions f on B for which
B
(1–|z|2)|f(z)|
p
d(z)<, and by D
p
the Dirichlet space of C
1 functions f on B for which |
f|L
p
. Also, for C, we denote by X
the set of C
2 real, or complex-valued functions f on B for which
f=f. The main result of the paper is as follows: Let 0<p< and suppose R with –n
2. Then L
p
X
={0}, and for 0, D
p
X
={0}(a) for all n+
when p1, and(b) for all
when 0<p<1.By example it is shown that the result is best possible for all values of p with pn/(n+
. 相似文献
5.
We consider the partially ordered set ([k]
n, ), which is defined asn-th product of the chain [k] = {0, 1, 2,...,k – 1}, and study pairs (A, B) of incomparable setsA, B [k]
n, that is,a b, a b for alla A, b B or (in short notation) A
BWe are concerned with the growth of the functionsf
n: {0, 1,...,k
n} {0, 1,...,k
n},n , defined byf
n() = max {|B|: A, B [k]
n with|A| = and A
B} and a characterisation of pairs (A, B), which assume this bound.In the previously studied casek = 2 our results are considerably sharper than earlier results by Seymour, Hilton, Ahlswede and Zhang. 相似文献
6.
Jürgen Weyer 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1985,36(4):499-507
We consider the nonlinear diffusion equationu
t
–a(x, u
x
x
)+b(x, u)=g(x, u) with initial boundary conditions
andu(t, 0)=u(t, 1)=0. Here,a, b, andg denote some real functions which are monotonically increasing with respect to the second variable. Then, the corresponding stationary problem has a positive solution if and only if(0,
*) or(0,
*]. The endpoint
* can be estimated by
, where
1
u denotes the first eigenvalue of the stationary problem linearized at the pointu. The minimal positive steady state solutions are stable with respect to the nonlinear parabolic equation.
Zusammenfassung Wir betrachten die nichtlineare Diffusionsgleichungu t –a(x, u x ) x +b(x, u)=g(x, u) mit Randbedingungen undu (t, 0)=u (t, 1)=0. Dabei sinda, b, undg monoton wachsende Funktionen bzgl. des zweiten Argumentes. Das zugehörige stationäre Problem hat genau dann eine positive Lösung, falls (0, *) oder(0, *]. Der Endpunkt * kann durch abgeschätzt werden, wobei 1 u den ersten Eigenwert des an der Stelleu linearisierten stationären Problems bezeichnet. Die minimale positive stationäre Lösung ist stabil bzgl. der obigen nichtlinearen parabolischen Gleichung.相似文献
7.
Let B be a domain in the complex plane, let pn(z) and Pn(z) be polynomials of degree n where the zeros of Pn(z) lie in
, let(z) be a finite function,(z) 0, z
. We consider the problem of estimating from above the functions L[pn(z)]=(z)pn(z) – wpn(z), z
, if ¦pn(z)¦ ¦Pn(z)¦ for zB. Under some very general conditions on B, z, (z), and w we prove the inequality ¦L[pn(z)]¦ ¦L[Pn(z)]¦.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 431–440, April, 1968. 相似文献
8.
B. Yousefi 《Czechoslovak Mathematical Journal》2004,54(1):261-266
Let
be a sequence of positive numbers and 1 p< . We consider the space H
p() of all power series
such that
. We investigate strict cyclicity of
the weakly closed algebra generated by the operator of multiplication by zacting on H
p(), and determine the maximal ideal space, the dual space and the reflexivity of the algebra
. We also give a necessary condition for a composition operator to be bounded on H
p() when
is strictly cyclic. 相似文献
9.
N. Palinchak 《Mathematical Notes》1996,59(2):158-162
In the article strongly nondegenerate (k, n)-quadrics all of whose linear automorphisms are of the formzz, ¦¦2, {0} are considered. Quadrics all of whose linear automorphisms are of this form were calledc-rigid by V. Beloshapka. The main result of the article is the following: anyc-rigid strongly nondegenerate (k, n)-quadric has no nonlinear automorphisms. A table indicating the relationship between linear and nonlinear automorphisms for (k, n)-quadrics is presented.Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 224–229, February, 1996. 相似文献
10.
Summary In each lattice point , of a rectangular net a numerical valueu
is given. A bicubical and twice continuously differentiable function is constructed interpolating the valuesu
. The method is known as «spline interpolation». 相似文献
11.
Gordon Simons 《Probability Theory and Related Fields》1978,42(2):167-173
Summary Let denote the class of infinite product probability measures =
1×
2× defined on an infinite product of replications of a given measurable space (X, A), and let denote the subset of for which (A) =0 or 1 for each permutation invariant event A. Previous works by Hewitt and Savage, Horn and Schach, Blum and Pathak, and Sendler (referenced in the paper) discuss very restrictive sufficient conditions under which a given member , of belongs to . In the present paper, the class is shown to possess several closure properties. E.g., if and
0
n
for some n 1, then
0×
1×
2×.... While the current results do not permit a complete characterization of they demonstrate conclusively that is a much larger subset of than previous results indicated. The interesting special case X={0,1} is discussed in detail.Research supported by the National Science Foundation under grant No. MCS75-07556 相似文献
12.
L. N. Gordeev 《Journal of Mathematical Sciences》1981,15(1):22-28
A new approach is proposed for the construction of constructive analogs of set theory in hyperarithmetic languages
, where is a scale of constructive ordinals. For every ordinal in the language
, a special relation of equality = is defined for codes of one-parameter formulas (conditions) of the level in a constructive hyperarithmetic hierarchy corresponding to the scale . The membership relation, (also expressible in the language
), is defined by the conditionx
y=z(z=
x&z
y), where the relation is obtained by suitable refinement of the traditional representations of the constructive relation of membership. This results in a hierarchy of constructive analogsM
of the theory of sets (in which the sets are represented by codes of conditions of level , identified modulo the relation =, and is taken as the relation of membership). Some properties of this hierarchy are introduced which show that for the limits ,M
is sufficiently rich from the traditional set theoretic standpoint.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 68, pp. 38–49, 1977. 相似文献
13.
Paolo Lipparini 《Archive for Mathematical Logic》1996,35(2):63-87
We develop a method for extending results about ultrafilters into a more general setting. In this paper we shall be mainly concerned with applications to cardinality logics. For example, assumingV=L, Gödel's Axiom of Constructibility, we prove that if > then the logic with the quantifier there exist many is (,)-compact if and only if either is weakly compact or is singular of cofinality<. As a corollary, for every infinite cardinals and , there exists a (,)-compact non-(,)-compact logic if and only if either < orcf<cf or < is weakly compact.Counterexamples are given showing that the above statements may fail, ifV=L is not assumed.However, without special assumptions, analogous results are obtained for the stronger notion of [,]-compactness. 相似文献
14.
We show that the mean quadratic variation of a self-similar measure under certain open set condition exhibits asymptotic periodicity. Through a generalized Wiener's Tauberian Theorem, we obtain some new identities and equivalences of the mean quadratic variation of a bounded measurev and its Fourier average
. They are used to sharpen some recent results of Strichartz concerning the asymptotic behavior ofH
a(T); ) asT, where is the self-similar measure as above. In the development some results concerning the open set condition are also obtained. 相似文献
15.
K. Maciej Przyluski 《Applied Mathematics and Optimization》1980,6(1):97-112
This paper is devoted to a study of the properties of the equationA
*FA–F=–G, where FL() is unknown, AL(), GL() is positive and is a Hilbert space. It is shown that necessary and sufficient (in some sense) conditions for the existence of positive definite solutions of this equation are directly connected with the stability of infinite dimensional linear systemx
k+1=Ax
k
. The relationships between stability of such a system and stability of a continuous-time system generated by a strongly continuous semigroup are given also. As an example the case of the delayed system in Rn
is considered.This work was supported in part by the Polish Academy of Sciences under the contract Problem Miedzyresortowy I.1, Grupa Tematyczna 3 This paper was written while the author was with the Instytut Automatyki, the same university. 相似文献
16.
The following Riemann–Hilbert problem is solved: find an analytical function <> from the Smirnov class E
p(D), whose angular boundary values satisfy the condition
The boundary of the domain D is assumed to be a piecewise smooth curve whose nonintersecting Lyapunov arcs form, with respect to D, the inner angles with values , 0 < 2. 相似文献
17.
Randolf Arnold 《Monatshefte für Mathematik》1989,108(4):277-293
LetK andL be convex bodies of then-dimensional Euclidean spaceE
n
. The -distance ofK andL is defined by
, whereh
k
andh
L
denote the support functions ofK andL restricted to the unit sphereS
n–1
E
n
. We consider the problem of best approximation ofL by the images k ofK under proper rigid motions :E
n
E
n
. A motion that minimizes 2(K
L) is called optimal for (K, L) in the sense of the metric 2. The results in the general case (n2 arbitrary) base on the fact that the Steiner points of K andL coincide if is optimal for (K, L). Forn=2 we obtain a relationship between convex convolution bodies and the underlying approximation problem. 相似文献
18.
B. B. Bhattacharyya X. Li M. Pensky G. D. Richardson 《Annals of the Institute of Statistical Mathematics》2000,52(1):71-83
The limiting distribution of the normalized periodogram ordinate is used to test for unit roots in the first-order autoregressive model st= s-1,t+s,t-1- s-1,t-1+st. Moreover, for the sequence
n
= e
c/n
,
n
= e
d/n
of local Pitman-type alternatives, the limiting distribution of the normalized periodogram ordinate is shown to be a linear combination of two independent chi-square random variables whose coefficients depend on c and d. This result is used to tabulate the asymptotic power of a test for various values of c and d. A comparison is made between the periodogram test and a spatial domain test. 相似文献
19.
Michel Talagrand 《Inventiones Mathematicae》1992,107(1):41-59
Summary Consider a sequence(x
i
)
in
of norm one vectors in a Banach space. For a subsetJ of {1,...,n} consider the equivalence constant (J) between(x
i
)
iJ
and the 1 basis, and consider (k)=min{(J); cardJ=k}. We give a near optimal relationship between the rate of decay of (k) and the averageE of
over all choices of signs. In particular, we show that one can choosek such that, for some universal constantK, kE
2
/Kn and
. This is optimal within the logarithmic term. We also prove, that forp<2, the notions of type and infratype coincide.Oblatum 27-III-1991Work partially supported by an NSF grant 相似文献
20.
Generalized ornstein-uhlenbeck process having a characteristic operator with polynomial coefficients
Itaru Mitoma 《Probability Theory and Related Fields》1987,76(4):533-555
Summary Let be a weighted Schwartz's space of rapidly decreasing functions, the dual space and (t) a perturbed diffusion operator with polynomial coefficients from into itself. It is proven that (t) generates the Kolmogorov evolution operator from into itself via stochastic method. As applications, we construct a unique solution of a Langevin's equation on : whereW(t) is a Brownian motion and *(t) is the adjoint of (t) and show a central limit theorem for interacting multiplicative diffusions. 相似文献