共查询到20条相似文献,搜索用时 31 毫秒
1.
2.
Sequences of the form (P(n)f(Q(n)))
n=1
∞
,P andQ polynomials,f a “highly differentiable” periodic function, are considered. The results of [3] concerning the recurrence of this sequence
to its value forn=0 are given a quantitative form. Density and uniform distribution modulo 1 are studied for specialQ’s. 相似文献
3.
György Gát 《数学学报(英文版)》2007,23(12):2269-2294
A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of
the Fejér (or (C, 1)) means of functions on unbounded Vilenkin groups. There are several papers of
the author of this paper concerning this. That is, we know the a.e. convergence σ
n
f → f (n → ∞)
for functions f ∈ L
p
, where p > 1 (Journal of Approximation Theory, 101(1), 1–36, (1999)) and also
the a.e. convergence σM
n
f → f (n → ∞) for functions f ∈ L
1 (Journal of Approximation Theory,
124(1), 25–43, (2003)). The aim of this paper is to prove the a.e. relation lim
n
→ σ
n
f = f for each
integrable function f on any rarely unbounded Vilenkin group. The concept of the rarely unbounded
Vilenkin group is discussed in the paper. Basically, it means that the generating sequence m may be
an unbounded one, but its "big elements" are not "too dense".
Research supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. M
36511/2001 and T 048780 相似文献
4.
G. Lepsveridze 《Georgian Mathematical Journal》1998,5(2):157-176
It is proved that for any given sequence (σ
n
,n ∈ ℕ)=Γ0 ⊂ Γ, where Γ is the set of all directions in ℝ2 (i.e., pairs of orthogonal straight lines) there exists a locally integrable functionf on ℝ2 such that: (1) for almost all directionsσ ∈ Γ\Γ0 the integral ∫f is differentiable with respect to the familyB
2σ
of open rectangles with sides parallel to the straight lines fromσ: (2) for every directionσ
n
∈ Γ0 the upper derivative of ∫f with respect toB
2σ
n
equals +∞; (3) for every directionσ ∈ Γ the upper derivative of ∫ |f| with respect toB
2σ
equals +∞. 相似文献
5.
S. J. Gardiner 《Constructive Approximation》2001,17(1):139-146
Let Ω be a domain in the extended complex plane such that ∞∈Ω . Further, let K= C / Ω and, for each n , let Q
n
be a monic polynomial of degree n with all its zeros in K . This paper is concerned with whether (Q
n
) can be chosen so that, if f is any holomorphic function on Ω and P
n
is the polynomial part of the Laurent expansion of Q
n
f at ∞ , then (P
n
/Q
n
) converges to f locally uniformly on Ω . It is shown that such a sequence (Q
n
) can be chosen if and only if either K has zero logarithmic capacity or Ω is regular.
January 21, 1999. Date accepted: August 17, 1999. 相似文献
6.
Chen 《Discrete and Computational Geometry》2002,28(2):175-199
Abstract. Let σ be a simplex of R
N
with vertices in the integral lattice Z
N
. The number of lattice points of mσ (={mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0 . In this paper we present: (i) a formula for the coefficients of the polynomial L(σ,t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the
sequence L(σ,m) , m ≥ 0 ; (iii) an explicit formula for the coefficients of the polynomial L(σ,t) in terms of torsion. As an application of (i), the coefficient for the lattice n -simplex of R
n
with the vertices (0,. . ., 0, a
j
, 0,. . . ,0) (1≤ j≤ n) plus the origin is explicitly expressed in terms of Dedekind sums; and when n=2 , it reduces to the reciprocity law about Dedekind sums. The whole exposition is elementary and self-contained. 相似文献
7.
Daniel Berend 《Journal d'Analyse Mathématique》1985,45(1):255-284
The study of jointly ergodic measure preserving transformations of probability spaces, begun in [1], is continued, and notions
of joint weak and strong mixing are introduced. Various properties of ergodic and mixing transformations are shown to admit
analogues for several transformations. The case of endomorphisms of compact abelian groups is particularly emphasized. The
main result is that, given such commuting endomorphisms σ1σ2,...,σ, ofG, the sequence ((1/N)Σ
n=0
N−1
σ
1
n
f
1·σ
2
n
f
2· ··· · σ
s
n
f
sconverges inL
2(G) for everyf
1,f
2,…,f
s∈L
∞(G). If, moreover, the endomorphisms are jointly ergodic, i.e., if the limit of any sequence as above is Π
i=1
s
∫
G
f
1
d
μ, where μ is the Haar measure, then the convergence holds also μ-a.e. 相似文献
8.
Chen 《Discrete and Computational Geometry》2008,28(2):175-199
Abstract. Let σ be a simplex of R
N
with vertices in the integral lattice Z
N
. The number of lattice points of mσ (={mα : α ∈ σ}) is a polynomial function L(σ,m) of m ≥ 0 . In this paper we present: (i) a formula for the coefficients of the polynomial L(σ,t) in terms of the elementary symmetric functions; (ii) a hyperbolic cotangent expression for the generating functions of the
sequence L(σ,m) , m ≥ 0 ; (iii) an explicit formula for the coefficients of the polynomial L(σ,t) in terms of torsion. As an application of (i), the coefficient for the lattice n -simplex of R
n
with the vertices (0,. . ., 0, a
j
, 0,. . . ,0) (1≤ j≤ n) plus the origin is explicitly expressed in terms of Dedekind sums; and when n=2 , it reduces to the reciprocity law about Dedekind sums. The whole exposition is elementary and self-contained. 相似文献
9.
Domenico A. Catalano Marston D. E. Conder Shao Fei Du Young Soo Kwon Roman Nedela Steve Wilson 《Journal of Algebraic Combinatorics》2011,33(2):215-238
An orientably-regular map is a 2-cell embedding of a connected graph or multigraph into an orientable surface, such that the
group of all orientation-preserving automorphisms of the embedding has a single orbit on the set of all arcs (incident vertex-edge
pairs). Such embeddings of the n-dimensional cubes Q
n
were classified for all odd n by Du, Kwak and Nedela in 2005, and in 2007, Jing Xu proved that for n=2m where m is odd, they are precisely the embeddings constructed by Kwon in 2004. Here, we give a classification of orientably-regular
embeddings of Q
n
for all n. In particular, we show that for all even n (=2m), these embeddings are in one-to-one correspondence with elements σ of order 1 or 2 in the symmetric group S
n
such that σ fixes n, preserves the set of all pairs B
i
={i,i+m} for 1≤i≤m, and induces the same permutation on this set as the permutation B
i
↦
B
f(i) for some additive bijection f:ℤ
m
→ℤ
m
. We also give formulae for the numbers of embeddings that are reflexible and chiral, respectively, showing that the ratio
of reflexible to chiral embeddings tends to zero for large even n. 相似文献
10.
Carl W. Lee 《Israel Journal of Mathematics》1984,47(4):261-269
Letf(P
s
d
) be the set of allf-vectors of simpliciald-polytopes. ForP a simplicial 2d-polytope let Σ(P) denote the boundary complex ofP. We show that for eachf ∈f(P
s
d
) there is a simpliciald-polytopeP withf(P)=f such that the 11 02 simplicial diameter of Σ(P) is no more thanf
0(P)−d+1 (one greater than the conjectured Hirsch bound) and thatP admits a subdivision into a simpliciald-ball with no new vertices that satisfies the Hirsch property. Further, we demonstrate that the number of bistellar operations
required to obtain Σ(P) from the boundary of ad-simplex is minimum over the class of all simplicial polytopes with the samef-vector. This polytopeP will be the one constructed to prove the sufficiency of McMullen's conditions forf-vectors of simplicial polytopes. 相似文献
11.
Summary For P∈ F2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of N (cf. [9]) such that Σn≧0 p(A,n)zn ≡ P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, d∈A d, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n≧1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula
to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1 on the orbit <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>z_i$
is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z] of the same odd order. 相似文献
12.
LetR
n be n-dimensional Euclidean space with n>-3. Demote by Ω
n
the unit sphere inR
n. ForfɛL(Ω
n
) we denote by σ
N
δ
its Cesàro means of order σ for spherical harmonic expansions. The special value
l = \tfracn - 22\lambda = \tfrac{{n - 2}}{2}
of σ is known as the critical one. For 0<σ≤λ, we set
p0 = \tfrac2ld+ lp_0 = \tfrac{{2\lambda }}{{\delta + \lambda }}
.
This paper proves that
limN ? ¥ || sNd (f) - f ||p0 = 0\mathop {\lim }\limits_{N \to \infty } \left\| {\sigma _N^\delta (f) - f} \right\|p_0 = 0 相似文献
13.
LetT be a Markov operator onL
1(X, Σ,m) withT*=P. We connect properties ofP with properties of all productsP ×Q, forQ in a certain class: (a) (Weak mixing theorem)P is ergodic and has no unimodular eigenvalues ≠ 1 ⇔ for everyQ ergodic with finite invariant measureP ×Q is ergodic ⇔ for everyu ∈L
1 with∝ udm=0 and everyf ∈L
∞ we haveN
−1Σ
n
≠1/N
|<u, P
nf>|→0. (b) For everyu ∈L
1 with∝ udm=0 we have ‖T
nu‖1 → 0 ⇔ for every ergodicQ, P ×Q is ergodic. (c)P has a finite invariant measure equivalent tom ⇔ for every conservativeQ, P ×Q is conservative. The recent notion of mild mixing is also treated.
Dedicated to the memory of Shlomo Horowitz
An erratum to this article is available at . 相似文献
14.
Yu. A. Kilizhekov 《Mathematical Notes》1996,60(4):378-382
LetW
n
2
M be the class of functionsf: Δ
n
→ ℝ (when Δ
n
is ann-simplex) with bounded second derivative (whose absolute value does not exceedM>0) along any direction at an arbitrary point of the simplex Δ
n
. LetP
1,n
(f;x) be the linear polynomial interpolatingf at the vertices of the simplex. We prove that there exists a functiong ∈ W
n
2
M such that for anyf ∈W
n
2
M and anyx ∈ Δ
n
one has |f
(x)−P
1,
n
(f;x)|≤g(x).
Translated fromMatematicheskie Zametki, Vol. 60, No. 4, pp. 504–510, October, 1996.
I thank Yu. N. Subbotin for posing the problem and for his attention to my work. 相似文献
15.
Laurent-Padé (Chebyshev) rational approximantsP
m
(w, w
−1)/Q
n
(w, w
−1) of Clenshaw-Lord type [2,1] are defined, such that the Laurent series ofP
m
/Q
n
matches that of a given functionf(w, w
−1) up to terms of orderw
±(m+n)
, based only on knowledge of the Laurent series coefficients off up to terms inw
±(m+n)
. This contrasts with the Maehly-type approximants [4,5] defined and computed in part I of this paper [6], where the Laurent
series ofP
m
matches that ofQ
n
f up to terms of orderw
±(m+n
), but based on knowledge of the series coefficients off up to terms inw
±(m+2n). The Clenshaw-Lord method is here extended to be applicable to Chebyshev polynomials of the 1st, 2nd, 3rd and 4th kinds and
corresponding rational approximants and Laurent series, and efficient systems of linear equations for the determination of
the Padé-Chebyshev coefficients are obtained in each case. Using the Laurent approach of Gragg and Johnson [4], approximations
are obtainable for allm≥0,n≥0. Numerical results are obtained for all four kinds of Chebyshev polynomials and Padé-Chebyshev approximants. Remarkably
similar results of formidable accuracy are obtained by both Maehly-type and Clenshaw-Lord type methods, thus validating the
use of either. 相似文献
16.
Abraham Neyman 《Israel Journal of Mathematics》1984,48(2-3):129-138
For fixed 1≦p<∞ theL
p-semi-norms onR
n
are identified with positive linear functionals on the closed linear subspace ofC(R
n
) spanned by the functions |<ξ, ·>|
p
, ξ∈R
n
. For every positive linear functional σ, on that space, the function Φσ:R
n
→R given by Φσ is anL
p-semi-norm and the mapping σ→Φσ is 1-1 and onto. The closed linear span of |<ξ, ·>|
p
, ξ∈R
n
is the space of all even continuous functions that are homogeneous of degreep, ifp is not an even integer and is the space of all homogeneous polynomials of degreep whenp is an even integer. This representation is used to prove that there is no finite list of norm inequalities that characterizes
linear isometric embeddability, in anyL
p unlessp=2.
Supported by the National Science Foundation MCS-79-06634 at U.C. Berkeley. 相似文献
17.
Paul F. X. Müller 《Israel Journal of Mathematics》1987,59(2):195-212
LetF
n be an increasing sequence of finite fields on a probability space (Ω,F
n,P) whereF denotes the σ-algebra generated by ∪F
n. ThenF
n is isomorphic to one of the following spaces:H
1(δ), ΣH
n
1
,l
l. 相似文献
18.
Given a linear transformation L:?
n
→?
n
and a matrix Q∈?
n
, where ?
n
is the space of all symmetric real n×n matrices, we consider the semidefinite linear complementarity problem SDLCP(L,?
n
+,Q) over the cone ?
n
+ of symmetric n×n positive semidefinite matrices. For such problems, we introduce the P-property and its variants, Q- and GUS-properties. For a matrix A∈R
n×n
, we consider the linear transformation L
A
:?
n
→?
n
defined by L
A
(X):=AX+XA
T
and show that the P- and Q-properties for L
A
are equivalent to A being positive stable, i.e., real parts of eigenvalues of A are positive. As a special case of this equivalence, we deduce a theorem of Lyapunov.
Received: March 1999 / Accepted: November 1999?Published online April 20, 2000 相似文献
19.
Zhen Guo 《数学学报(英文版)》2009,25(1):77-84
Let x : Mn^n→ R^n+1 be an n(≥2)-dimensional hypersurface immersed in Euclidean space Rn+1. Let σi(0≤ i≤ n) be the ith mean curvature and Qn = ∑i=0^n(-1)^i+1 (n^i)σ1^n-iσi. Recently, the author showed that Wn(x) = ∫M QndM is a conformal invariant under conformal group of R^n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. 相似文献
20.
Restricted Fault Diameter of Hypercube Networks 总被引:1,自引:0,他引:1
This paper studies restricted fault diameter of the n-dimensional hypercube networks Qn (n ≥ 2).It is shown that for arbitrary two vertices x and y with the distance d in Qn and any set F with at most 2n-3 vertices in Qn - {x, y}, if F contains neither of neighbor-sets of x and y in Qn, then the distance between x andy in Qn - F is given by D(Qn-F;x,y){=1 , for=1;≤d 4 , for 2≤d≤n-2,n≥4;≤n 1, for d=n-1,n≥3; =n, for d=n. Furthermore, the upper bounds are tight. As an immediately consequence, Qn can tolerate up to 2n-3 vertices failures and remain diameter 4 if n = 3 and n 2 if n ≥ 4 provided that for each vertex x in Qn, all the neighbors of x do not fail at the same time. This improves Esfahanian‘s result. 相似文献
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