共查询到20条相似文献,搜索用时 78 毫秒
1.
Suppose thatA ⊂R
n
is a bounded set of diameter 1 and that:f:A →l
2 is a map satisfying the nearisometry condition |x−y|−ɛ≤|fx−fy|≤|x−y|+ɛ withɛ≤1. Then there is an isometryS:A →l
2 such that |Sx−fx|≤c
n √ɛ for allx inA. IfA satisfies a thickness condition and iff:A →R
n
, then there is an isometryS:R
n
→R
n
with |Sx−fx|≤c
nɛ/q, whereq is a thickness parameter. 相似文献
2.
M. Laurent 《Journal of Mathematical Sciences》2012,180(5):592-598
Let Γ = Z
A + Z
n
⊂ R
n
be a dense subgroup of rank n + 1 and let [^(w)] \hat{w} (A) denote the exponent of uniform simultaneous rational approximation to the generating point A. For any real number v ≥
[^(w)] \hat{w} (A), the Hausdorff dimension of the set B
v
of points in R
n
that are v-approximable with respect to Γ is shown to be equal to 1/v. 相似文献
3.
Stefan Eilertsen 《Arkiv f?r Matematik》2000,38(1):53-75
A sufficient condition for the Wiener regularity of a boundary point with respect to the operator (− Δ)μ inR
n
,n≥1, is obtained, for μ∈(0,1/2n)/(1,1/2n−1). This extends some results for the polyharmonic operator obtained by Maz'ya and Maz'ya-Donchev.
As in the polyharmonic case, the proof is based on a weighted positivity property of (− Δ)μ, where the weight is a fundamental solution of this operator. It is shown that this property holds for μ as above while there
is an interval [A
n
, 1/2n−A
n
], whereA
n
→1, asn→∞, with μ-values for which the property does not hold. This interval is non-empty forn≥8. 相似文献
4.
MiaoLI QuanZHENG 《数学学报(英文版)》2004,20(5):821-828
Let T = (T(t))t≥0 be a bounded C-regularized semigroup generated by A on a Banach space X and R(C) be dense in X. We show that if there is a dense subspace Y of X such that for every x ∈ Y, σu(A, Cx), the set of all points λ ∈ iR to which (λ - A)^-1 Cx can not be extended holomorphically, is at most countable and σr(A) N iR = Ф, then T is stable. A stability result for the case of R(C) being non-dense is also given. Our results generalize the work on the stability of strongly continuous senfigroups. 相似文献
5.
A measurable set Q ⊂
R
n
is a wavelet set for an expansive matrix A if F
−1
(ΧQ) is an A-dilation wavelet. Dai, Larson, and Speegle [7] discovered the existence of wavelet sets in
R
n
associated with any real n ×n expansive matrix. In this work, we construct a class of compact wavelet sets which do not contain the origin and which are,
up to a certain linear transformation, finite unions of integer translates of an integral selfaffine tile associated with
the matrix B = A
t. Some of these wavelet sets may have good potential for applications because of their tractable geometric shapes. 相似文献
6.
Arrangements and cohomology 总被引:11,自引:0,他引:11
Michael Falk 《Annals of Combinatorics》1997,1(1):135-157
7.
On invariant additive subgroups 总被引:1,自引:0,他引:1
C. L. Chuang 《Israel Journal of Mathematics》1987,57(1):116-128
Suppose thatR is a prime ring with the centerZ and the extended centroidC. An additive subgroupA ofR is said to be invariant under special automorphisms if (1+t)A(1+t)−1 ⊆A for allt ∈R such thatt
2=0. Assume thatR possesses nontrivial idempotents. We prove: (1) If chR ≠ 2 or ifRC ≠C
2, then any noncentral additive subgroup ofR invariant under special automorphisms contains a noncentral Lie ideal. (2) If chR=2,RC=C
2 andC ≠ {0, 1}, then the following two conditions are equivalent: (i) any noncentral additive subgroup invariant under special
automorphisms contains a noncentral Lie ideal; (ii) there isα ∈Z / {0} such thatα
2
Z ⊆ {β
2:β ∈Z}. 相似文献
8.
Camillo De Lellis Stefan Müller 《Calculus of Variations and Partial Differential Equations》2006,26(3):283-296
Let Σ ⊂ R
3 be a smooth compact connected surface without boundary. Denote by A its second fundamental form and by Å the tensor A−(tr A/2)Id. In [4] we proved that, if ‖Å‖
L
2 (Σ) is small, then Σ is W
2,2-close to a round sphere. In this note we show that, in addition, the metric of Σ is C
0–close to the standard metric of S
2.The first author was supported by a grant of the Swiss National Science Foundation. 相似文献
9.
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
10.
L. I. Danilov 《Theoretical and Mathematical Physics》2000,124(1):859-871
The absolute continuity of the spectrum for the periodic Dirac operator
, is proved given that A∈C(R
n;R
n)⊂H
loc
q(R
n;R
n), 2q>n−2, and also that the Fourier series of the vector potential A:R
n→R
n is absolutely convergent. Here,
are continuous matrix functions and
for all anticommuting Hermitian matrices
.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 124, No. 1, pp. 3–17, July, 2000. 相似文献
11.
Jouko Tervo 《Israel Journal of Mathematics》1988,63(1):41-66
The paper considers a boundary value problem with the help of the smallest closed extensionL
∼ :H
k →H
k
0×B
h
1×...×B
h
N
of a linear operatorL :C
(0)
∞
(R
+
n
) →L(R
+
n
)×L(R
n−1)×...×L(R
n−1). Here the spacesH
k (the spaces ℬ
h
) are appropriate subspaces ofD′(R
+
n
) (ofD′(R
n−1), resp.),L(R
+
n
) andC
(0)
∞
(R
+
n
)) denotes the linear space of smooth functionsR
n
→C, which are restrictions onR
+
n
of a function from the Schwartz classL (fromC
0
∞
, resp.),L(R
n−1) is the Schwartz class of functionsR
n−1 →C andL is constructed by pseudo-differential operators. Criteria for the closedness of the rangeR(L
∼) and for the uniqueness of solutionsL
∼
U=F are expressed. In addition, ana priori estimate for the corresponding boundary value problem is established. 相似文献
12.
J. Matoušek 《Discrete and Computational Geometry》2001,25(3):389-403
Motivated by problems from calculus of variations and partial differential equations, we investigate geometric properties
of D-convexity. A function f: R
d → R is called D-convex, where D is a set of vectors in R
d, if its restriction to each line parallel to a nonzero v ∈ D is convex. The D-convex hull of a compact set A ⊂ R
d, denoted by coD(A), is the intersection of the zero sets of all nonnegative D-convex functions that are zero on A. It also equals the zero set of the D-convex envelope of the distance function of A. We give an example of an n-point set A ⊂ R
2 where the D-convex envelope of the distance function is exponentially close to zero at points lying relatively far from co
D(A), showing that the definition of the D-convex hull can be very nonrobust. For separate convexity in R
3 (where D is the orthonormal basis of R
3), we construct arbitrarily large finite sets A with co
D(A) ≠ A whose proper subsets are all equal to their D-convex hull. This implies the existence of analogous sets for rank-one convexity and for quasiconvexity on 3 × 3 (or larger)
matrices.
This research was supported by Charles University Grants No. 158/99 and 159/99. 相似文献
13.
LetR be a commutative noetherian ring and ƒ1, …, ƒr ∃ R. In this article we give (cf. the Theorem in §2) a criterion for ƒ1, …, ƒr to be regular sequence for a finitely generated module overR which strengthens and generalises a result in [2]. As an immediate consequence we deduce that if V(g
1, …,g
r
) ⊆ V(ƒ1, …, ƒr) in SpecR and if ƒ1, …, ƒr is a regular sequence inR, theng
1, …,g
r is also a regular sequence inR. 相似文献
14.
In this paper we study the asymptotics of the discrete spectrum in the gap (−1, 1) of the perturbed Dirac operatorD(α)=D
0−αV1 acting inL
2(R
3;C
4) with large coupling constant α. In particular some “non-standard” asymptotic formulae are obtained. 相似文献
15.
V. M. Petrogradsky 《Monatshefte für Mathematik》2006,149(3):243-249
Let R be a finitely generated associative algebra with unity over a finite field
. Denote by a
n
(R) the number of left ideals J ⊂ R such that dim R/J = n for all n ≥ 1. We explicitly compute and find asymptotics of the left ideal growth for the free associative algebra A
d
of rank d with unity over
, where d ≥ 1. This function yields a bound a
n
(R) ≤ a
n
(A
d
),
, where R is an arbitrary algebra generated by d elements. Denote by m
n
(R) the number of maximal left ideals J ⊂ R such that dim R/J = n, for n ≥ 1. Let d ≥ 2, we prove that m
n
(A
d
) ≈ a
n
(A
d
) as n → ∞. 相似文献
16.
We consider complex-valued functions f ∈ L 1 (R+2),where R +:= [0,∞),and prove sufficient conditions under which the double sine Fourier transform f ss and the double cosine Fourier transform f cc belong to one of the two-dimensional Lipschitz classes Lip(α,β) for some 0 α,β≤ 1;or to one of the Zygmund classes Zyg(α,β) for some 0 α,β≤ 2.These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1 (R+2). 相似文献
17.
V. M. Petrogradsky 《Monatshefte für Mathematik》2006,49(6):243-249
Let R be a finitely generated associative algebra with unity over a finite field
\Bbb Fq{\Bbb F}_q
. Denote by a
n
(R) the number of left ideals J ⊂ R such that dim R/J = n for all n ≥ 1. We explicitly compute and find asymptotics of the left ideal growth for the free associative algebra A
d
of rank d with unity over
\Bbb Fq{\Bbb F}_q
, where d ≥ 1. This function yields a bound a
n
(R) ≤ a
n
(A
d
),
n ? \Bbb Nn\in{\Bbb N}
, where R is an arbitrary algebra generated by d elements. Denote by m
n
(R) the number of maximal left ideals J ⊂ R such that dim R/J = n, for n ≥ 1. Let d ≥ 2, we prove that m
n
(A
d
) ≈ a
n
(A
d
) as n → ∞. 相似文献
18.
Luong Dang Ky 《分析论及其应用》2011,27(3):251-264
Let 0 p ≤ 1 and w in the Muckenhoupt class A1. Recently, by using the weighted atomic decomposition and molecular characterization, Lee, Lin and Yang[11] es- tablished that the Riesz transforms Rj, j = 1,2,··· ,n, are bounded on Hwp(Rn). In this note we extend this to the general case of weight w in the Muckenhoupt class A∞ through molec- ular characterization. One difficulty, which has not been taken care in [11], consists in passing from atoms to all functions in Hwp(Rn). Furthermore, the Hwp-boundedness of θ- Calderón-Zygmund operators are also given through molecular characterization and atomic decomposition. 相似文献
19.
An extension of a classical theorem of Rellich to the exterior of a closed proper convex cone is proved: Let Γ be a closed
convex proper cone inR
n and −Γ′ be the antipodes of the dual cone of Γ. Let
be a partial differential operator with constant coefficients inR
n, whereQ(ζ)≠0 onR
n−iΓ′ andP
i is an irreducible polynomial with real coefficients. Assume that the closure of each connected component of the set {ζ∈R
n−iΓ′;P
j(ζ)=0, gradP
j(ζ)≠0} contains some real point on which gradP
j≠0 and gradP
j∉Γ∪(−Γ). LetC be an open cone inR
n−Γ containing both normal directions at some such point, and intersecting each normal plane of every manifold contained in
{ξ∈R
n;P(ξ)=0}. Ifu∈ℒ′∩L
loc
2
(R
n−Γ) and the support ofP(−i∂/∂x)u is contained in Γ, then the condition
implies that the support ofu is contained in Γ. 相似文献
20.
Guido Cortesani 《Annali dell'Universita di Ferrara》1997,43(1):27-49
Let Ω be an open and bounded subset ofR
n
with locally Lipschitz boundary. We prove that the functionsv∈SBV(Ω,R
m
) whose jump setS
vis essentially closed and polyhedral and which are of classW
k, ∞ (S
v,R
m) for every integerk are strongly dense inGSBV
p(Ω,R
m
), in the sense that every functionu inGSBV
p(Ω,R
m
) is approximated inL
p(Ω,R
m
) by a sequence of functions {v
k{j∈N with the described regularity such that the approximate gradients ∇v
jconverge inL
p(Ω,R
nm
) to the approximate gradient ∇u and the (n−1)-dimensional measure of the jump setsS
v
j converges to the (n−1)-dimensional measure ofS
u. The structure ofS
v can be further improved in casep≤2.
Sunto Sia Ω un aperto limitato diR n con frontiera localmente Lipschitziana. In questo lavoro si dimostra che le funzioniv∈SBV(Ω,R m ) con insieme di saltoS v essenzialmente chiuso e poliedrale che sono di classeW k, ∞ (S v,R m ) per ogni interok sono fortemente dense inGSBV p(Ω,R m ), nel senso che ogni funzioneu∈GSBV p(Ω,R m ) è approssimata inL p(Ω,R m ) da una successione di funzioni {v j}j∈N con la regolaritá descritta tali che i gradienti approssimati ∇v jconvergono inL p(Ω,R nm ) al gradiente approssimato ∇u e la misura (n−1)-dimensionale degli insiemi di saltoS v jconverge alla misura (n−1)-dimensionale diS u. La struttura diS vpuó essere migliorata nel caso in cuip≤2.相似文献