共查询到20条相似文献,搜索用时 31 毫秒
1.
V. I. Ruban 《Mathematical Notes》1974,15(3):222-225
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
2.
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
3.
R. Schneider 《Numerische Mathematik》1990,58(1):855-873
Summary We consider a spline collocation method for strongly elliptic zero order pseudodifferential equationsp
gw
Au=f on a cube =(0, 1)
m
. Utilizing multilinear spline functions which are zero at the boundary we collocate at the meshpoints inside . For classical strongly elliptic translation invariant pseudodifferential operators, we verify the stability of the considered collocation method inL
2(). Afterwards, form2 and a right hand sidefH
8(),s>m/2, we prove an asymptotic convergence estimate.The author has been supported by a grant of Deutsche Forschungsgemeinschaft under grant number Ko 634/32-1 相似文献
4.
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
5.
Exact values are obtained for the upper bounds on the norms,fL, on the classes W
(r)
H(r =0, 1, 2,...) of r-fold differentiable functions f(x), of periodicity2, for which (f(r);t)(t),where (t) is a given convex modulus of continuity.Translated from Matematicheskie Zametki, Vol. 2, No. 6, pp. 569–576, December, 1967. 相似文献
6.
We study the cardinalities of countably compact, locally countableT
3 spaces. For alln(<), there exists one of cardinality
n
. IfV=L, then there exists one of cardinalityx iffx= orx
=x. MA implies that there exists one of cardinality>2. 相似文献
7.
N. P. Khoroshko 《Mathematical Notes》1969,6(1):487-491
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
8.
N. K. Smolentsev 《Siberian Mathematical Journal》2001,42(6):1165-1169
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
9.
Summary LetT()=+F() be a transformation from the Wiener space to itself with the range ofF() assumed to be in the Cameron-Martin space. The absolute continuity and the density function associated withT is considered;T is assumed to be embedded in or defined through a parameterizationT
t
=+F
t
() andF
t
is assumed to be differentiable int. The paper deals first with the case where the range of thet-derivative ofF
t
() is also in the Cameron-Martin space and new representations for the Radon-Nikodym derivative and the Carleman-Fredholm determinant are derived. The case where thet-derivative ofF
t
is not in the Cameron-Martin space is considered next and results on the absolute continuity and the density function, under conditions which are considerably weaker than previously known conditions, are presented.The work of the second author was supported by the fund for promotion of research at the Technion 相似文献
10.
Daniel Guan 《Geometriae Dedicata》1996,63(2):217-225
In this note we prove a splitting theorem for compact complex homogeneous spaces with a cohomology 2 class [] such that the top power [
n
]0.Dedicated to Professor W. C. Hsiang on the occasion of his 60th birthdayPartially supported by NSF Grant DMS-9401755. 相似文献
11.
V. V. Kamotski 《Journal of Mathematical Sciences》2002,108(5):665-673
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
12.
Let q,n denote the complex Stiefel bundle over the complex Grassmannian
and let 0 be the universal connection on this bundle. Consider the Chern character form of 0 defined by the formula
where 0 is the curvature form of the connection 0. Let M be a manifold of dimension m and a closed 2k-form on M. Suppose, there exists a continuous map
which pulls back the cohomology class of chk(0) onto the cohomology class of . We prove that if q and n are greater than certain numbers (which we determine in this paper) then there exists a smooth map
such that f*chk(0) = . 相似文献
13.
V. L. Selivanov 《Algebra and Logic》2005,44(2):95-108
We deal with the Borel and difference hierarchies in the space P of all subsets of endowed with the Scott topology. (The spaces P and 2
coincide set-theoretically but differ topologically.) We look at the Wadge reducibility in P. The results obtained are applied to the problem of characterizing 1-terms t which satisfy C = t(
1
0
) for a given Borel-Wadge class C. We give its solution for some levels of the Wadge hierarchy, in particular, all levels of the Hausdorff difference hierarchy. Finally, we come up with a discussion of some relevant facts and open questions.__________Translated from Algebra i Logika, Vol. 44, No. 2, pp. 173–197, March–April, 2005. 相似文献
14.
Jean Bertoin 《Journal of Theoretical Probability》1994,7(3):551-563
One says thatt>0 is an increase time for a real-valued path if stays above the level (t) immediately after timet, and below (t) immediately before timet. Dvoretzkyet al.,(10) proved that Brownian motion has no increase times a.s. This result is extended here to (strictly) stable processes. Specifically, the probability that a stable processX possesses increase times is 0 if and only ifP(X
10)1/2. 相似文献
15.
J. Wu 《Monatshefte für Mathematik》1994,117(3-4):303-322
Let (n) be the number of all prime divisors ofn and (n) the number of distinct prime divisors ofn. We definev
q
(x)=|{nx(n)–(n)=q}|. In this paper, we give an asymptotic development ofv
q
(x); this improves on previous results. 相似文献
16.
On the Absolute Convergence of Fourier Series 总被引:1,自引:0,他引:1
The necessary and sufficient conditions of the absolute convergence of a trigonometric Fourier series are established for continuous 2-periodic functions which in [0, 2] have a finite number of intervals of convexity, and whose nth Fourier coefficients are O((l/n; f)/n), where ( f) is the continuity modulus of the function f. 相似文献
17.
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
18.
Susanne Beer 《manuscripta mathematica》1969,1(2):201-209
Let k be a field which is locally compact with respect to a valuation ||, let X denote the subset X={ k, ||1}. This paper is concerned with sequences of elements of X with respect to the theory of uniform distribution. Let DN() denote the discrepancy of the sequence =(xn). It is proved that for archimedian valuations with a certain constant for every sequence . In the non-archimedian case there exist sequences with
. 相似文献
19.
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
20.
D. V. Millionshchikov 《Mathematical Notes》2005,77(1-2):61-71
The cohomology H* (G/,) of the de Rham complex *(G/) of a compact solvmanifold G/ with deformed differential d = d + , where is a closed 1 -form, is studied. Such cohomologies naturally arise in Morse-Novikov theory. It is shown that, for any completely solvable Lie group G containing a cocompact lattice G, the cohomology H*(G/, ) is isomorphic to the cohomology H*(
) of the tangent Lie algebra
of the group G with coefficients in the one-dimensional representation :
defined by () = (). Moreover, the cohomology H
*(G/,) is nontrivial if and only if -[] belongs to a finite subset
of H
1(G/,) defined in terms of the Lie algebra
.Translated from Matematicheskie Zametki, vol. 77, no. 1, 2005, pp. 67–79.Original Russian Text Copyright © 2005 by D. V. Millionshchikov.This revised version was published online in April 2005 with a corrected issue number. 相似文献