共查询到20条相似文献,搜索用时 46 毫秒
1.
Shahar Mendelson Alain Pajor Nicole Tomczak-Jaegermann 《Geometric And Functional Analysis》2007,17(4):1248-1282
We present a randomized method to approximate any vector from a set . The data one is given is the set T, vectors of and k scalar products , where are i.i.d. isotropic subgaussian random vectors in , and . We show that with high probability, any for which is close to the data vector will be a good approximation of , and that the degree of approximation is determined by a natural geometric parameter associated with the set T.
We also investigate a random method to identify exactly any vector which has a relatively short support using linear subgaussian
measurements as above. It turns out that our analysis, when applied to {−1, 1}-valued vectors with i.i.d. symmetric entries,
yields new information on the geometry of faces of a random {−1, 1}-polytope; we show that a k- dimensional random {−1, 1}-polytope with n vertices is m-neighborly for
The proofs are based on new estimates on the behavior of the empirical process when F is a subset of the L
2 sphere. The estimates are given in terms of the γ
2 functional with respect to the ψ
2 metric on F, and hold both in exponential probability and in expectation.
Received: November 2005, Revision: May 2006, Accepted: June 2006 相似文献
2.
Zhongwei Tang 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):810-833
In this paper, we are concerned with the multiplicity of standing wave solutions of nonlinear Schr?dinger equations with electromagnetic
fields
for sufficiently large λ, where i is the imaginary unit, for N ≥ 3 and 2 < p < + ∞ for N = 1, 2. a(x) is a real continuous function on is such that A
j
(x) is a real local H?lder continuous function on for j = 1, 2, ... ,N. We assume that a(x) is nonnegative and has a potential well consisting of k components . We show that for any non-empty subset has a standing wave solution which is trapped in a neighborhood of for λ large.
相似文献
3.
Ricardo Abreu Blaya Juan Bory Reyes Dixan Peña Peña Frank Sommen 《Advances in Applied Clifford Algebras》2007,17(2):145-152
Starting with an integral representation for the class of continuously differentiable solutions
of the system
where
is the complex Clifford algebra constructed over
are some suitable Clifford vectors and
their corresponding Dirac operators, we define the isotonic Cauchy transform and establish the Sokhotski-Plemelj formulae.
Some consequences of this result are also derived. 相似文献
4.
Michael R. Darnel 《Algebra Universalis》2007,57(3):273-290
It is well known that the quasitorsion class of archimedean -groups is the class of -groups G such that every closed convex -subgroup is a polar, and it is also well known that the class of -groups G such that every convex -subgroup is a polar is a torsion class. By defining a selection on -groups, these two results are generalized to show, whenever and are selections on -groups, the class of -groups G such that is a radical class. Three selections in particular — all convex -subgroups, all polars, and all closed convex -subgroups — and the radical classes determined by them are studied in some detail.
Received March 7, 2006; accepted in final form August 29, 2006. 相似文献
5.
Jaume Llibre Clàudia Valls 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,15(2):237-245
We study the analytical integrability of the FitzHugh–Nagumo systems in with parameters
相似文献
6.
Peter Bundschuh 《Results in Mathematics》2007,51(1-2):29-42
Let K be or an imaginary quadratic number field, and q
K an integer with |q| > 1. We give a quantitative version of the linear independence over K of the three numbers 1, , and an equivalent power series version. We also mention several open problems.
Received: February 5, 2007. Revised: April 18, 2007. 相似文献
7.
John W. Snow 《Algebra Universalis》2008,58(1):59-71
We prove that if is a finite algebra which satisfies a nontrivial idempotent Mal’cev condition, and if Con contains a copy of an order polynomially complete lattice other than , , or Con, then Con is not hereditary.
Received March 7, 2006; accepted in final form December 5, 2006. 相似文献
8.
Mohab Safey El Din 《Mathematics in Computer Science》2007,1(1):177-207
Let f be a polynomial in of degree D. We focus on testing the emptiness and computing at least one point in each connected component of the semi-algebraic set
defined by f > 0 (or f < 0 or f ≠ 0). To this end, the problem is reduced to computing at least one point in each connected component of a hypersurface
defined by f − e = 0 for
positive and small enough. We provide an algorithm allowing us to determine a positive rational number e which is small enough in this sense. This is based on the efficient computation of the set of generalized critical values of the mapping which is the union of the classical set of critical values of the mapping f and the set of asymptotic critical values of the mapping f. Then, we show how to use the computation of generalized critical values in order to obtain an efficient algorithm deciding
the emptiness of a semi-algebraic set defined by a single inequality or a single inequation. At last, we show how to apply
our contribution to determining if a hypersurface contains real regular points. We provide complexity estimates for probabilistic
versions of the latter algorithms which are within arithmetic operations in . The paper ends with practical experiments showing the efficiency of our approach on real-life applications.
相似文献
9.
William E. Hornor 《Complex Analysis and Operator Theory》2007,1(4):549-569
We develop a translation-type model for univalent self-maps φ of the unit disc having an interior fixed-point and use the model to classify the φ-invariant measures on . We are particularly interested in maps which can be embedded in continuous semigroups of holomorphic self-maps of .
Received: February 2, 2007. Revised: June 18, 2007. Accepted: July 4, 2007. 相似文献
10.
Let ∑ be either an oriented hyperplane or the unit sphere in
, let
be open and connected and let
be an open and connected domain in
such that
. If in
is a null solution of the Dirac operator (also called a monogenic function in
) which is continuously extendable to
, then conditions upon
are given enabling the monogenic extension of
across
. In such a way Schwarz reflection type principles for monogenic functions are established in the Spin (1) and Spin
cases. The Spin (1) case includes the classical Schwarz reflection principle for holomorphic functions in the plane. The
Spin
case deals with so-called “half boundary value problems” for the Dirac operator.
Received: 2 February 2006 相似文献
11.
Given a set of “empirical” points, whose coordinates are perturbed by errors, we analyze whether it contains redundant information, that
is whether some of its elements could be represented by a single equivalent point. If this is the case, the empirical information
associated to could be described by fewer points, chosen in a suitable way. We present two different methods to reduce the cardinality
of which compute a new set of points equivalent to the original one, that is representing the same empirical information. Though
our algorithms use basic notions of Cluster Analysis they are specifically designed for “thinning out” redundant data. We
include some experimental results which illustrate the practical effectiveness of our methods.
相似文献
12.
In the first part [16] of this work, we described the commutative C*-algebras generated by Toeplitz operators on the unit ball whose symbols are invariant under the action of certain Abelian groups of biholomorphisms of . Now we study the geometric properties of these symbols. This allows us to prove that the behavior observed in the case of
the unit disk (see [3]) admits a natural generalization to the unit ball . Furthermore we give a classification result for commutative Toeplitz operator C*-algebras in terms of geometric and “dynamic” properties of the level sets of generating symbols.
This work was partially supported by CONACYT Projects 46936 and 44620, México. 相似文献
13.
Naoki Murabayashi 《Mathematische Annalen》2008,342(3):657-671
It is known that in the moduli space of elliptic curves, there exist precisely nine -rational points represented by an elliptic curve with complex multiplication by the maximal order of an imaginary quadratic
field. In Murabayashi and Umegaki (J Algebra 235:267–274, 2001) and Umegaki [Determination of all -rational CM-points in the moduli spaces of polarized abelian surfaces, Analytic number theory (Beijng/Kyoto, 1999). Dev.
Math., vol 6. Kluwer, Dordrecht, pp 349–357, 2002] we determined all -rational points in (the moduli space of d-polarized abelian surfaces) represented by a d-polarized abelian surface whose endomorphism ring is isomorphic to the maximal order of a quartic CM-field by using the result
in Murabayashi (J Reine Angew Math 470:1–26, 1996). In this paper, we prove that polarized abelian surfaces corresponding
to these -rational CM points have a -rational model by constructing certain Hecke characters. 相似文献
14.
Gioconda Moscariello Carlo Sbordone 《Journal of Fixed Point Theory and Applications》2007,1(2):337-350
Let
be a sequence of Borel measurable functions satisfying, for a function
the inequalities
and suppose
Then there exists a sequence of increasing homeomorphisms
converging to a homeomorphism
weakly in
and locally uniformly, such that
Dedicated to the memory of Jean Leray 相似文献
15.
Moshe Dubiner 《Journal d'Analyse Mathématique》1995,67(1):39-116
We consider the problem of polynomial approximation to a real valued functionf defined on a compact set
. An approximation theorem is proven in terms of the newly defined modulus of approximation. It is shown to imply a multidimensional
Jackson type theorem which is stronger than previously known results even for the interval [−1, 1]. A strong multidimensional
Bernstein type inverse theorem is also proven. We allow quite general approximation quasi-norms including
for 0<q≤∞.
We have found that the space of polynomials ℙ on a compact setX induces a semimetric
which encapsulates the local structure of ℙ. Any semimetric ρ equivalent to
suffices for the rough theory presented here. Many examples of sets
and their metrics are presented. 相似文献
16.
Michel Weber 《Results in Mathematics》2007,51(1-2):141-179
Let where are independent Bernoulli random variables. In relation with the divisor problem, we evaluate the almost sure asymptotic
order of the sums , where and is a sequence of positive integers.
Received: May 23, 2007. Revised: June 8, 2007. 相似文献
17.
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with
respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies
for all z ∈
.
Tolokonnikov’s Lemma for
means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in
, such that F = [ f f
c
] for some f
c
in
. In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over
, then it has a doubly coprime factorization in
. We prove the lemma for the real disc algebra
as well. In particular,
and
are Hermite rings.
The work of the first author was supported by Magnus Ehrnrooth Foundation.
Received: December 5, 2006. Revised: February 4, 2007. 相似文献
18.
It is proved that the Stokes operator in Lq -space on an infinite cylindrical domain of
,
, with several exits to infinity generates a bounded and exponentially decaying analytic semigroup and admits a bounded
-calculus. For the resolvent estimates, the Stokes resolvent system with a prescribed divergence in an infinite straight
cylinder with bounded cross-section
is studied in L
q
where
and
is an arbitrary Muckenhoupt weight. The proofs use cut-off techniques and the theory of Schauder decomposition of UMD spaces based on
-boundedness of operator families and on square function estimates involving Muckenhoupt weights. 相似文献
19.
The standard correspondence between the normal subgroups of the group G and some ideals of the group algebra FG is described. There is the problem of what we can say (or even prove) about a two-sided ideal of that does not contain any element of the form 1 − g ≠ 0, g ∈G of the standard basis of the augmentation ideal of . The main part of the argument of [2] yields the insight that, for such an ideal I there exists an expansion such that the ideal J of spanned by I contains an element 1 − h, h ∈ H \ G. Using the ideas of [2], we construct -thick groups H such that for every ideal J ≠ (0) of there are elements 1 − h ≠ 0 in J. This construction allows many variations. Examples of simple -thick groups were pointed out in [2]. A natural class of (in general non-simple) -full groups are the normal sections of the groups
(Here, Fin(M) is the subgroup of all finitary permutations of M.)
Received: July 2007 相似文献