A comparison study on responsiveness of three mechanisms to affirmative action in school choice

This note provides a comparison study on responsiveness of three popular mechanisms to affirmative action in school choice. When the exogenous school choice environment gives full priority to the minority, the student-proposing deferred acceptance (DA) mechanism is responsive to both the quota-based and reserve-based affirmative action policies. In comparison with DA mechanism, the top trading cycles (TTC) mechanism is responsive to neither the quota-based nor the reserve-based affirmative action even when the exogenous school choice environment gives full priority to the minority. When each minority student has higher priority than each majority student at each school, the TTC mechanism is responsive to the quota-based affirmative action. However, under the environment as above, the Boston mechanism is not responsive to the quota-based affirmative action.     

On Fourier frame of absolutely continuous measures

Let μ be a compactly supported absolutely continuous probability measure on Rn, we show that L²(K,dμ) admits a Fourier frame if and only if its Radon-Nikodym derivative is bounded above and below almost everywhere on the support K. As a consequence, we prove that if μ is an equal weight absolutely continuous self-similar measure on R¹ and L²(K,dμ) admits a Fourier frame, then the density of μ must be a characteristic function of self-similar tile. In particular, this shows for almost everywhere 1/2<λ<1, the L² space of the λ-Bernoulli convolutions cannot admit a Fourier frame.     

Integer points in backward orbits

A theorem of J. Silverman states that a forward orbit of a rational map φ(z) on P¹(K) contains finitely many S-integers in the number field K when (φ°φ)(z) is not a polynomial. We state an analogous conjecture for the backward orbits using a general S-integrality notion based on the Galois conjugates of points. This conjecture is proven for the map φ(z)=zd, and consequently Chebyshev polynomials, by uniformly bounding the number of Galois orbits for zn−β when β≠0 is a non-root of unity. In general, our conjecture is true provided that the number of Galois orbits for φn(z)−β is bounded independently of n.     

在其Sylow子群上作用双传递的有限群

本文完全确定了下述类型的有限群：（１）对于某个素数ｐ，在其Ｓｙｌｏｗｐ－子群的集合上作用双传递的所有几乎单群；（２）所有的非交换单群Ｔ，其自同构群在Ｔ的某个Ｓｙｌｏｗｐ－子群的集合上作用双传递；（３）在其所有的Ｓｙｌｏｗ子群上双传递的全部有限群．     

Editorial Addresses

We study the existence and structure of extremals for one-dimensional variational problems on a torus and the properties of the minimal average action as a function of the rotation number. We show that, for a generic integrand f, the minimum of the minimal average action is attained at a rational point mn ^–1 where n1 and m are integers; also, for each initial value, there exists an (f)-weakly optimal solution over an infinite horizon.     

Totally Geodesic Orbits of Isometries

We study cohomogeneity one Riemannian manifolds and we establish some simple criterium to test when a singular orbit is totally geodesic. As an application, we classify compact, positively curved Riemannian manifolds which are acted on isometrically by a non-semisimple Lie group with an hypersurface orbit.     

隐性约束机制的设计研究

文章研究在多阶段动态博弈情况下隐蔽行为的隐性约束机制设计问题，用博弈论方法和信息经济学的委托-代理理论方法，建立多阶段委托-代理关系约束问题重复博弈的声誉模型，对隐蔽行为的隐性约束机制进行研究，证明了多阶段委托-代理关系中隐性约束机制的存在，给出了这种情况下的有效约束条件，隐性约束机制的设计方法以及其他结论。     

Estimating the Hausdorff dimensions of univoque sets for self-similar sets

An approach is given for estimating the Hausdorff dimension of the univoque set of a self-similar set. This sometimes allows us to get the exact Hausdorff dimensions of the univoque sets.