共查询到20条相似文献,搜索用时 15 毫秒
1.
Jeff Edmonds 《Discrete and Computational Geometry》2008,39(4):747-765
We give a new algorithm for enumerating all possible embeddings of a metric space (i.e., the distances between every pair
within a set of n points) into ℝ2 Cartesian space preserving their l
∞ (or l
1) metric distances. Its expected time is
(i.e., within a poly-log of the size of the input) beating the previous
algorithm. In contrast, we prove that detecting l
∞3 embeddings is NP-complete. The problem is also NP-complete within l
12 or l
∞2 with the added constraint that the locations of two of the points are given or alternatively that the two dimensions are
curved into a three-dimensional sphere. We also refute a compaction theorem by giving a metric space that cannot be embedded
in l
∞3; however, it can be embedded if any single point is removed.
This research is partially supported by NSERC grants. I would like to thank Steven Watson for his extensive help on this paper. 相似文献
2.
3.
Let K be a field of characteristic 0 and let p, q, G
0
, G
1
, P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G
n
(x))
n=0
∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G
n
(x) = G
m
(P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we
present also bounds for the cardinality of the set
In the last part we specialize our results to certain families of orthogonal polynomials.
This work was supported by the Austrian Science Foundation FWF, grant S8307-MAT.
The second author was supported by the Hungarian National Foundation for Scientific Research Grants No 16741 and 38225.
Received June 5, 2001; in revised form February 26, 2002
RID="a"
ID="a" Dedicated to Edmund Hlawka on the occasion of his 85th birthday 相似文献
4.
Letting F be a homogeneous(α1, α2) metric on the reductive homogeneous manifold G/H, we first characterize the natural reductiveness of F as a local f-product between naturally reductive Riemannian metrics. Second, we prove the equivalence among several properties of F for its mean Berwald curvature and S-curvature. Finally, we find an explicit flag curvature formula for G/H when F is naturally reductive. 相似文献
5.
Let K be a field of characteristic 0 and let p, q, G 0 , G 1 , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G n (x)) n=0 ∞ be defined by the second order linear recurring sequence
In this paper we give conditions under which the diophantine equation G n (x) = G m (P(x)) has at most exp(1018) many solutions (n, m) ε ℤ2, n, m ⩾ 0. The proof uses a very recent result on S-unit equations over fields of characteristic 0 due to Evertse, Schlickewei and Schmidt [14]. Under the same conditions we present also bounds for the cardinality of the set
相似文献
6.
7.
Let Σ_1 and Σ_2 be m and n dimensional Riemannian manifolds of constant curvature respectively. We assume that w is a unit constant m-form in Σ_1 with respect to which Σ_0 is a graph. We set v = 〈e_1 ∧ … ∧ e_m, 〉), where {e_1, …, e_m} is a normal frame on Σ_t. Suppose that Σ_0 has bounded curvature. If v(x, 0) ≥ v0 > \frac{\sqrt{p}}{2} for all x, then the mean curvature flow has a global solution F under some suitable conditions on the curvatrue of Σ_1 and Σ_2. 相似文献
8.
We prove that the quasi-Banach spaces 1 (p) and p (1), 0 < p < 1 have a unique unconditional basis up to permutation 相似文献
9.
10.
Oleg Okunev 《Central European Journal of Mathematics》2011,9(5):978-983
We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C
p
(X, M) is a continuous image of a closed subspace of C
p
(X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindel?f number of C
p
(X)×C
p
(X) coincides with the Lindel?f number of C
p
(X). We also prove that l(C
p
(X
n
)κ) ≤ l(C
p
(X)κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces. 相似文献
11.
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
12.
Donald I. Cartwright 《Monatshefte für Mathematik》2001,247(1):93-109
To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C *-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C *-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2. 相似文献
13.
14.
本文定义了环F2+uF2+vF2到域F2的广义Gray映射φ像,研究了环F2+uF2+vF2上线性码的广义Gray像.利用广义Gray映射φ的线性性,证明了环F2+uF2+vF2上线性码C的广义Gray像φ(C)满足dH(C)=dH(φ(C))且φ(C⊥)φ(C)⊥.同时,给出了F2+uF2+vF2上循环码C的广义Gray像φ(C)为F2上的4-拟循环码. 相似文献
15.
16.
17.
David Soudry 《Israel Journal of Mathematics》2000,120(1):511-561
In this paper we prove the full multiplicativity (in both variables) of gamma factors for generic representations of SO2ℓ+1 × GL
n
. These gamma factors are initially defined as proportionality factors of local functional equations, derived from a corresponding
global theory of certain Rankin-Selberg integrals which interpolate standardL-functions for SO2ℓ+1 × GL
n
. 相似文献
18.
无理函数y=(a1x+b1)1/2+(a2x+b2)1/2(a1,a2,b1,b2均不为0)(1)的最值问题,是代数中较为典型的一类最值问题之一.当a1a2≥0时,函数(1)为单调函数,求出定义域后利用单调性很容易确定最大值和最小值.但当a1a2<0时,函数(1)最值的求解具有一定的难度.其实,当a1a2<0时,无理函数(1)可改写成如下形式:y=a(x-b)1/2+c(d-x)1/2(a,c>0,b,d≠0)(2)当b≤d时,函数才有意义.当b=d时,函数值域为单点集{0}.本文考虑b相似文献
19.
测量了(YBa2Cu3O7)24/(PrBa2Cu3O7)2 多层膜在强磁场下的超导转变展宽 .这种YBa2Cu3O7层间具有耦合 退耦合的临界绝缘层PrBa2Cu3O7厚度以及由 3D向 2D过渡的YBa2Cu3O7层厚度的多层膜 ,其不可逆场遵守H ∝ ( 1-t)μ关系 ,其 μ值约为1 ,介于3D( μ =3/2 )和2D( μ =1 /2 )之间 .磁通运动的热激活能的结果表明 ,对于H∥c和H⊥J的磁场位形 ,遵守U∝lnH关系 ,即磁通涡旋处于2D区 .而对于H∥ab和H⊥J ,H∥ab和H∥J两种磁场位形 ,激活能U随磁场的增加而线性减小 ,表明磁通涡旋处于3D态 .讨论了上述维度变化的可能物理机制 . 相似文献