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1.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):359-364
It is proved that there is a positive function Φ(∈) defined for sufficiently small ∈>0 such that lim∈→0 Φ(∈)=0 and for every integerk and everyk-dimensionalP
1+∈ spaceE, d(E, l
∞
k
)<1+Φ(∈).
Author was partially supported by N.S.F. Grant MCS 79-03042.
An erratum to this article is available at . 相似文献
2.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
3.
Dorin Bucur Ioan R. Ionescu 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2006,57(6):1042-1056
We consider an eigenvalue problem associated to the antiplane shearing on a system of collinear faults under a slip-dependent
friction law. Firstly we consider a periodic system of faults in the whole plane. We prove that the first eigenvalues/eigenfunctions
of different physical periodicity are all equal and that the other eigenvalues converge to this first common eigenvalue as
their physical period becomes indefinitely large. Secondly we consider a large scale fault system composed on a small scale
collinear faults periodically disposed. If β0* is the first eigenvalue of the periodic problem in the whole plane, we prove that the first eigenvalue of the microscopic
problem behaves as β0*/∈ when ∈→ 0 regardless the geometry of the domain (here ∈ is the scale quotient). The geophysical implications of this result
is that the macroscopic critical slip Dc scales with Dc∈/∈ (here Dc∈ is the small scale critical slip). 相似文献
4.
M. A. Nalbandyan 《Russian Mathematics (Iz VUZ)》2009,53(10):45-56
For any sequence {ω(n)}
n∈ℕ tending to infinity we construct a “quasiquadratic” representation spectrum Λ = {n
2 + o(ω(n))}
n∈ℕ: for any almost everywhere (a. e.) finite measurable function f(x) there exists a series in the form $
\mathop \sum \limits_{k \in \Lambda }
$
\mathop \sum \limits_{k \in \Lambda }
α
k
ω
k
(x) that converges a. e. to this function, where {w
k
(x)}
k∈ℕ is the Walsh system. We find representation spectra in the form {n
l
+ o(n
l
)}
n∈ℕ, where l ∈ {2
k
}
k∈ℕ. 相似文献
5.
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
6.
F. Redig 《Bulletin of the Brazilian Mathematical Society》2002,33(3):427-446
We consider one-dimensional Gibbs measures on spin configurations σ ∈ {–1,+1}ℤ. For N ∈ ℕ let l
N
denote the length of the longest interval of consecutive spins of the same kind in the interval [0,N]. We show that the distribution of a suitable continuous modification l
c
(N) of l
N
converges to the Gumbel distribution, i.e., for some α, β ∈ (0, ∞) and γ ∈ ℝ,
lim
N
→∞ ℙ(l
c
(N) ≤ α log N + βx + γ) = e
–e
–x
.
Received: 2 September 2002 相似文献
7.
Given the integer polyhedronP
t
:= conv{x ∈ℤ
n
:Ax⩽b}, whereA ∈ℤ
m × n
andb ∈ℤ
m
, aChvátal-Gomory (CG)cut is a valid inequality forP
1 of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ
+
m
such that λτA∈ℤ
n
. In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2}
m
. We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary
clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a
convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of
strong inequalities forP
1. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering
polytopes are briefly discussed. 相似文献
8.
Balázs Csikós György Kiss Konrad J. Swanepoel P. Oloff de Wet 《Periodica Mathematica Hungarica》2009,58(2):129-138
A family {A
i
| i ∈ I} of sets in ℝ
d
is antipodal if for any distinct i, j ∈ I and any p ∈ A
i
, q ∈ A
j
, there is a linear functional ϕ:ℝ
d
→ ℝ such that ϕ(p) ≠ ϕ(q) and ϕ(p) ≤ ϕ(r) ≤ ϕ(q) for all r ∈ ∪
i∈I
A
i
. We study the existence of antipodal families of large finite or infinite sets in ℝ3.
The research was supported by the Hungarian-South African Intergovernmental Scientific and Technological Cooperation Programme,
NKTH Grant no. ZA-21/2006 and South African National Research Foundation Grant no. UID 61853, as well as Hungarian National
Foundation for Scientific Research Grants no. NK 67867, no. T47102, and no. K72537. 相似文献
9.
Let S′ be the class of tempered distributions. For ƒ ∈ S′ we denote by J
−α
ƒ the Bessel potential of ƒ of order α. We prove that if J
−α
ƒ ∈ BMO, then for any λ ∈ (0, 1), J
−α
(f)λ ∈ BMO, where (f)λ = λ−n
f(φ(λ−1)), φ ∈ S. Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order
α > 0 belongs to the VMO space. 相似文献
10.
IBN rings and orderings on grothendieck groups 总被引:2,自引:0,他引:2
Tong Wenting 《数学学报(英文版)》1994,10(3):225-230
LetR be a ring with an identity element.R∈IBN means thatR
m⋟Rn impliesm=n, R∈IBN
1 means thatR
m⋟Rn⊕K impliesm≥n, andR∈IBN
2 means thatR
m⋟Rm⊕K impliesK=0. In this paper we give some characteristic properties ofIBN
1 andIBN
2, with orderings on the Grothendieck groups. In addition, we obtain the following results: (1) IfR∈IBN
1 and all finitely generated projective leftR-modules are stably free, then the Grothendieck groupK
0(R) is a totally ordered abelian group. (2) If the pre-ordering of the Grothendieck groupK
0(R) of a ringR is a partial ordering, thenR∈IBN
1 orK
0(R)=0.
Supported by National Nature Science Foundation of China. 相似文献
11.
Soulaymane Korry 《Israel Journal of Mathematics》2003,133(1):357-367
Letp∈(1, +∞) ands ∈ (0, +∞) be two real numbers, and letH
p
s
(ℝ
n
) denote the Sobolev space defined with Bessel potentials. We give a classA of operators, such thatB
s,p
-almost all points ℝ
n
are Lebesgue points ofT(f), for allf ∈H
p
s
(ℝ
n
) and allT ∈A (B
s,p
denotes the Bessel capacity); this extends the result of Bagby and Ziemer (cf. [2], [15]) and Bojarski-Hajlasz [4], valid
wheneverT is the identity operator. Furthermore, we describe an interesting special subclassC ofA (C contains the Hardy-Littlewood maximal operator, Littlewood-Paley square functions and the absolute value operatorT: f→|f|) such that, for everyf ∈H
p
s
(ℝ
n
) and everyT ∈C, T(f) is quasiuniformly continuous in ℝ
n
; this yields an improvement of the Meyers result [10] which asserts that everyf ∈H
p
s
(ℝ
n
) is quasicontinuous. However,T (f) does not belong, in general, toH
p
s
(ℝ
n
) wheneverT ∈C ands≥1+1/p (cf. Bourdaud-Kateb [5] or Korry [7]). 相似文献
12.
We prove the uniqueness of weak solutions of the time-dependent 3-D Ginzburg-Landau model for superconductivity with (Ψ
0, A
0) ∈ L
2(Ω) initial data under the hypothesis that (Ψ, A) ∈ C([0, T]; L
3(Ω)) using the Lorentz gauge.
相似文献
13.
S. A. Ould Abdi S. Dabo-Niang A. Diop A. Ould Abdi 《Mathematical Methods of Statistics》2010,19(1):1-21
Given a stationary multidimensional spatial process (Z
i
= (X
i
, Y
i
) ∈ ℝ
d
× ℝ, i ∈ ℤ
N
), we investigate a kernel estimate of the spatial conditional quantile function of the response variable Y
i
given the explicative variable X
i
. Almost complete convergence and consistency in L
2r
norm (r ∈ ℕ*) of the kernel estimate are obtained when the sample considered is an α-mixing sequence. 相似文献
14.
Consider the Cauchy problem ∂u(x, t)/∂t = ℋu(x, t) (x∈ℤd, t≥ 0) with initial condition u(x, 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ. Here Δ is the discrete Laplacian, κ∈ (0, ∞) is a diffusion constant,
and ξ = {ξ(x): x∈ℤ
d
} is an i.i.d.random field taking values in ℝ. G?rtner and Molchanov (1990) have shown that if the law of ξ(0) is nondegenerate,
then the solution u is asymptotically intermittent.
In the present paper we study the structure of the intermittent peaks for the special case where the law of ξ(0) is (in the
vicinity of) the double exponential Prob(ξ(0) > s) = exp[−e
s
/θ] (s∈ℝ). Here θ∈ (0, ∞) is a parameter that can be thought of as measuring the degree of disorder in the ξ-field. Our main result
is that, for fixed x, y∈ℤ
d
and t→∈, the correlation coefficient of u(x, t) and u(y, t) converges to ∥w
ρ∥−2
ℓ2Σz ∈ℤd
w
ρ(x+z)w
ρ(y+z). In this expression, ρ = θ/κ while w
ρ:ℤd→ℝ+ is given by w
ρ = (v
ρ)⊗
d
with v
ρ: ℤ→ℝ+ the unique centered ground state (i.e., the solution in ℓ2(ℤ) with minimal l
2-norm) of the 1-dimensional nonlinear equation Δv + 2ρv log v = 0. The uniqueness of the ground state is actually proved only for large ρ, but is conjectured to hold for any ρ∈ (0, ∞).
empty
It turns out that if the right tail of the law of ξ(0) is thicker (or thinner) than the double exponential, then the correlation
coefficient of u(x, t) and u(y, t) converges to δ
x, y
(resp.the constant function 1). Thus, the double exponential family is the critical class exhibiting a nondegenerate correlation
structure.
Received: 5 March 1997 / Revised version: 21 September 1998 相似文献
15.
The ordered fieldR(M) consists of the realsR with a transcendentalM adjoined, which is larger than any realr ∈R. Given any semi-infinite matrix (s.i.m.) interpreted as linear inequalities:u
tPi≧c
i, ∀
i
∈I, an arbitrary index set, it is also shown that the following are equivalent. (1) For every finiteJ ⊆I the systemu
tPi≧c
i,i ∈J is consistent, and (2) the s.i.m. has a solutionu ∈R(M)
n. Some consequences for “duality gaps” are also given.
These results were obtained as part of the activities of the Management Science Research Group and School of Urban and Public
Affairs, Carnegie-Mellon University. 相似文献
16.
Marshall A. Whittlesey 《Arkiv f?r Matematik》1999,37(2):409-423
Let Δ be the closed unit disk in C, let Γ be the circle, let Π: Δ×C→Δ be projection, and letA(Δ) be the algebra of complex functions continuous on Δ and analytic in int Δ. LetK be a compact set in C2 such that Π(K)=Γ, and letK
λ≠{w∈C|(λ,w)∈K}. Suppose further that (a) for every λ∈Γ,K
λ is the union of two nonempty disjoint connected compact sets with connected complement, (b) there exists a function Q(λ,w)≠(w-R(λ))2-S(λ) quadratic in w withR,S∈A(Δ) such that for all λ∈Γ, {w∈C|Q(λ,w)=0}υ intK
λ, whereS has only one zero in int Δ, counting multiplicity, and (c) for every λ∈Γ, the map ω→Q(λ,ω) is injective on each component
ofK
λ. Then we prove that К/K is the union of analytic disks 2-sheeted over int Δ, where К is the polynomial convex hull ofK. Furthermore, we show that БК/K is the disjoint union of such disks. 相似文献
17.
Consider the system with perturbation g
k
∈ ℝ
n
and output z
k
= Cx
k
. Here, A
k
,A
k
(s) ∈ ℝ
n × n
, B
k
(1) ∈ ℝ
n × p
, B
k
(2) ∈ ℝ
n × m
, C ∈ ℝ
p × n
. We construct a special Lyapunov-Krasovskii functional in order to synthesize controls u
k
(1) and u
k
(2) for which the following properties are satisfied:
$
z_{k + 1} = qz_k ,0 < q < 1(outputinvariance)
$
z_{k + 1} = qz_k ,0 < q < 1(outputinvariance)
相似文献
18.
Summary We prove a Schur test for mixed-norm spaces Lp,q, 1 < p,q < ∞. Also we prove another version of the Schur test for discrete weighted mixed-norm spaces lp,q w, 1 < p,q < ∞, and wis a weight. We show that if w 1, and w 2are two weight functions on the index sets Jx Iand K x Lrespectively, and A =(a ji, kl ) j∈J, i∈I, k∈K, l∈L is an infinite matrix, then under certain conditions, Ais a bounded operator from lp,q w1, 1 < p,q < ∞ to lp,q w2. This will be a key result in proving boundedness of important operators in our work in time-frequency analysis.</o:p> 相似文献
19.
Yosef Stein 《Israel Journal of Mathematics》1989,68(1):109-122
LetK be an algebraically closed field of characteristic zero. ForA ∈K[x, y] let σ(A) = {λ ∈K:A − λ is reducible}. For λ ∈ σ(A) letA − λ = ∏
i=1
n(λ)
A
iλ
k
μ whereA
iλ are distinct primes. Let ϱλ(A) =n(λ) − 1 and let ρ(A) = Σλɛσ(A)ϱλ(A). The main result is the following:
Theorem.If A ∈ K[x, y] is not a composite polynomial, then ρ(A) < degA. 相似文献
20.
Let Ω be a bounded Lipschitz domain. Define B
0,1
1,
r
(Ω) = {f∈L
1 (Ω): there is an F∈B
0,1
1 (ℝ
n
) such that F|Ω = f} and B
0,1
1
z
(Ω) = {f∈B
0,1
1 (ℝ
n
) : f = 0 on ℝ
n
\}. In this paper, the authors establish the atomic decompositions of these spaces. As by-products, the authors obtained the
regularity on these spaces of the solutions to the Dirichlet problem and the Neumann problem of the Laplace equation of ℝ
n
+.
Received June 8, 2000, Accepted October 24, 2000 相似文献
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