共查询到20条相似文献,搜索用时 31 毫秒
1.
András Kroó 《Constructive Approximation》2012,35(2):181-200
We consider the problem of the approximation of regular convex bodies in ℝ
d
by level surfaces of convex algebraic polynomials. Hammer (in Mathematika 10, 67–71, 1963) verified that any convex body in ℝ
d
can be approximated by a level surface of a convex algebraic polynomial. In Jaen J. Approx. 1, 97–109, 2009 and subsequently in J. Approx. Theory 162, 628–637, 2010 a quantitative version of Hammer’s approximation theorem was given by showing that the order of approximation of convex bodies
by convex algebraic level surfaces of degree n is
\frac1n\frac{1}{n}. Moreover, it was also shown that whenever the convex body is not
regular (that is, there exists a point on its boundary at which the convex body possesses two distinct supporting hyperplanes), then
\frac1n\frac{1}{n} is essentially the sharp rate of approximation. This leads to the natural question whether this rate of approximation can
be improved further when the convex body is regular. In this paper we shall give an affirmative answer to this question. It
turns out that for regular convex bodies a o(1/n) rate of convergence holds. In addition, if the body satisfies the condition of C
2-smoothness the rate of approximation is
O(\frac1n2)O(\frac{1}{n^{2}}). 相似文献
2.
Sorin G. Gal 《Complex Analysis and Operator Theory》2012,6(2):515-527
Attaching to a compact disk
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} in the quaternion field
\mathbbH{\mathbb{H}} and to some analytic function in Weierstrass sense on
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} the so-called q-Bernstein operators with q ≥ 1, Voronovskaja-type results with quantitative upper estimates are proved. As applications, the exact orders of approximation
in
[`(\mathbbDr)]{\overline{\mathbb{D}_{r}}} for these operators, namely
\frac1n{\frac{1}{n}} if q = 1 and
\frac1qn{\frac{1}{q^{n}}} if q > 1, are obtained. The results extend those in the case of approximation of analytic functions of a complex variable in disks
by q-Bernstein operators of complex variable in Gal (Mediterr J Math 5(3):253–272, 2008) and complete the upper estimates obtained for q-Bernstein operators of quaternionic variable in Gal (Approximation by Complex Bernstein and Convolution-Type Operators, 2009; Adv Appl Clifford Alg, doi:, 2011). 相似文献
3.
G. C. Calafiore 《Journal of Optimization Theory and Applications》2009,143(2):405-412
In this note, we derive an exact expression for the expected probability V of constraint violation in a sampled convex program (see Calafiore and Campi in Math. Program. 102(1):25–46, 2005; IEEE Trans. Autom. Control 51(5):742–753, 2006 for definitions and an introduction to this topic):
V=\fracexpected number of support constraints1+number of constraints.V=\frac{\mbox{expected number of support constraints}}{1+\mbox{number of constraints}}. 相似文献
4.
Nikolaos Bournaveas Timothy Candy 《NoDEA : Nonlinear Differential Equations and Applications》2012,19(1):67-78
It is known from Czubak (Anal PDE 3(2):151–174, 2010) that the space–time Monopole equation is locally well-posed in the Coulomb gauge for small initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} for ${s>\frac{1}{4}}${s>\frac{1}{4}}. Here we prove local well-posedness for arbitrary initial data in
Hs(\mathbbR2){H^s(\mathbb{R}^2)} with ${s>\frac{1}{4}}${s>\frac{1}{4}} in the Lorenz gauge. 相似文献
5.
The Alexander-Orbach conjecture holds in high dimensions 总被引:1,自引:0,他引:1
We examine the incipient infinite cluster (IIC) of critical percolation in regimes where mean-field behavior has been established,
namely when the dimension d is large enough or when d>6 and the lattice is sufficiently spread out. We find that random walk on the IIC exhibits anomalous diffusion with the spectral
dimension
ds=\frac43d_{s}=\frac{4}{3}
, that is, p
t
(x,x)=t
−2/3+o(1). This establishes a conjecture of Alexander and Orbach (J. Phys. Lett. (Paris) 43:625–631, 1982). En route we calculate the one-arm exponent with respect to the intrinsic distance. 相似文献
6.
Li Wang 《Journal of Theoretical Probability》2010,23(2):401-416
We establish an almost sure scaling limit theorem for super-Brownian motion on ℝ
d
associated with the semi-linear equation
ut=\frac12Du+bu-au2u_{t}=\frac{1}{2}\Delta u+\beta u-\alpha u^{2}
, where α and β are positive constants. In this case, the spectral theoretical assumptions required in Chen et al. (J. Funct. Anal. 254:1988–2019,
2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in ℝ
d
. 相似文献
7.
Florent Hivert Jean-Gabriel Luque Jean-Christophe Novelli Jean-Yves Thibon 《Journal of Algebraic Combinatorics》2011,33(2):277-312
We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero
and leaving the other ones invariant. As a “transformation of alphabets”, this is the
(1-\mathbbE)(1-\mathbb{E})-transform, where
\mathbbE\mathbb{E} is the “exponential alphabet,” whose elementary symmetric functions are
en=\frac1n!e_{n}=\frac{1}{n!}. In the case of noncommutative symmetric functions, we recover Schocker’s idempotents for derangement numbers (Schocker,
Discrete Math. 269:239–248, 2003). From these idempotents, we construct subalgebras of the descent algebras analogous to the peak algebras and study their
representation theory. The case of WQSym leads to similar subalgebras of the Solomon–Tits algebras. In FQSym, the study of the transformation boils down to a simple solution of the Tsetlin library in the uniform case. 相似文献
8.
Dongho Byeon 《The Ramanujan Journal》2009,19(1):71-77
We shall show that the number of quadratic fields with absolute discriminant ≤x and noncyclic 5- or 7-class group is ≫x
1/4 improving the existing known bound
for g=5 and
for g=7 in Byeon (Ramanujan J. 11:159–163, 2006).
This work was supported by KRF-2005-070-C00004. 相似文献
9.
The max-cut problem asks for partitioning the nodes V of a graph G=(V,E) into two sets (one of which might be empty), such that the sum of weights of edges joining nodes in different partitions
is maximum. Whereas for general instances the max-cut problem is NP-hard, it is polynomially solvable for certain classes of graphs. For planar graphs, there exist several polynomial-time
methods determining maximum cuts for arbitrary choice of edge weights. Typically, the problem is solved by computing a minimum-weight
perfect matching in some associated graph. The most efficient known algorithms are those of Shih et al. (IEEE Trans. Comput.
39(5):694–697, 1990) and that of Berman et al. (WADS, Lecture Notes in Computer Science, vol. 1663, pp. 25–36, Springer, Berlin, 1999). The running time of the former can be bounded by
O(|V|\frac32log|V|)O(|V|^{\frac{3}{2}}\log|V|). The latter algorithm is more generally for determining T-joins in graphs. Although it has a slightly larger bound on the
running time of
O(|V|\frac32(log|V|)\frac32)a(|V|)O(|V|^{\frac{3}{2}}(\log|V|)^{\frac{3}{2}})\alpha(|V|), where α(|V|) is the inverse Ackermann function, it can solve large instances in practice. 相似文献
11.
We present a characterisation of {e1 (q+1)+e0,e1 ;n,q}{\{\epsilon_1 (q+1)+\epsilon_0,\epsilon_1 ;n,q\}} -minihypers, q square, q = p
h
, p > 3 prime, h ≥ 2, q ≥ 1217, for
e0 + e1 < \fracq7/122-\fracq1/42{\epsilon_0 + \epsilon_1 < \frac{q^{7/12}}{2}-\frac{q^{1/4}}{2}}. This improves a characterisation result of Ferret and Storme (Des Codes Cryptogr 25(2): 143–162, 2002), involving more Baer subgeometries contained in the minihyper. 相似文献
12.
We consider the wave equation on an interval of length 1 with an interior damping at ξ. It is well-known that this system is well-posed in the energy space and that its natural energy is dissipative. Moreover,
as it was proved in Ammari et al. (Asymptot Anal 28(3–4):215–240, 2001), the exponential decay property of its solution is equivalent to an observability estimate for the corresponding conservative
system. In this case, the observability estimate holds if and only if ξ is a rational number with an irreducible fraction
x = \fracpq,\xi=\frac{p}{q}, where p is odd, and therefore under this condition, this system is exponentially stable in the energy space. In this work, we are
interested in the finite difference space semi-discretization of the above system. As for other problems (Zuazua, SIAM Rev
47(2):197–243, 2005; Tcheugoué Tébou and Zuazua, Adv Comput Math 26:337–365, 2007), we can expect that the exponential decay of this scheme does not hold in general due to high frequency spurious modes.
We first show that this is indeed the case. Secondly we show that a filtering of high frequency modes allows to restore a
quasi exponential decay of the discrete energy. This last result is based on a uniform interior observability estimate for
filtered solutions of the corresponding conservative semi-discrete system. 相似文献
13.
Let B = (B
1(t), . . . , B
d
(t)) be a d-dimensional fractional Brownian motion with Hurst index α ≤ 1/4, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals
of B is a difficult task because of the low H?lder regularity index of its paths. Yet rough path theory shows it is the key to
the construction of a stochastic calculus with respect to B, or to solving differential equations driven by B. We intend to show in a forthcoming series of papers how to desingularize iterated integrals by a weak singular non-Gaussian
perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using “standard” tools
of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates
of the moments and call for an extension of the Gaussian tools such as for instance the Malliavin calculus. This first paper
aims to be both a presentation of the basics of rough path theory to physicists, and of perturbative field theory to probabilists;
it is only heuristic, in particular because the desingularization of iterated integrals is really a non-perturbative effect. It is also meant to be a general motivating introduction to the subject, with some insights into quantum field theory
and stochastic calculus. The interested reader should read for a second time the companion article (Magnen and Unterberger
in From constructive theory to fractional stochastic calculus. (II) The rough path for
\frac16 < a < \frac14{\frac{1}{6} < \alpha < \frac{1}{4}}: constructive proof of convergence, 2011, preprint) for the constructive proofs. 相似文献
14.
We show that the multi-commodity max-flow/min-cut gap for series-parallel graphs can be as bad as 2, matching a recent upper
bound (Chakrabarti et al. in 49th Annual Symposium on Foundations of Computer Science, pp. 761–770, 2008) for this class, and resolving one side of a conjecture of Gupta, Newman, Rabinovich, and Sinclair.
This also improves the largest known gap for planar graphs from
\frac32\frac{3}{2}
to 2, yielding the first lower bound that does not follow from elementary calculations. Our approach uses the coarse differentiation method of Eskin, Fisher, and Whyte in order to lower bound the distortion for embedding a particular family of shortest-path
metrics into L
1. 相似文献
15.
We study a necessary and sufficient condition for Jacobi integrals of weight
-r+\fracj2-r+\frac{j}{2}, r∈ℤ≥0, and index ℳ(j) on ℋ×ℂ
j
to have a dual Jacobi form of weight
r+\fracj2+2r+\frac{j}{2}+2 and index ℳ(j). Such a meromorphic Jacobi integral with a dual Jacobi form is called a mock Jacobi form whose concept was first introduced
by Zagier in Séminaire Bourbaki, 60éme année, 2006–2007, N° 986. In fact, we show the map Lr+1M(j)L^{r+1}_{\mathcal{M}^{(j)}} from the space of mock Jacobi forms to that of Jacobi forms is surjective by constructing the corresponding inverse image
via Eichler integral of vector valued modular forms which are coming from the theta decomposition of Jacobi forms. We discuss
Lerch sums as a typical example. 相似文献
16.
Witold Bednorz 《Journal of Theoretical Probability》2007,20(4):917-934
For a Young function φ and a Borel probability measure m on a compact metric space (T,d) the minorizing metric is defined by
17.
In this paper, we introduce the concept of (1, 1)-q-coherent pair of linear functionals (U,V)(\mathcal{U},\mathcal{V}) as the q-analogue to the generalized coherent pair studied by Delgado and Marcellán in (Methods Appl Anal 11(2):273–266, 2004). This means that their corresponding sequences of monic orthogonal polynomials {P
n
(x)}
n ≥ 0 and {R
n
(x)}
n ≥ 0 satisfy
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