共查询到20条相似文献,搜索用时 15 毫秒
1.
Chen Jixiang 《数学学报(英文版)》1997,13(4):553-562
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH
B over a fixed spaceB ([5]). This paper extendsH
B to the track homotopy categoryH
b over a fixed mapb:
, such that there exists a split fibration of categoriesL:H
b →H
B andH
b possesses some construction as inH
B.
Supported by National Natural Science Foundation of China and the Doctoral Foundation of the National Educational Committee
of China 相似文献
2.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献
3.
Götz Gelbrich 《Aequationes Mathematicae》1997,54(1-2):108-116
Summary Suppose given a quasi-periodic tiling of some Euclidean space E
u
which is self-similar under the linear expansiong: Eμ→Eμ. It is known that there is an embedding of Eμ into some higher-dimensional space ℝ
N
and a linear automorphism
with integer coefficients such that E
u
⊂ ℝ
N
is invariant under
andg is the restriction of
to E
u
.
Let E
s
be the
-invariant complement of E
u
, and
. If certain conditions are fulfilled (e.g.
must be a lattice automorphism,g
* is an expansion), we construct a self-similar tiling of E
s
whose expansion isg
*, using the information contained in the original tiling of Eμ. The term “Galois duality” of tilings is motivated by the fact that the eigenvalues ofg
* are Galois conjugates of those ofg. Our method can be applied to find the Galois duals which are given by Thurston, obtained in a somewhat other way for the
case that dim Eμ=1, andg is the multiplication by a cubic Pisot unit.
Bandt and Gummelt have found fractally shaped tilings which can be considered as strictly self-similar modifications of the
kites-and-darts, and the rhombi tilings of Penrose. As one of the examples, we show that these fractal versions can be constructed
by dualizing tilings by Penrose triangles. 相似文献
4.
Shi Niandong 《数学学报(英文版)》1988,4(1):14-17
A Boolean algebraB=
is recursive ifB is a recursive subset of ω and the operations Λ, v and ┌ are partial recursive. A subalgebraC ofB is recursive an (r.e.) ifC is a recursive (r.e.) subset of B. Given an r.e. subalgebraA, we sayA can be split into two r.e. subalgebrasA
1 andA
2 if (A
1 ∪A
2)*=A andA
1 ∩A
2={0, 1}. In this paper we show that any nonrecursive r.e. subalgebra ofB can be split into two nonrecursive r.e. subalgebras ofB. This is a natural analogue of the Friedberg's splitting theorem in ω recursion theory. 相似文献
5.
Zheng Zukang 《数学学报(英文版)》1994,10(4):337-347
LetX
1,X
2, ...,X
n
be a sequence of nonnegative independent random variables with a common continuous distribution functionF. LetY
1,Y
2, ...,Y
n
be another sequence of nonnegative independent random variables with a common continuous distribution functionG, also independent of {X
i
}. We can only observeZ
i
=min(X
i
,Y
i
), and
. LetH=1−(1−F)(1−G) be the distribution function ofZ. In this paper, the limit theorems for the ratio of the Kaplan-Meier estimator
or the Altshuler estimator
to the true survival functionS(t) are given. It is shown that (1)P(δ(n)=1 i.o.)=0 ifF(τ
H
) < 1 andP(δ
n
=0 i.o. )=0 ifG(τH) > 1 where δ(n) is the corresponding indicator function of
and
have the same order
a.s., where {T
n
} is a sequence of constants such that 1−H(T
n
)=n
−α(logn)β(log logn)γ. 相似文献
6.
The question of which r.e. setsA possess major subsetsB which are alsor-maximal inA (A⊂rm
B) arose in attempts to extend Lachlan’s decision procedure for the αε-theory of ℰ*, the lattice of r.e. sets modulo finite sets, and Soare’s theorem thatA andB are automorphic if their lattice of supersets ℒ*(A) and ℒ*(B) are isomorphic finite Boolean algebras. We characterize the r.e. setsA with someB⊂rm
A as those with a Δ3 function that for each recursiveR
i
specifiesR
i
or
as infinite on
and to be preferred in the construction ofB. There are r.e.A andB with ℒ*(A) and ℒ*(B) isomorphic to the atomless Boolean algebra such thatA has anrm subset andB does not. Thus 〈ℰ*,A〉 and 〈ℰ*,B〉 are not even elementarily equivalent. In every non-zero r.e. degree there are r.e. sets with and withoutrm subsets. However the classF of degrees of simple sets with norm subsets satisfies
.
The authors were partially supported by NSF Grants MCS 76-07258, MCS 77-04013 and MCS 77-01965 respectively. 相似文献
7.
A mapT: X→X on a normed linear space is callednonexpansive if ‖Tx-Ty‖≤‖x-y‖∀x, y∈X. Let (Ω, Σ,P) be a probability space,
an increasing chain of σ-fields spanning Σ,X a Banach space, andT: X→X. A sequence (xn) of strongly
-measurable and stronglyP-integrable functions on Ω taking on values inX is called aT-martingale if
.
LetT: H→H be a nonexpansive mapping on a Hilbert spaceH and let (xn) be aT-martingale taking on values inH. If
then x
n
/n converges a.e.
LetT: X→X be a nonexpansive mapping on ap-uniformly smooth Banach spaceX, 1<p≤2, and let (xn) be aT-martingale (taking on values inX). If
then there exists a continuous linear functionalf∈X
* of norm 1 such that
If, in addition, the spaceX is strictly convex, x
n
/n converges weakly; and if the norm ofX
* is Fréchet differentiable (away from zero), x
n
/n converges strongly.
This work was supported by National Science Foundation Grant MCS-82-02093 相似文献
8.
Choonkil PARK Jian Lian CUI 《数学学报(英文版)》2007,23(11):1919-1936
Let X and Y be vector spaces. The authors show that a mapping f : X →Y satisfies the functional equation 2d f(∑^2d j=1(-1)^j+1xj/2d)=∑^2dj=1(-1)^j+1f(xj) with f(0) = 0 if and only if the mapping f : X→ Y is Cauchy additive, and prove the stability of the functional equation (≠) in Banach modules over a unital C^*-algebra, and in Poisson Banach modules over a unital Poisson C*-algebra. Let A and B be unital C^*-algebras, Poisson C^*-algebras or Poisson JC^*- algebras. As an application, the authors show that every almost homomorphism h : A →B of A into is a homomorphism when h((2d-1)^nuy) =- h((2d-1)^nu)h(y) or h((2d-1)^nuoy) = h((2d-1)^nu)oh(y) for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,....
Moreover, the authors prove the stability of homomorphisms in C^*-algebras, Poisson C^*-algebras or Poisson JC^*-algebras. 相似文献
9.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献
10.
LetX andY denote two complex Banach spaces and letB(Y, X) denote the algebra of all bounded linear operators fromY toX. ForA∈B(X)
n
,B∈B(Y)
n
, the elementary operator acting onB(Y, X) is defined by
. In this paper we obtain the formulae of the spectrum and the essential spectrum of Δ(A, B) by using spectral mapping theorems. Forn=1, we prove thatS
p
(L
A
,R
B
)=σ(A)×σ(B) and
. 相似文献
11.
Mikhail Lifshits et Michel Weber 《Journal d'Analyse Mathématique》2003,89(1):1-14
We develop a spectral regularization technique for moving averages
, where ϕ is a nondecreasing map andU: H→H is a contraction of a Hilbert space (H, ‖·‖). We obtain a spectral regularization inequality which allows one to evaluate efficiently the increments ‖B
m
U
, ϕ (f)−B
n
U
, ϕ (f)‖,f∈H, by means of
where
is a properly regularized version of the spectral measure off with respect toU. We apply this inequality to an investigation of metric properties of the sets of moving averages {B
n
U, ϕ
(f), n ∈N} with fixedf∈H andN⊂ N. In particular, we obtain estimates of the associated covering numbers as well as of the related Littlewood-Paley-type
square functions. This work extends our previous results concerning the case of classical averages (ϕ(n)=0). Since it is well-known that the structure of general moving averages is more complicated, there is no surprise that
the general results we obtain are sometimes less complete than their classical counterparts and need suitable moment assumptions
on the spectral measure (depending on the growth of the shift function ϕ). Nevertheless, when applied to the classical situation,
our estimates still yield optimal bounds.
Avec pour le premier author, le soutien de la fondation russe pour la recherche fondamentale, subvention 99-01-00112 et INTAS subvention 99-01317. 相似文献
Avec pour le premier author, le soutien de la fondation russe pour la recherche fondamentale, subvention 99-01-00112 et INTAS subvention 99-01317. 相似文献
12.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
13.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
14.
ToddCOCHRANE ChunLeiLIU ZhiYongZHENG 《数学学报(英文版)》2003,19(2):327-338
We obtain formulac and estimates for character sums of the type S(x,f,p^m)=∑x=1^p^mx(f(f)),where p^m is a prime power with m≥2,x is a multiplicative character(mod p^m),and f=f1/f2 is a rational function over Z.In particular,if p is odd,d=deg(f1) deg(f2) and d^*=max(deg(f1),deg(f2)) then we obtain |S(x,f,p^m)|≤(d-1)p^m(1-1/d^*) for any non-constant f (mod p) and primitive character x.For p=2 an extra factor of 2√2 is needed. 相似文献
15.
Letf: Y → X be a continuous map between connectedCW complexes. The homologyH
*
(F) of the homotopy fibre is then a module over the loop space homologyH
* (ΩX).
Theorem:If H
*
(F; R) and H
*
(ΩX; R) are R-free (R a principal ideal domain) then for some H
*
(ΩX; R)-projective module
P=P>0
and for some m ≤ cat f:
Some applications are also given.
Research partially supported by a NATO travel grant.
Research partially supported by an NSERC operating grant.
U.A. au CNRS 751. 相似文献
16.
A subgroup H of a finite group G is said to be c*-supplemented in G if there exists a subgroup K such that G = HK and H ⋂ K is permutable in G. It is proved that a finite group G that is S
4-free is p-nilpotent if N
G
(P) is p-nilpotent and, for all x ∈ G\N
G
(P), every minimal subgroup of
is c*-supplemented in P and (if p = 2) one of the following conditions is satisfied: (a) every cyclic subgroup of
of order 4 is c*-supplemented in P, (b)
, (c) P is quaternion-free, where P a Sylow p-subgroup of G and
is the p-nilpotent residual of G. This extends and improves some known results.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 8, pp. 1011–1019, August, 2007. 相似文献
17.
LetX andY be smooth varieties of dimensionsn−1 andn over an arbitrary algebraically closed field,f: X→Y a finite map that is birational onto its image. Suppose thatf is curvilinear; that is, for allxεX, the Jacobian ϱf(x) has rank at leastn−2. Forr≥1, consider the subschemeN
r
ofY defined by the (r−1)th Fitting ideal of the
-module
, and setM
r
∶=f
−1
N
r
. In this setting—in fact, in a more general setting—we prove the following statements, which show thatM
r
andN
r
behave like reasonable schemes of source and targetr-fold points off.
If each component ofM
r
, or equivalently ofN
r
, has the minimal possible dimensionn−r, thenM
r
andN
r
are Cohen-Macaulay, and their fundamental cycles satisfy the relation,f
*[M
r
]=r[N
r
]. Now, suppose that each component ofM
s
, or ofN
s
, has dimensionn−s fors=1,...,r+1. Then the blowup Bl(N
r
,N
r+1
) is equal to the Hilbert scheme Hilb
f
r
and the blowup Bl(M
r
,M
r+1
) is equal to the universal subscheme Univ
f
r
of Hilb
f
r
×
Y
X; moreover, Hilb
f
r
and Univ
f
r
are Gorenstein. In addition, the structure maph:Hilb
f
r
→Y is finite and birational onto its image; and its conductor is equal to the ideal
ofN
r+1
inN
r
, and is locally self-linked. Reciprocally,
is equal to
. Moreover,h
*
[h
−1
N
r+1
]=(r+1)[N
r+1
]. Similar assertions hold for the structure maph
1: Univ
f
r
→X ifr≥2.
Supported in part by NSF grant 9106444-DMS.
Supported in part by NSA grant MDA904-92-3007, and at MIT 21–30 May 1989 by Sloan Foundation grant 88-10-1.
Supported in part by NSF grant DMS-9305832. 相似文献
18.
Xi Mei WU Qin YUE 《数学学报(英文版)》2007,23(11):2061-2068
Let F = Q(√-p1p2) be an imaginary quadratic field with distinct primes p1 = p2 = 1 mod 8 and the Legendre symbol (p1/p2) = 1. Then the 8-rank of the class group of F is equal to 2 if and only Pl if the following conditions hold: (1) The quartic residue symbols (p1/p2)4 = (p2/p1)4 = 1; (2) Either both
p1 and p2 are represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=x^2-2p1y^2,x,y∈Z,or both p1 and p2 are not represented by the form a^2 + 32b^2 over Z and p^h2+(2p1)/4=ε(2x^2-p1y^2),x,y∈Z,ε∈{±1},where h+(2p1) is the narrow class number of Q(√2p1),Moreover, we also generalize these results. 相似文献
19.
Summary Let
a plane angle of opening α∈(π, 2π). LetP
D andP
N the Dirichlet and Neumann problems associated to the Poisson equation in
. ForP
D andP
N it is proved non existence of solution in L
p
(
) whenp=2/(1±π/α). In other words, the ranges of elliptic operators naturally associated toP
D andP
N are not-closed in L
p
(
) forp=2/(1±π/α).
Sunto Sia } un angolo piano di apertura α∈(π, 2π). SianoP D eP N i problemi di Dirichlet e di Neumann associati all'equazione di Poisson in . PerP D eP N si prova non esistenza di soluzioni in L p ( ) quandop=2/(1±π/α). Vale a dire i ranges degli operatori ellittici naturalmente associati aP D eP N sono non-chiusi in π--AgBrα K L p ( ) perp=2/(1±π/α).相似文献
20.
Nakao HAYASHI Pavel I. NAUMKIN 《数学学报(英文版)》2006,22(5):1441-1456
We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation ut+uux-uxx+uxxx=0,x∈R,t〉0. We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that if the initial data u0 ∈H^s (R)∩L^1 (R), where s 〉 -1/2, then there exists a unique solution u (t, x) ∈C^∞ ((0,∞);H^∞ (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u(t)=t^-1/2fM((·)t^-1/2)+0(t^-1/2) as t →∞, where fM is the self-similar solution for the Burgers equation. Moreover if xu0 (x) ∈ L^1 (R), then the asymptotics are true u(t)=t^-1/2fM((·)t^-1/2)+O(t^-1/2-γ) where γ ∈ (0, 1/2). 相似文献