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1.
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   

2.
Let (,A,P) denote some probability space and some sub--algebra ofA. It is shown that there exists a semiregular versionQ (A),A, , of the conditional distributionP(A|), AA, i.e., Q (A), (AA fixed) is andAQ (A),AA ( fixed), is a probability charge satisfyingQ (N)=0, , for allP-zero setsN, if and only ifL 1(,P|) has a lifting, which exists for any sub--algebra ofA ifL 1(,A P) is separable. Separability ofL 1(,A,P) implies also the existence of a strongly semiregular versionQ (A),A, , ofP(A|), A , i.e., Q (A), (AA fixed), is -measurable andAQ (A),A ( fixed), is a probability charge. Furthermore,P can be written as P 1+(1–)P 2, 01, whereP 1 are probability measures onA such thatP 1(A|),AA, has a semiregular version vanishing for anyP-zero setN andP 2 is singular with respect to any probability measure onA of the type ofP 1. In the case 0<<1 the probability measuresP j ,j=1, 2, are uniquely determined. The decomposition can be carried over to the case, where the additional condition thatQ (N)=0 for all and anyP-zero setN is valid, is omitted respectively semiregularity is replaced by (i) strong semiregularity, or (ii) classical regularity. In the last mentioned case (ii) the decomposition is multiplicative.  相似文献   

3.
This paper is an expository survey of recent research on the application of Szegö polynomials and PPC-continuedfractions to the frequency analysis problem described as follows: We want to determine the unknown frequencies 1, 2, ..., I from a sample of N observed values x N (m), m = 0, 1, ..., N– 1, arising from a continuous waveform that is the superposition of a finite number of sinusoidal waves with frequencies 1,2, ..., I . The method is based on the property that certain zerosof the Szegö polynomials (and poles of the PPC-fraction approximants) converge (as N ) to the frequency points e i j , j = ±1, ± 2, ..., ± I. The remaining zeros are bounded away from the unit circle |z|=1, asN . The Levinson algorithm is used to construct the Szegö polynomials and PPC-fractions from the values x N (m). A discussion is given on connections between the topics: Carathéodory functions,the trigonometric moment problem, Szegö polynomials and PPC-fractions. We also describe applications to Doppler radar, medicine, speech processing, speech therapy, meteorology and ocean tides.  相似文献   

4.
Summary A stochastic differential equation with smooth coefficients is considered, which defines a continuous flow t , (, .) of C +8 mappings of R d in R d . If z t is a continuous semi-martingale, t ,(,zt)s> is proved to be a semi-martingale, for which an Ito type formula is established. It is shown that a.s., for any t, t (, .) is an onto diffeomorphism. If z t is a continuous semi-martingale, t –1 ,(,z t ) is proved to be a semi-martingale, whose Ito decomposition is explicitly found.The support of the University of British Columbia is gratefully acknowledged.  相似文献   

5.
We present order relations for a group of deviations of a function f(·) H in terms of partial Fourier sums of this function in a generalized Hölder metric defined in a generalized Hölder space H * H .  相似文献   

6.
In the present paper we establish a criterion of algebraic independence of complex numbers 1, ..., n over a field of finite transcendence type using a sequence of nonzero polynomials in several variables with integral coefficients, which satisfy simultaneously certain upper and lower estimates in different orders of magnitude at the point ( 1, ..., q , 1, ..., n ), where { 1, ..., q } is a transcendence basis of over .The Project Supported by the National Natural Science Foundation of China  相似文献   

7.
Let A M be the space of all almost Kahlerian smooth metrics on a symplectic manifold M 2n , such that the fundamental form of each metric coincides with . It is well known that A M is a retractor of the space M of all smooth metrics on M. We show that M is a smooth trivial bundle over A M . A similar fact holds also in the case of a contact manifold.  相似文献   

8.
Summary Consider a Hamiltonian system (H, 2n ,). LetM be a symplectic submanifold of (2n ,). The system (H, 2n ,) constrained toM is (HM, M, M). In this paper we give an algorithm which normalizes the system on 2n in such a way that restricted toM we have normalized the constrained system. This procedure is then applied to perturbed Kepler systems such as the lunar problem and the main problem of artificial satellite theory.
Zusammenfassung Wir betrachten ein Hamiltonisches System (H, 2n ,). SeiMein symplectisches Submanifold von (2n ,). Das System (H, 2n ,), aufM beschränkt, ist (HM,M,M). In der vorliegenden Arbeit wird ein Algorithmus vorgeschlagen, der dieses System so auf 2n normalisiert, daß das aufM beschränkte System auch normalisiert ist. Dieser Algorithmus wird dann auf gestörte Keplersysteme, wie z. B. das Hill-sche Mondproblem und das Hauptproblem der Theorie der künstlichen Satelliten, angewendet.
  相似文献   

9.
Let H, H L be classes of functionsf(x) whose modulus of continuity (f; t) and, respectively, integral modulus of continuity(f; t)L do not exceed a given modulus of continuity(t), while Hv is a class of functionsf(x) whose variation fdoes not exceed a given number V > 0. Bounds are obtained for the upper limit of the best approximations in the metric of L by Haar-system polynomials on the classes just introduced (on the class H L only when (t)=Kt). These bounds are exact for class HV and, in case(t) is convex, also for the classes H and H L .Translated from Matematicheskie Zametki, Vol. 6, No. 1, pp. 47–54, July, 1969.The author wishes to thank N. P. Korneichuk for having posed the problem and for his constant attention to this work.  相似文献   

10.
In the power setP(E) of a setE, the sets of a fixed finite cardinalityk form across-cut, that is, a maximal unordered setC such that ifX, Y E satisfyXY, X someX inC, andY someY inC, thenXZY for someZ inC. ForE=, 1, and 2, it is shown with the aid of the continuum hypothesis thatP(E) has cross-cuts consisting of infinite sets with infinite complements, and somewhat stronger results are proved for and 1.The work reported here has been partially supported by NSERC Grant No. A8054.  相似文献   

11.
LetG be a domain inC n ,EG, mes E=0 for (r)=r 2n–1(r), where (r) is a nondecreasing non-negative function (r>0). Iff(z) is holomorphic inGE and (,f, GE)(), C=const, thenf(z) is holomorphic inG.The impossibility of the relaxation of the stipulations on () and(r) is also established.The statement above is a corollary to a more general result about the representation of a holomorphic function from a certain class in the form of an integral with respect to -measure, extended over the set of singular points of the function.  相似文献   

12.
Let a,b,c () be the number of factorizations of a Gaussian number in the form = 1 a 2 b 3 c , where a, b, and c are natural numbers. In the ring of Gaussian numbers, we construct an asymptotic formula for a summatory function of a,b,c () weighted by the generalized Klosterman function.  相似文献   

13.
The non-commutative torus C *(n,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C *n/S, 1) for a totally skew multiplier 1 on n/S. D. Poguntke [9] proved that A is stably isomorphic to C(S) C(*( Zn/S, 1) C(S) A Mkl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule.  相似文献   

14.
We consider the approximation by piecewise-constant functions for classes of functions of many variables defined by moduli of continuity of the form (1, ..., n ) = 1(1) + ... + n ( n ), where i ( i ) are ordinary moduli of continuity that depend on one variable. In the case where i ( i ) are convex upward, we obtain exact error estimates in the following cases: (i) in the integral metric L 2 for (1, ..., n ) = 1(1) + ... + n ( n ); (ii) in the integral metric L p (p 1) for (1, ..., n ) = c 11 + ... + c n n ; (iii) in the integral metric L (2, ..., 2, 2r) (r = 2, 3, ...) for (1, ..., n ) = 1(1) + ... + n – 1( n – 1) + c n n .  相似文献   

15.
We establish sufficient conditions for a nonlinear system of difference equations x(t + 1) =x(t) + + P(x(t),t)+ to be reducible to the system y(t + 1) =y(t) + . Here, P(x, t) is a function 2-periodic in xi(i = 1, ...,n) and almost periodic int with a frequency basis .Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 404–412, April, 1994.This work was supported by Ukrainian State Committee on Science and Technology.  相似文献   

16.
Let G be a graph with order p, size q and component number . For each i between p – and q, let be the family of spanning i-edge subgraphs of G with exactly components. For an integer-valued graphical invariant if H H is an adjacent edge transformation (AET) implies |(H)-(H')|1 then is said to be continuous with respect to AET. Similarly define the continuity of with respect to simple edge transformation (SET). Let M j() and m j() be the invariants defined by . It is proved that both M p–() and m p–(;) interpolate over , if is continuous with respect to AET, and that M j() and m j() interpolate over , if is continuous with respect to SET. In this way a lot of known interpolation results, including a theorem due to Schuster etc., are generalized.  相似文献   

17.
Two methods of calculating the scattering amplitude f(, 0) of a wave scattered by the vertex of an arbitrarily shaped cone are justified. It is shown that the approximation f d (, 0,t) obtained by a method similar to the AbelPoisson method of summation converges uniformly in the regularity region for f. Also, the possibility of calculating f(, 0) for N 1( 0) with the help of rapidly convergent integrals is proved. Bibliography: 7 titles.  相似文献   

18.
Summary The local homogeneity property is defined as in [Mak]. We show thatL (Q1) and some related logics do not have the local homogeneity property, whereas cofinality logicL (Q cf) has the homogeneity property. Both proofs use forcing and absoluteness arguments.  相似文献   

19.
We investigate the asymptotic behaviour of the summatory functions of z(n, ), k(n, ) z (n) and k(n, ) z (n).  相似文献   

20.
For even values of n we find the exact values of the diameters dn(W(r)H) of the classes of 2-periodic functions ((t) is an arbitrary convex upwards modulus of continuity) in the space C2. We find that d2n(W(r)H)=d2n–1(W(r)H) (n=1, 2, ... r=0, 1, 2, ...).Translated from Matematicheskie Zametki, Vol. 15, No. 3, pp. 387–392, March, 1974.The author expresses his thanks to N. P. Korneichuk for his interest in my work.  相似文献   

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