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1.
S. V. Lapin 《Mathematical Notes》1977,21(5):346-352
For a given -function (u), a condition on a -function (u) is found such that it is necessary and sufficient for the following to hold: if fn(x) f(x) and f
n
(x)M (n=1, 2, ...) where M>0 is an absolute constant, then f
n
(x)–f(x)0(n). An analogous condition for convergence in Orlicz spaces is obtained as a corollary.Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 615–626, May, 1977.The author thanks V. A. Skvortsov for his constant attention and guidance on this paper. 相似文献
2.
Hansmartin Zeuner 《Journal of Theoretical Probability》1989,2(1):51-63
Let (S
nn>-1) be a random walk on a hypergroup (
+
, *), i.e., a Markov chain with transition kernelN(x, A) = x * (A), where is a fixed probability measure on
+
such that the second moment exists. Then depending on the growth of the hypergroup two situations can occur: when (
+
, *) is of exponential growth then it is shown thatS
n is asymptotically normal. In the case of polynomial growth {more precisely, if the densityA of the Haar measure of (
+
, *) satisfies lim[A()/A()]=}, the normalized variablesS
n/[n Var()/(+1)]1/2 converge to a Rayleigh distribution
with parameter . 相似文献
3.
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
4.
In this paper equivalent classes of the classes M and S
pr
, p > 1, > 0. r { 0,1,2, ... ,[]} defined by Shuyun [3] are obtained. Then, it is shown that the class S
pr
, 1 > p 2, 0, r {0,1,2,...,[]} is a subclass of BVC
r
, where S
pr
is the equivalent class of the Shuyun's class S
pr
, BV is the class of null sequences of bounded variation and C
r
is the extension of the Garrett--Stanojevic class. As a corollary of this result, we have obtained the theorem, proved in [7]. 相似文献
5.
If Exc is the set of all excessive measures associated with a submarkovian resolvent on a Lusin measurable space and B is a balayage on Exc then we show that for any mExc there exists a basic set A (determined up to a m-polar set) such that B=(BA)* for any Exc, m. The m-quasi-Lindelöf property (for the fine topology) holds iff for any B there exists the smallest basic set A as above. We characterize the case when any B is representable i.e. there exists a basic set such that B=(BA)* on Exc. 相似文献
6.
Keiko Kotani 《Annals of Combinatorics》1998,2(2):137-144
LetG be a graph, andk1 an integer. LetU be a subset ofV(G), and letF be a spanning subgraph ofG such that deg
F
(x)=k for allx V(G)–U. If deg
F
(x)k for allxU, thenF is called an upper semi-k-regular factor with defect setU, and if deg
F
(x)k for allxU, thenF is called a lower semi-k-regular factor with defect setU. Now letG=(X, Y;E(G)) be a bipartite graph with bipartition (X,Y) such that X=Yk+2. We prove the following two results.(1) Suppose that for each subsetU
1X such that U
1=max{k+1, X+1/2},G has an upper semi-k-regular factor with defect setU
1Y, and for each subsetU
2Y such that U
2=max{k+1, X+1/2},G has an upper semi-k-regular factor with defect setXU
2. ThenG has ak-factor.(2) Suppose that for each subsetU
1X such that U
1=X–1/k+1,G has a lower semi-k-regular factor with defect setU
1Y, and for each subsetU
2Y such that U
2=X–1/k+1,G has a lower semi-k-regular factor with defect setXU
2. ThenG has ak-factor. 相似文献
7.
Reiterated homogenization is studied for divergence structure parabolic problems of the form u
/t–div (a(x,x/,x/2,t,t/ k)u
)=f. It is shown that under standard assumptions on the function a(x, y
1,y
2,t,) the sequence {u
} of solutions converges weakly in L
2 (0,T; H
0
1
()) to the solution u of the homogenized problem u/t– div(b(x,t)u)=f.This revised version was published online in April 2005 with a corrected missing date string. 相似文献
8.
Hans-Heinrich Kairies 《Aequationes Mathematicae》1996,51(1-2):115-128
Summary The following Artin type characterization of : + + is proved: Assume thatf: + + satisfies the Gauss multiplication formula for some fixedp 2,f is absolutely continuous on [l/p, 1 + ] for some > 0 and lim
x 0
xf(x) = 1. Thenf(x) = (x) forx > 0.The optimality of this result is checked by means of counterexamples. For instance, it is shown that the result is no longer true, if f is absolutely continuous is replaced by f is continuous and of finite variation. 相似文献
9.
An extension operator c in a category is an assignment, to each object A a monomorphism c
A
: AcA. Seeking to approximate such a c by a functor, in our earlier paper Maximum monoreflections, we showed that with some hypotheses on the category, and on c, there is a monoreflection (c) maximum beneath c. Thus, in a suitable category of rings, using the complete ring of quotients operator Q, each object A has a maximum functorial ring of quotients (Q)A. But the proof gave no hint of how to calculate the general (c)A's, nor the particular (Q)A's. In the present paper, we give an explicit formula (and separate proof of existence) for the (c)A's, under more complicated hypotheses on the category and assuming the c
A
's are essential monomorphisms. We discuss briefly how the formula proves adequate to calculate the (Q)A's in Archimedean f-rings, and some related and necessary constructs in Archimedean l-groups. 相似文献
10.
Let {T
p:q
1 p q
2} be a family of consistent C
0 semigroups on L
p(), with q
1,q
2 [1,) and open. We show that certain commutator conditions on T
p and on the resolvent of its generator A
p ensure the p independence of the spectrum of A
p for p [q
1,q
2.Applications include the case of Petrovskij correct systems with Hölder continuous coefficients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coefficients. 相似文献
11.
Shiqi Song 《应用数学学报(英文版)》1993,9(2):115-124
LetX be the solution of the SDE:dX
t = (X
t)dB
t +b(X
t)dt, with andb C
b
(R) such that >0 for some constant , andB a real Brownian motion. Let be the law ofX onE=C([0, 1],R) andk E* – {0}, whereE* is the topological dual space ofE. Consider the classical form:
k
(u, v)=u / kv / kd, whereu andv are smooth functions onE. We prove that, if
k
is closable for anyk in a dense subset ofE* and if the smooth functions are contained in the domain of the generator of the closure of
k
, must be a constant function. 相似文献
12.
Summary Let (X
t
n
) be a Poisson sequence of independent Brownian motions in
d
,d3; Let be a compact oriented submanifold of d, of dimensiond–2 and volume ; let t be the sum of the windings of (X
s
n
, 0st) around ; then t/t converges in law towards a Cauchy variable of parameter /2. A similar result is valid when the winding is replaced by the integral of a harmonic 1-form in
d
. 相似文献
13.
Let X be a separable compact Abelian group, Aut(X) the group of topological automorphisms of X, f
n: XX a homomorphism f
n(x)=nx, and X
(n)=Im f
n. Denote by I(X) the set of idempotent distributions on X and by (X) the set of Gaussian distributions on X. Consider linear statistics L
1=
1(
1)+
2(
2) and L
2=
1(
1)+
2(
2), where
j are independent random variables taking on values in X and with distributions
j, and
j,
jAut(X). The following results are obtained. Let X be a totally disconnected group. Then the independence of L
1 and L
2 implies that
1,
2I(X) if and only if X possesses the property: for each prime p the factor-group X/X
(p) is finite. If X is connected, then there exist independent random variables
j taking on values in X and with distributions
j, and
j,
jAut(X) such that L
1 and L
2 are independent, whereas
1,
2(X) * I(X). 相似文献
14.
We prove the existence of bounded solutions for a class of nonlinear elliptic problems of type–div(a(x,u,Du))=H(x,u,Du)+f,
uW
1,p
0()L
(),where a(x,,)b(||)||
p
, b is a continuous monotone decreasing function and |H(x,,)| k()||
p
, k is a continuous monotone increasing function. 相似文献
15.
We propose a fast summation algorithm for slowly convergent power series of the form
j=j
0
z
j
j
j
i=1
s
(j+
i
)–
i
, where R,
i
0 and
i
C, 1is, are known parameters, and
j
=(j), being a given real or complex function, analytic at infinity. Such series embody many cases treated by specific methods in the recent literature on acceleration. Our approach rests on explicit asymptotic summation, started from the efficient numerical computation of the Laurent coefficients of . The effectiveness of the resulting method, termed ASM (Asymptotic Summation Method), is shown by several numerical tests. 相似文献
16.
LetV be a finite dimensional complex linear space and letG be a compact subgroup of GL(V). We prove that an orbitG, V, is polynomially convex if and only ifG
is closed andG is the real form ofG
. For every orbitG which is not polynomially convex we construct an analytic annulus or strip inG
with the boundary inG. It is also proved that the group of holomorphic automorphisms ofG
which commute withG
acts transitively on the set of polynomially convexG-orbits. Further, an analog of the Kempf-Ness criterion is obtained and homogeneous spaces of compact Lie groups which admit only polynomially convex equivariant embeddings are characterized.Supported by Federal program Integratsiya, no. 586.Supported by INTAS grant 97/10170. 相似文献
17.
H. Woźniakowski 《Numerische Mathematik》1978,30(3):301-314
Summary We deal with the rounding error analysis of successive approximation iterations for the solution of large linear systemsA
x
=b. We prove that Jacobi, Richardson, Gauss-Seidel and SOR iterations arenumerically stable wheneverA=A
*>0 andA has PropertyA. This means that the computed resultx
k
approximates the exact solution with relative error of order A·A
–1 where is the relative computer precision. However with the exception of Gauss-Seidel iteration the residual vector Ax
k
–b is of order A2 A
–1 and hence the remaining three iterations arenot well-behaved.This work was partly done during the author's visit at Carnegie-Mellon University and it was supported in part by the Office of Naval Research under Contract N00014-76-C-0370; NR 044-422 and by the National Science Foundation under Grant MCS75-222-55 相似文献
18.
Wilfried Buchholz 《Archive for Mathematical Logic》1988,27(1):51-60
Summary In this paper we give a new and comparatively simple proof of the following theorem by Girard [1]:If x
y
(x,y) (where the relation is arithmetic and positive in Kleene's
), then there exists a recursive DilatorD such that x
<y
(x, y).The essential feature of our proof is its very direct definition of the dilatorD. Within a certain infinitary cutfree system of inductive logic (which in fact is a modification of Girard's system in [1]) we construct in a uniform way for each ordinal a derivation T of the formula x
<y
(x, y), and then defineD immediately from the family (T)On. Especially we set D():=Kleene-Brouwer length of (T). 相似文献
19.
A. Z. Mokhon'ko 《Ukrainian Mathematical Journal》1992,44(4):454-463
We obtain asymptotic estimates of meromorphic solutions to the differential equationP
n
(z, , )=P
n–1
(z, , ,...,
(m)
) in the angular domain P={z: arg z · }. Here Pn(z, w, w) is a polynomial in all variables, and of degree n with respect to w and w; Pn–1(z, w, w, ..., w(m)) is a polynomial in all variables, and of degree n –1 with respect to w, w, ..., w(m) In the particular case, when the solutions are entire functions, these estimates are more precise than the known estimates that are obtained by using the method of Wiman-Valiron, which cannot be applied to meromorphic solutions in the domain P.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 514–523, April, 1992. 相似文献
20.
Horst Alzer 《Aequationes Mathematicae》1988,36(2-3):246-250
Summary In this paper we prove the following:IfA
n
,G
n
andH
n
(resp.A
n
,G
n
andH
n
) denote the arithmetic, geometric and harmonic means ofa
1,, a
n
(resp. 1 –a
1,, 1 –a
n
) and ifa
i
(0, 1/2],i = 1,,n, then(G
n
/G
n
)
n
(A
n
/A
n
)
n-1
H
n
/H
n
, (*) with equality holding forn = 1,2. Forn 3 equality holds if and only ifa
1 = =a
n
. The inequality (*) sharpens the well-known inequality of Ky Fan:G
n
/G
n
A
n
/A
n
. 相似文献