共查询到20条相似文献,搜索用时 31 毫秒
1.
Guillaume Aubrun 《Proceedings of the American Mathematical Society》2007,135(5):1293-1303
We prove the following result: for any , only sample points are enough to obtain -approximation of the inertia ellipsoid of an unconditional convex body in . Moreover, for any , already sample points give isomorphic approximation of the inertia ellipsoid. The proofs rely on an adaptation of the moments method from Random Matrix Theory.
2.
Let be an -dimensional space of linear operators between the linear spaces and over an algebraically closed field . Improving results of Larson, Ding, and Li and Pan we show the following.
Theorem. Let be a basis of . Assume that every nonzero operator in has rank larger than . Then a linear operator belongs to if and only if for every , is a linear combination of .
3.
S. Artstein-Avidan O. Friedland V. Milman 《Proceedings of the American Mathematical Society》2006,134(6):1735-1742
In this paper we show that the euclidean ball of radius in can be approximated up to , in the Hausdorff distance, by a set defined by linear inequalities. We call this set a ZigZag set, and it is defined to be all points in space satisfying or more of the inequalities. The constant we get is , where is some universal constant. This should be compared with the result of Barron and Cheang (2000), who obtained . The main ingredient in our proof is the use of Chernoff's inequality in a geometric context. After proving the theorem, we describe several other results which can be obtained using similar methods.
4.
Let be the set of all linear transformations from to , where and are vector spaces over a field . We show that every -dimensional subspace of is algebraically -reflexive, where denotes the largest integer not exceeding , provided is less than the cardinality of .
5.
Sté phane R. Louboutin Joë l Rivat Andrá s Sá rkö zy 《Proceedings of the American Mathematical Society》2007,135(4):969-975
Let be an odd prime number. For we denote the inverse of modulo by with . Given , we prove that in any range of length the probability that has the same parity as tends to as . This result was previously known only to hold true in the full range of length . We will also obtain quantitative results on the pseudorandomness of the sequence for which we estimate the well-distribution and correlation measures as defined by Mauduit and Sárközy (1997).
6.
Alvaro Pelayo 《Proceedings of the American Mathematical Society》2007,135(1):277-288
We compute the homotopy type of the space of -equivariant symplectic embeddings from the standard -dimensional ball of some fixed radius into a -dimensional symplectic-toric manifold , and use this computation to define a -valued step function on which is an invariant of the symplectic-toric type of . We conclude with a discussion of the partially equivariant case of this result.
7.
Albin L. Jones 《Proceedings of the American Mathematical Society》2007,135(4):1197-1204
Consider an arbitrary partition of the triples of all countable ordinals into two classes. We show that either for each finite ordinal the first class of the partition contains all triples from a set of type , or for each finite ordinal the second class of the partition contains all triples of an -element set. That is, we prove that for each pair of finite ordinals and .
8.
Freddy Dumortier Daniel Panazzolo Robert Roussarie 《Proceedings of the American Mathematical Society》2007,135(6):1895-1904
The paper deals with classical polynomial Liénard equations, i.e. planar vector fields associated to scalar second order differential equations where is a polynomial. We prove that for a well-chosen polynomial of degree the equation exhibits limit cycles. It induces that for there exist polynomials of degree such that the related equations exhibit more than limit cycles. This contradicts the conjecture of Lins, de Melo and Pugh stating that for Liénard equations as above, with of degree the maximum number of limit cycles is The limit cycles that we found are relaxation oscillations which appear in slow-fast systems at the boundary of classical polynomial Liénard equations. More precisely we find our example inside a family of second order differential equations Here, is a well-chosen family of polynomials of degree with parameter and is a small positive parameter tending to We use bifurcations from canard cycles which occur when two extrema of the critical curve of the layer equation are crossing (the layer equation corresponds to . As was proved by Dumortier and Roussarie (2005) these bifurcations are controlled by a rational integral computed along the critical curve of the layer equation, called the slow divergence integral. Our result is deduced from the study of this integral.
9.
Kazem Khashyarmanesh 《Proceedings of the American Mathematical Society》2007,135(5):1319-1327
Let be a commutative Noetherian ring with non-zero identity, and ideals of with , and a finitely generated -module. In this paper, for fixed integers and , we study the finiteness of and in several cases.
10.
Ugur Madran 《Proceedings of the American Mathematical Society》2007,135(4):987-995
Let be a finite group of order divisible by a prime acting on an vector space where is the field with elements and . Consider the diagonal action of on copies of This note sharpens a lower bound for for groups which have an element of order whose Jordan blocks have sizes at most 2.
11.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
12.
S. Prashanth 《Proceedings of the American Mathematical Society》2007,135(1):201-209
Let denote the closure of in the norm Let and define the constants and Let We consider the following problem for We show an exact multiplicity result for for all small .
13.
In this paper some upper bounds for the volume and diameter of central sections of symmetric convex bodies are obtained in terms of the isotropy constant of the polar body. The main consequence is that every symmetric convex body in of volume one has a proportional section , dim ( ), of diameter bounded by whenever the polar body is in isotropic position ( is some absolute constant).
14.
Lifeng Ding 《Proceedings of the American Mathematical Society》2006,134(10):2881-2884
If every nonzero operator in an -dimensional operator space has rank , then is reflexive.
15.
Let be the number of solutions of the equation over the finite field , and let be the number of solutions of the equation . If , let be the least integer represented by . and play important roles in estimating . Based on a partition of , we obtain the factorizations of and , respectively. All these factorizations can simplify the corresponding calculations in most cases or give the explicit formulae for in some special cases.
16.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
17.
Jean-Pierre Gabardo Yun-Zhang Li 《Proceedings of the American Mathematical Society》2007,135(6):1775-1784
Given a expansive dilation matrix , a measurable set is called a -dilation generator of if is tiled (modulo null sets) by the collection . Our main goal in this paper is to prove certain results relating the support of the Fourier transform of functions generating a wavelet or orthonormal affine system associated with the dilation to an arbitrary set which is a -dilation generator of .
18.
Seon-Hong Kim 《Proceedings of the American Mathematical Society》2007,135(1):237-241
An upper bound for that implies the inequality between the arithmetic and geometric means is generalized with the introduction of a new parameter . The new upper bound is smoothly and densely algebraic in , and valid for for arbitrarily large positive provided that () is sufficiently close to . The range of its validity for negative is investigated through the study of a certain family of quadrinomials.
19.
Dong Zhe 《Proceedings of the American Mathematical Society》2007,135(1):191-200
In this paper, we first introduce the concept of single elements in a module. A systematic study of single elements in the Alg-module is initiated, where is a completely distributive subspace lattice on a Hilbert space . Furthermore, as an application of single elements, we study module isomorphisms between norm closed Alg-modules, where is a nest, and obtain the following result: Suppose that are norm closed Alg-modules and that is a module isomorphism. Then and there exists a non-zero complex number such that .
20.
Andreas Weingartner 《Proceedings of the American Mathematical Society》2007,135(9):2677-2681
Let be the sum of the positive divisors of . We show that the natural density of the set of integers satisfying is given by , where denotes Euler's constant. The same result holds when is replaced by , where is Euler's totient function.