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1.
Assume that each completely irrational noncommutative torus is realized as an inductive limit of circle algebras, and that for a completely irrational noncommutative torus Aw of rank m there are a completely irrational noncommutative torus Aρ of rank m and a positive integer d such that tr(Aw)=1/d.tr(Aρ).It is proved that the set of all C^*-algebras of sections of locally trivial C^*-algebra bundles over S^2 with fibres Aω has a group sturcture,denoted by π1^s(Aut(Aω)),which is isomorphic to Zif Ed>1 and {0} if d>1.Let Bcd be a cd-homogeneous C^*-algebra over S^2×T^2 of which no non-trivial matrix algebra can be factored out.The spherical noncommutative torus Sρ^cd is defined by twisting C^*(T2×Z^m-2) in Bcd ×C^*(Z^m-3) by a totally skew multiplier ρ on T^2×Z^m-2。It is shown that Sρ^cd×Mρ∞ is isomorphic to C(S^2)×C^*(T^2×Z^m-2,ρ)× Mcd(C)×Mρ∞ if and only if the set of prime factors of cd is a subset of the set of prime factors of p. 相似文献
2.
Y. -K. Choi 《Acta Mathematica Hungarica》2009,123(4):331-355
This paper establishes the general moduli of continuity for l
∞-valued Gaussian random fields {X(t):= (X
1(t),X
2(t), h.), t ∈ [0, ∞)
N
} indexed by the N-dimensional parameter t:= (t
1,…,t
N
), under the explicit condition yielding that the covariance function of distinct increments of X
k
(t) for fixed k ≧ 1 is positive or nonpositive.
Supported by KOSEF-R01-2008-000-11418-0. 相似文献
3.
A. N. Frolov 《Algebra and Logic》2006,45(3):201-209
It is proved that, for any n ∈ ω, there exist countable linear orderings Ln whose Δ
2
0
-spectrum consists of exactly all non n-low Δ
2
0
-degrees. Properties of such orderings are examined, for n = 1 and n = 2.
Supported by RFBR grant No. 02-01-00169 and by RF Ministry of Education grant No. E02-1.0-177.
__________
Translated from Algebra i Logika, Vol. 45, No. 3, pp. 354–370, May–June, 2006. 相似文献
4.
We give a necessary and sufficient condition for the uniformly non-l
n
(1)
property of Musielak-Orlicz sequence spacesl
Φ generated by a sequence Φ=(ϕn:n⩾l) of finite Orlicz functions such that
for eachn∈ℕ. As a result, forn
0⩾2, there exist spacesl
Φ which are only uniformly non-l
n
(1)
forn⩾n
0. Moreover we obtain a characterization of uniformly non-l
n
(1)
and reflexive Orlicz sequence spaces over a wide class of purely atomic measures and of uniformly non-l
n
(1)
Nakano sequence spaces. This extends a result of Luxemburg in [19].
Submitted in memory of Professor W. Orlicz 相似文献
5.
TAOYOUSHAN GAOGUOZHU 《高校应用数学学报(英文版)》1998,13(3):271-280
In this paper the forced neutral difterential equation with positive and negative coefficients d/dt [x(t)-R(t)x(t-r)] P(t)x(t-x)-Q(t)x(t-σ)=f(t),t≥t0,is considered,where f∈L^1(t0,∞)交集C([t0,∞],R^ )and r,x,σ∈(0,∞),The sufficient conditions to oscillate for all solutions of this equation are studied. 相似文献
6.
Song Li 《中国科学A辑(英文版)》2003,46(3):364-375
The purpose of this paper is to investigate the refinement equations of the form
where the vector of functions ϕ=(ϕ
1..., ϕ
r
)
T
is in (L
p
(ℝ
s
))
r
, 1⩽p⩽∞, a(α), α∈ℤ
s
is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vector of compactly supported functions φ
0∈(L
p
(ℝ
s
))
r
and use the iteration schemes f
n
:=Q
a
n
φ
0, n=1,2,..., where Q
n
is the linear operator defined on (L
p
(ℝ
s
))
r
given by
This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of some linear operators
determined by the sequence a and the set B restricted to a certain invariant subspace, where the set B is a complete set of representatives of the distinct cosets of the quotient group ℤs/Mℤs containing 0. 相似文献
7.
黄兆泳 《中国科学A辑(英文版)》2002,45(7):836-844
The structure of rightF-⊥
T-approximations of any finitely generated module over an artin algebra Λ is given, relative to an additive subbifunctorF of Ext
Λ
1
(-, -) and anF-cotilting moduleT. 相似文献
8.
G. Kuba 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2006,76(1):157-181
LetF be a field not of characteristic 2 andQ =F +F
i +F
j +F
k the quaternion algebra overF whereij = -ji =k andi
2 = α andj
2 = β with 0 ≠ α, β ∈F fixed. (IfF = ℝ and α = β = - 1 thenQ is the division algebra of the Hamilton quaternions.) IfF = ℚ and Q is a division algebra then by embedding certain quadratic number fields inQ we derive an efficient formula to compute the powers of any quaternion. This formula is even true in general and reads as
follows. If a, a1, a2, a3 ∈F andn ∈ ℕ then
where ω ig a square root of αa1
2 + βa
2
2 - αβa
3
2 in or overF and
andA
0 =na
n-1.
With the help of this formula and related ones we are able to solve the equationX
n
=q for arbitrary quaternionsq and positive integers n in case ofF = ℝ and hence in case ofF ⊂ ℝ as well. IfF = ℝ then the total number of all solutions equals 0, 1, 2, 4,n or ∞. (4 is possible even whenn < 4.) In case ofF = ℚ, which we are primarily interested in, there are always either at most six or infinitely many solutions. Further, for
everyq ≠ 0 there is at most one solution provided thatn is odd and not divisible by 3. The questions when there are infinitely many solutions and when there are none can always
be decided by checking simple conditions on the radicandq ifF = ℝ. ForF = ℚ the two questions are comprehensively investigatet in a natural connection with ternary and quaternary quadratic rational
forms. Finally, by applying some of our theorems on powers and roots of quate-rions we also obtain several nice results in
matrix theory. For example, for every k ∈ ℤ the mappingA ↦A
k
on the group of all nonsingular 2-by-2 matrices over ℚ is injective if and only ifk is odd and not divisible by 3.
相似文献
9.
B. Khani Robati 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):601-608
Let ℬ be a Banach space of analytic functions defined on the open unit disk. We characterize the commutant ofM
Z
2 (the operator of multiplication by the square of independent variable defined on ℬ) and show that for an operatorS in the commutantM
Z
2 ifSM
Z
2k+1−M
Z
2k+1
S is compact for some nonnegative integerk, thenS=M
ϕ whereϕ is a multiplier of ℬ. Letn be a positive integer andS be an operator in the commutant ofM
Z
n defined on a functional Hilbert spaces of analytic functions. We show that under certain conditionsS has the formM
ϕ.
Research supported by the Shiraz University Grant 78-SC-1188-657. 相似文献
10.
Let X be an infinite-dimensional Banach space with weight τ. By Cld
AW
(X), we denote the hyperspace of nonempty closed sets in X with the Attouch—Wets topology. By Fin
AW
(X), Comp
AW
(X) and Bdd
AW
(X), we denote the subspaces of Cld
AW
(X) consisting of finite sets, compact sets and bounded closed sets, respectively. In this paper, it is proved that
Fin
AW
(X)≈Comp
AW
(X)≈ℓ2(τ)×ℓ2
f
ℓandℓBdd
AW
(X)≈ℓ2(2τ)×ℓ2
f
where ≈ means ‘is homeomorphic to’, ℓ2(τ) is the Hilbert space with weight τ (ℓ2(ℵ0)=ℓ2 the separable Hilbert space) and
ℓ2
f
={(x
i
)
iεN
εℓ2∣x
i
=0 except for finitely many iεN}. 相似文献
11.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL
p[−π,π], algebraic polynomial approximation inL
p[−1,1], algebraic polynomial approximation inL
p(S), and entire function of exponential type approximation inL
p(R), and characterizeK-functionals for certain pairs of function spaces including (L
p[−π,π],B
s
a(L
p[−π,π])), (L
p(R),s
a(Lp(R))),
, and
, where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r.
This project is supported by the National Science Foundation of China. 相似文献
12.
Caisheng Chen 《Journal of Evolution Equations》2006,6(1):29-43
In this paper, we study the global existence, L∞ estimates and decay estimates of solutions for the quasilinear parabolic system ut = div (|∇ u|m ∇ u) + f(u, v), vt = div (|∇ v|m ∇ v) + g(u,v) with zero Dirichlet boundary condition in a bounded domain Ω ⊂ RN. In particular, we find a critical value for the existence and nonexistence of global solutions to the equation ut = div (|∇ u|m ∇ u) + λ |u|α - 1 u. 相似文献
13.
Alejandro Balbás José Garrido Silvia Mayoral 《Methodology and Computing in Applied Probability》2009,11(3):385-399
The current literature does not reach a consensus on which risk measures should be used in practice. Our objective is to give
at least a partial solution to this problem. We study properties that a risk measure must satisfy to avoid inadequate portfolio
selections. The properties that we propose for risk measures can help avoid the problems observed with popular measures, like
Value at Risk (VaR
α
) or Conditional VaR
α
(CVaR
α
). This leads to the definition of two new families: complete and adapted risk measures. Our focus is on risk measures generated by distortion functions. Two new properties are put forward for these:
completeness, ensuring that the distortion risk measure uses all the information of the loss distribution, and adaptability,
forcing the measure to use this information adequately.
This research was partially funded by
1,3
Welzia Management, SGIIC SA, RD Sistemas SA, Comunidad Autónoma de Madrid Grant s-0505/tic/000230, and MEyC Grant BEC2000-1388-C04-03 and by
2
the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 36860-06. 相似文献
14.
B. de Malafosse 《Acta Mathematica Hungarica》2009,122(3):217-230
We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between
s
h,l
(λ, μ) = s
α
0((Δ − λI)
h
) + s
β
(c)((Δ − μI)
l
) and s
γ
. Among other things the aim of this paper is to reduce the set (s
h,l
(λ, μ), s
γ
to a set of the form S
τ,γ
.
相似文献
15.
Robert S. Strichartz 《Journal of Geometric Analysis》1991,1(3):269-289
Let μ be a measure on ℝn that satisfies the estimate μ(B
r(x))≤cr
α for allx ∈ ℝn and allr ≤ 1 (B
r(x) denotes the ball of radius r centered atx. Let ϕ
j,k
(ɛ)
(x)=2
nj2ϕ(ɛ)(2
j
x-k) be a wavelet basis forj ∈ ℤ, κ ∈ ℤn, and ∈ ∈E, a finite set, and letP
j
(T)=Σɛ,k
<T,ϕ
j,k
(ɛ)
>ϕ
j,k
(ɛ)
denote the associated projection operators at levelj (T is a suitable measure or distribution). Iff ∈Ls
p(dμ) for 1 ≤p ≤ ∞, we show thatP
j(f dμ) ∈ Lp(dx) and ||P
j
(fdμ)||L
p(dx)≤c2
j((n-α)/p′))||f||L
p(dμ) for allj ≥ 0. We also obtain estimates for the limsup and liminf of ||P
j
(fdμ)||L
p(dx) under more restrictive hypotheses.
Communicated by Guido Weiss 相似文献
16.
Xiaodong Wang 《Journal of Geometric Analysis》2008,18(1):272-284
Let (M
n
,g) be a compact Riemannian manifold with Ric ≥−(n−1). It is well known that the bottom of spectrum λ
0 of its universal covering satisfies λ
0≤(n−1)2/4. We prove that equality holds iff M is hyperbolic. This follows from a sharp estimate for the Kaimanovich entropy.
The author was partially supported by NSF Grant 0505645. 相似文献
17.
R. Norvaiša 《Lithuanian Mathematical Journal》2008,48(4):418-426
Let B
H,K
= {B
H,K
(t)}
t⩾0 be a bifractional Brownian motion with parameters H ∈ (0, 1) and K ∈ (0, 1]. For a function Φ: [0, ∞) → [0, ∞) and for a partition κ = {t
i
}n
i=0 of an interval [0, T] with T > 0, let {ie418-01}. We prove that, for a suitable Φ depending on H and K, {ie418-02} almost surely.
The research was partially supported by the Lithuanian State Science and Studies Foundation, grant No. T-16/08 相似文献
18.
Guyan Robertson 《K-Theory》2004,33(4):347-369
Let (G, I, N, S) be an affine topological Tits system, and let Γ be a torsion-free cocompact lattice in G. This article studies the coinvariants H
0(Γ; C(Ω,Z)), where Ω is the Furstenberg boundary of G. It is shown that the class [1] of the identity function in H
0(Γ; C(Ω, Z)) has finite order, with explicit bounds for the order. A similar statement applies to the K
0 group of the boundary crossed product C
*-algebra C(Ω)Γ. If the Tits system has type ?
2, exact computations are given, both for the crossed product algebra and for the reduced group C
*-algebra. 相似文献
19.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
20.
This work is concerned with the proof of Lp -Lq decay estimates for solutions of the Cauchy problem for utt -λ2(t)b2(t)/Δu =0. The coefficient consists of an increasing smooth function λ and an oscillating smooth and bounded function b which are uniformly separated from zero. The authors‘ main interest is devoted to the critical case where one has an interesting interplay between the growing and the oscillating part. 相似文献