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1.
In the class F1 of functions f(), regular and univalent in the annulus ={<||<1} and satisfying the conditions ¦f()¦ < 1 and f() 0 for , ¦f()¦=1 ¦¦=1, for f(l)=1, one finds the set of the values D(A)=f(A): f for an arbitrary fixed point A. One makes use of the method of variations and certain facts from the theory of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 82–92, 1985.  相似文献   

2.
Let Xu, uRq, be a weakly dependent random field, EXu=0, let be the Lebesque measure in Rq, let Vu be an increasing system of subsets in Rq, and let. One obtains a central limit theorem for u and estimates for the moments E¦n¦t, t2.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 142, pp. 39–47, 1985.  相似文献   

3.
Let Rj : |j| m, be a given set of n×n matrices. Necessary and sufficient conditions for the existence and uniqueness of an invertible function F() = Fjj in the Wiener algebra of n×n matrix valued functions on the unit circle || = 1 such that Fj=Rj for |j| m, and F admits either a right or a left canonical factorization and the matrix Fourier coefficients of F–1 vanish for |j| > m are presented and discussed. In the special case that the block Toeplitz matrix based on the given Rj is positive definite there is exactly one such extension: the so-called maximum entropy or autoregressive extension of statistical estimation theory. Some special properties of this extension are discussed.  相似文献   

4.
Let (x) denote the number of those integers n with (n) x, where denotes the Euler function. Improving on a well-known estimate of Bateman (1972), we show that (x)-Ax R(x), where A=(2)(3)/(6) and R(x) is essentially of the size of the best available estimate for the remainder term in the prime number theorem.  相似文献   

5.
Thewidth (chain number) of a partial order P, < is the smallest cardinal such that ¦A¦< 1 + whenever A is an antichain (chain) in P. We prove that, if a partial order (P, <) has width and cf()=, then P contains antichains An (n<) such that ¦A 0¦<¦A1¦ <...<={¦An¦: n < < } and either A01 A2< ... or A0>A1 >A2> ... A similar structure result is obtained for partial orders with chain number if cf()=. As an application we solve a problem of van Douwen, Monk and Rubin [1] by showing that if a Boolean algebra has width , thencf() .This work has been partially supported by NATO grant No. 339/84.Presented by Bjarni Jonsson.  相似文献   

6.
Section 1 of the paper is devoted to extremal problems in the classes of conformal homeomorphisms of the circle and the annulus, connected directly with the problem on the maximum of the conformal modulus in the family of doubly connected domains. In Secs. 2 and 3 one considers the class R of functions f()=c1+c22+... regular and univalent in the circleU={||<1} and such that f(1)f(2)=1 for 12U (the class of Bieberbach-Eilenberg functions). Here one solves the problem of the maximum of |f(0)| in the class of functions f()R with a fixed value f(0, where 0 is an arbitrary point U, and of the maximum of |f(0)| in the entire class R. For the proof one makes use of the method of the moduli of families of curves.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 94–114, 1985.  相似文献   

7.
Let a, a0, a, be a fixed point in the z-plane, (a, 0, ), the class of all systemsf k()l 3 of functions z=f k(), k=1, 2, 3, of which the first two map conformally and in a s ingle-sheeted manner the circle ¦¦<1, and the third maps in a similar manner the region ¦¦>1, into pair-wise nonintersecting regions Bk, k=1, 2, 3, containing the points a, 0, and , respectively, so thatf 1(0)=a,f 2(0)=0 andf 3()=. The region of values (a, 0, ) of the system M(¦f 1'(0)¦, ¦f 2'(0)¦, 1/¦f 3'()¦) in the class (a, 0, ) is determined.Translated from Matematicheskie Zametki, Vol. 6, No. 4, pp. 417–424, October, 1969.  相似文献   

8.
It is proved that for anyf(x, y) L(R), where R=[-,,-, ], a function (x, y), exists such that ¦(x, y) ¦=¦f(x, y) ¦ for almost all (x, y) R. The Fourier series of the function (x, y) and all conjugate trigonometric series are A*-summable almost everywhere.Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 145–150, February, 1972.  相似文献   

9.
This paper is a sequel to [5] and [6]. We continue our study of occupation time large deviation probabilities for some simple infinite particle systems by analysing the so-called voter model t (see e.g., [11] or [8]). In keeping with our previous results, we show that the large deviations are classical in high dimensions (d5 for t) but fat in low dimensions (d4). Interaction distinguishes the voter model from the independent particle systems of [5] and [6], and consequently exact computations no longer seem feasible. Instead, we derive upper and lower bounds which capture the asymptotic decay rate of the large deviation tails.Dedicated to Frank Spitzer on his 60th birthdayPartially supported by the National Science Foundation under Grant DMS-831080Partially supported by the National Science Foundation under Grant DMS-841317Partially supported by the National Science Foundation under Grant DMS-830549  相似文献   

10.
By simultaneously considering two moduli problems for pairs of homotopic classes of curves a complete solution is obtained of the problem of the range of functions of the class SR, where SR is the class of functions in S with real coefficients, at a fixed point 0 of the disk ¦¦<1, and min¦f(0¦ in the class SRis also found. Partial results in this problem were obtained earlier by J. Jenkins and V. V. Chernikov.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 139, pp. 156–167, 1984.  相似文献   

11.
The stability of a large class of numerical methods to solve initial value problems of ordinary differential equations is governed by a two-variable polynomial (,) when the method is applied toy'=qy. Here=hq, whereh is the stepsize. This class of methods includes Runge-Kutta methods, linear multistep methods, predictor-corrector methods, composite multistep methods and linear multistep-multiderivative methods. An algebraic test is given to determineA 0-stability of such methods in a finite number of operations (additions, subtractions, multiplications and divisions). It is shown that the number of multiplications and divisions is of order 1/82(4 +O(3)), where is the degree of (,) in the variable and the degree in the variable. The test has been implemented for multistep-multiderivative methods in a symbol manipulation language. For Enright's second derivativek-step methods it is proved that the methods areA 0-stable if and only ifk<8.Supported by the Swiss National Foundation Grant No. 82.524.077. On leave from Institute of Mathematics, Ruhr-University Bochum, D-463 Germany.  相似文献   

12.
Let the self-adjoint operator A and the bounded operator B be specified in Hilbert space We let denote the spectral family of the operator A. If (E – E N ) B 2+E–NB 2 0 npnN , then in the complex plane z=+ there will exist the curve ¦ ¦ =f (), limf () = 0 for ± such that the entire spectrum of the operator A+B lies within the region ¦ ¦ f(). In particular, the condition of the theorem will be satisfied when B is a completely continuous operator.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 415–420, April, 1968.The author expresses his appreciation to R. S. Ismagilov for his discussion of the results.  相似文献   

13.
It is well known that any recursively enumerable set S of natural numbers can be represented by formulas of the following types a S x yx, z1...Zn (D (a,x,y,z1,...,zn)=0)¦(Davis normal form); aS z1...zn (E (a,z1..., zn)=E2(a,z1,...,zn)) (exponential diophantine representation); and aS z1... zn, (D (a-, z1),...)Zn)=0) (diophantine representation). Each of these three representations yields a different measure for the complexity of S as a whole and the complexity of accepting individual members of S. A survey is presented of various results concerning such complexity measures, due to different authors.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeliniya Matematicheskogo Instituta im. V. A. Steklova Akad. Nauk SSSR, Vol. 174, pp. 122–131, 1988.  相似文献   

14.
A relation between Chung's and Strassen's laws of the iterated logarithm   总被引:2,自引:0,他引:2  
Summary Let W(t) be a standard Wiener process and let f(x) be a function from the compact class in Strassen's law of the iterated logarithm. We investigate the lim inf behavior of the variable sup ¦W(xT)(2T loglog T)–1/2f(x)¦, 0x1 suitably normalized as T.This extends Chung's result valid for f(x)0, stating that lim inf.[ sup ¦(2T loglogT)–1/2 W(xT)¦(loglog T)–1]=/4 a.s. T 0x1  相似文献   

15.
[0,1], - H .

This paper was written during the author's scholarship at the State University of Odessa in the USSR.  相似文献   

16.
This paper is devoted to results belonging to the theory of rational approximation of analytic functions. We study the rate of decrease of the best approximations n of a functionf holomorphic in a disk ¦z ¦z¦< , >1> by rational functions of order at most n in the uniform metric on the unit disk with center at z=0. We prove theorems that connect the rate of decrease of the quantities n with the order 0 and type 0 of the functionf. The proofs of these results are based on the methods of the theory of Hankel operators.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 32–39.The author is grateful to Prof. V. A. Prokhorov for posing this problem and assistance with the preparation of this article.  相似文献   

17.
In this article we obtain sufficient conditions for the univalence of n-symmetric analytic functions in the region ¦¦>–1 and in the disk ¦¦<–1. We examine the question of univalent variation of functions analytic in ¦¦<–1 and mapping ¦¦=1 onto a contour with two zero angles. We give an application of these results to the fundamental converse boundary-value problems.Translated from Matematicheskie Zametki, Vol. 19, No. 3, pp. 331–346, March, 1976.In conclusion the author would like to thank L. A. Aksent'ev for his guidance, and those who took part in his seminar for their useful advice.  相似文献   

18.
The solution of the following problems is offered. Suppose a multiset J (¦J¦=p) is given. For each pair of elements and J, a number 1 P is given. Moreover, if 1 < x<p then x is undefined. If x=1, then x=p. Problem 1. Find the permutation 1...F of elements of the multiset J satisfying the following conditions. Let i, i=. If i,j < x, thenj <i. If i,j > x, then i<j. Such a permutation is called a PC-schedule. Problem 2. Find a PC-schedule in which the following property holds: if i < x < j, i=, j=, then. Such a PC-schedule is called an SC-schedule. The conditions under which these problems have solutions are studied. For their solution an algorithm of shifts is used with the complexity O(¦B(J)¦2¦J¦).Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 124, pp. 44–72, 1983.  相似文献   

19.
Conditions are found under which for an entire function f represented by a Dirichlet series with finite Ritt order on some sequence (xk), 0 < xk , as k one has ¦f(xk)¦=Mt((1 + 0(1) xk), Mf(x)=sup {¦ f (z) ¦:Re z x}.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 2, pp. 265–269, February, 1991.  相似文献   

20.
Summary Let X={X(t), t N} be a centred Gaussian random field with covariance X(t)X(s)=r(t–s) continuous on N×N and r(0)=1. Let (t,s)=((X(t)–X(s)) 2)1/2; (t,s) is a pseudometric on N. Assume X is -separable. Let D 1 be the unit cube in N and for 0<k, D k= {xN: k –1 xD1}, Z(k)=sup{X(t),tD k}. If X is sample continuous and ¦r(t)¦ =o(1/log¦t¦) as ¦t¦8 then Z(k)-(2Nlogk) 1/20 as k a.s.  相似文献   

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