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1.
Р. С. Юлмухаметов 《Analysis Mathematica》1985,11(3):257-282
The following statement is proved. Letu be a subharmonic function in the region and
u
the associated measure. Then there exists a functionf holomorphic in and such that if
f
is the associated measure of the function in ¦f¦, then ¦u(z)–ln¦f(z)¦ A¦ln s¦+B¦ln diam¦+ s(¦lns¦+1)+C. hold at every point z for which the setsD(z, t)={w: ¦w–z¦},t(0,s) lie in and satisfy(D(z, t))t both for=
u
and for=
f
. In the case where is an unbounded region, In diam should be replaced by ln ¦z¦. The constants, , do not depend on andu.
. . . 相似文献
. . . 相似文献
2.
L. E. Payne G. A. Philippin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1991,42(6):864-873
Summary In this paper we study various overdetermined problems involving harmonic functions. In particular, we show that if the second eigenfunctionu
2 of the Stekloff eigenvalue problem in a bounded simply connected plane domain has a constant value of u
2 on , then is a disk
Résumé Cet article est consacré à l'étude de certains problèmes surdéterminés pour des fonctions harmoniques. En particulier, nous montrons que si le gradient de la seconde fonction propre du problème de Stekloff défini dans un domaine borné, simplement connexe du plan, a son module constant sur la frontière , alors est nécessairement un disque.相似文献
3.
L
p
, 0<<1, . 相似文献
4.
Aparna W. Higgins 《Algebra Universalis》1985,20(2):179-193
Given a group G and a descending chainG
0,G
1,...,G
n, of normal subgroups ofG, we prove that there exists a universal algebra
, such that the chain ...Wn(
)...W1(
}) W0(
)W(
) is isomorphic to the chain ...G
n ...G
1G
0G, where W(
) is the group of weak automorphisms of
, and Wn(
) is the group of weak automorphisms of
that leaves alln-ary operations fixed.We also prove that there are an infinite number of non-isomorphic algebras that satisfy the above.These results are a generalization of those proved by J. Sichler, in the special case when G=G0, and G1=G2=...=Gn=....Presented by J. Mycielski.This paper comprises part of the author's doctoral dissertation at the University of Notre Dame in 1983. The author wishes to express her deep gratitude to Professor Abraham Goetz for suggesting this problem, for being extremely generous with his time and experience, and for giving her his constant encouragement. The author also thanks the reviewer for his helpful comments. 相似文献
5.
Lu(t)+(u,F)g(t)=f(t), tS. , ( F, g). .
The authors wish to thank Professor Yu. A. Rozanov for his help and discussions. 相似文献
The authors wish to thank Professor Yu. A. Rozanov for his help and discussions. 相似文献
6.
Jin-Ming Chao 《Geometriae Dedicata》1999,74(1):91-94
Let m2(n,q), m2(n,q) be, respectively, the maximum value, the second largest value of k for which there exists a complete k-cap in PG(n,q). In this paper, the known upper bound on m2(3,q), q even, q 8, is improved. This new upper bound on m2(3,q) is then used to improve the upper bounds on m2(n,q), q even, q 8 and n 4. 相似文献
7.
F. Móricz 《Analysis Mathematica》1979,5(2):135-147
Z
d — k=(k
1, ...,k
d) k
j,d1.d- (8), . .
a
k s
m=
a
k s, >0 N, min (m
1,...,m
d)N, ¦s
m–s¦. , , >0 N, min (m
1,...,m
d)N min (n
1,...,n
d)N, ¦s
m–s
n. . , (8) , >0 N, max (b
1,...,b
d) N, m — Z
d
, m1, ¦s(b, m)¦ where
相似文献
8.
Simeon Reich 《manuscripta mathematica》1981,36(2):163-178
Let E be a Banach space and E(–,] a proper lower semi-continuous convex function. The main purpose of this paper is to characterize those m-accretive operators AE x E that are also -accretive. This is done by using the semigroup S generated by -A, and by first establishing a necessary and sufficient condition for to be a Lyapunov function for S. We also obtain similar results for accretive operators that are not necessarily m-accretive, and deduce invariance and order-preserving criteria for nonlinear semigroups.This research was partially supported by the National Science Foundation under Grant MCS-8102086. 相似文献
9.
G. G. Gevorkyan 《Analysis Mathematica》1986,12(3):185-190
, (t) >0 E(–, +),E<, , ¦f(t)¦ (t)
xE, f(t)=0 (–, +). 相似文献
10.
We consider the boundary-value problem u
tt + u
t + (1 + cos2)sin u =2
u
xx, u
x|x=0=ux|x==0, where 0<1, =(1+)t, ,> 0, and the sign of is arbitrary. It is proved that for an appropriate choice of the external parameters and and for sufficiently small the number of exponentially stable solutions 2-periodic in can be made equal to an arbitrary predefined number. 相似文献
11.
Let m
, 0 m+ in Kato's class. We investigate the spectral function s( + m) where s( + m) denotes the upper bound of the spectrum of the Schrödinger operator + m. In particular, we determine its derivative at 0. If m- is sufficiently large, we show that there exists a unique 1 > 0 such that s( + 1m) = 0. Under suitable conditions on m+ it follows that 0 is an eigenvalue of + 1m with positive eigenfunction. 相似文献
12.
A. M. Kagan 《Journal of Mathematical Sciences》1986,34(2):1482-1487
Summary Denote by
k
a class of familiesP={P} of distributions on the line R1 depending on a general scalar parameter , being an interval of R1, and such that the moments µ1()=xdP
,...,µ2k
()=x
2k
dP
are finite, 1 (), ..., k (), k+1 () ...,
k
() exist and are continuous, with 1 () 0, and
j
+1 ()= 1 ()
j
() +[2() -1()2]
j
()/ 1 (), J=2, ..., k. Let 1=¯x=x
1 + ... +x
n/n, 2=x
1
2 + ... +x
n
2/n, ...,
k
=(x
1
k
+ ... +x
n
k/n denote the sample moments constructed for a sample x1, ..., xn from a population with distribution Pg. We prove that the estimator of the parameter by the method of moments determined from the equation 1= 1() and depending on the observations x1, ..., xn only via the sample mean ¯x is asymptotically admissible (and optimal) in the class
k
of the estimators determined by the estimator equations of the form 0 () + 1 () 1 + ... +
k
()
k
=0 if and only ifP
k
.The asymptotic admissibility (respectively, optimality) means that the variance of the limit, as n (normal) distribution of an estimator normalized in a standard way is less than the same characteristic for any estimator in the class under consideration for at least one 9 (respectively, for every ).The scales arise of classes
1
2... of parametric families and of classes 1 2 ... of estimators related so that the asymptotic admissibility of an estimator by the method of moments in the class
k
is equivalent to the membership of the familyP in the class
k
.The intersection consists only of the families of distributions with densities of the form h(x) exp {C0() + C1() x } when for the latter the problem of moments is definite, that is, there is no other family with the same moments 1 (), 2 (), ...Such scales in the problem of estimating the location parameter were predicted by Linnik about 20 years ago and were constructed by the author in [1] (see also [2, 3]) in exact, not asymptotic, formulation.Translated from Problemy Ustoichivosti Stokhasticheskikh Modelei, pp. 41–47, 1981. 相似文献
13.
L. Leindler 《Analysis Mathematica》1995,21(1):23-33
, , . .
Dedicated to Academician S. M. Nikol'skii on his 90th birthday
This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # 234. 相似文献
Dedicated to Academician S. M. Nikol'skii on his 90th birthday
This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # 234. 相似文献
14.
15.
For a partition ={1230} of non-negative integers, we calculate the Euler characteristic of the local system on the moduli space of genus 3 hyperelliptic curves using a suitable stratification. For some of low degree, we make a guess for the motivic Euler characteristic of using counting curves over finite fields.Mathematics Subject Classification (1991): 14J15, 20B25 相似文献
16.
A variety of Galerkin methods are studied for the parabolic equationu
t
=(a(x)
u),x
n
,t (O,T], subject to the nonlinear boundary conditionu
v
=g(x,t,u),x,t (O,T] and the usual initial condition. Optimal order error estimates are derived both inL
2 () andH
1 () norms for all methods treated, including several that produce linear computational procedures.The authors were partially supported by The National Science Foundation during the preparation of this paper. 相似文献
17.
Thorsten Kröncke 《Integral Equations and Operator Theory》2001,40(1):80-105
Let T- S, be a family of not necessarily bounded semi-Fredholm operators, where T and S are operators acting between Banach spaces X and Y, and where S is bounded with D(S) D(T). For compact sets , as well as for certain open sets , we investigate existence and minimal rank of bounded feedback perturbations of the form F=BE such that min.ind (T-S+F)=0 for all . Here B is a given operator from a linear space Z to Y and E is some operator from X to Z.We give a simple characterization of that situation, when such regularizing feedback perturbations exist and show that for compact sets the minimal rank never exceeds max { min.ind (T-S) }+1. Moreover, an example shows that the minimal rank, in fact, may increase from max {...} to max {...}+1, if the given B enforces a certain structure of the feedbachk perturbation F.However, the minimal rank is equal to max { min.ind (T-S) }, if is an open set such that min.ind (T-S) already vanishes for all but finitely many points . We illustrate this result by applying it to the stabilization of certain infinite-dimensional dynamical systems in Hilbert space. 相似文献
18.
19.
— [0,1] ,E — - e=1 [0,1]. I —
E
=1, E=L
2 x
e
=xL
2 x E.
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
This work was prepared when the second author was a visiting professor of the CNR at the University of Firenze. He was supported by the Soros International Fund. 相似文献
20.
А. В. Резцов 《Analysis Mathematica》1995,21(2):129-135
Q (.. , L). Q . P(Sr(2)) — 2 (S
r(2) (r — ). , M(P(S
r(m=sup{t(·)t(·)1:t P(S
r(2)),t 0}. , /4+(1)M(P(S
r(2)))/r
215/17+(1)(r+). (Q), Q L. 相似文献