高中教材中数学史料的教育价值

我国著名数学家吴文俊曾说:"假如你对数学史的历史发展,对一个领域的发生和发展,对于一个理论的兴旺和衰落,对一个概念的来龙去脉,对一种重要思想的产生和影响等许多历史因素都弄清了,我想对数学就会了解得多了,对数学的现状就会知     

数学学习与数学思想方法

数学学习,实际上就是对数学知识的理解和对数学思想方法的掌握与运用,数学思想方法是对数学知识的概括,也是数学知识的本质所在.对数学思想方法进行层次性划分,使数学学习具有针对性,同时也从方法论角度提供了数学学习的方法.全面地掌握数学方法,不仅有助于对数学知识的理解和运用,能有效提高数学的学习效率,对提高个体的整体素养也具有重要的现实意义.     

具有导子的Lie-Yamaguti代数

本文研究具有导子的Lie-Yamaguti代数,称之为LieYDer对.首先给出LieYDer对的上同调.其次,研究LieYDer对的中心扩张.最后,根据其上同调考虑LieYDer对的形变.     

导数中几个易混淆的问题对

现行高中数学教材将导数知识提升到了必修的高度．的确,导数的出现极大丰富了我们研究函数的手段,但是,导数中却存在着几个极易混淆的问题对,许多同学因为对它们的理解不到位,导致做题时频频出错．本文旨在通过对这些问题对的辨析,加深对导数相关概念的理解．     

出行选择行为的演化博弈分析

为缓解城市交通拥堵,通过分析出行者出行选择方式的博弈心理,建立了交管部门与出行者策略选择的决策博弈模型,应用演化博弈的思想分析了交管部门对私家车管理与不管理、出行者选择私家车与选择公交车出行各自两种策略选择的演化过程.根据雅克比矩阵的局部稳定性,对演化稳定状态进行了分析,并对一些主要参数对选择行为的影响进行了研究,结果表明,交管部门对公交车的激励效应以及对私家车管理效应对出行者出行方式选择行为的演化起着至关重要的作用.在讨论过程中,对各种情况做了详细地分析和解释,可以为政府决策部门提供相应的参考.     

CFO的红酒人生

葡萄酒用与其他酒类不同的方式呼唤着我们,引领我们靠近自然的怀抱,让我们能够在人生里深深呼吸,又温和地接近我们人生中的欲望。葡萄酒让我们回想起我们一直忘却了的渴望,也就是对自然的渴望、对人生的渴望、对爱情的渴望、对美丽的渴望,以及对普经遗失的自己所有的渴望。     

Hilbert空间中连续K-对偶的性质

文章引入Hilbert空间连续K-对偶,连续K-对偶对的概念,应用算子论的方法,讨论了Hilbert空间H上连续K-对偶和连续K-对偶对的若干性质及稳定性,并对已有文献的相关结论进行了推广.     

导数在单调性与极值应用中的错解辨析

由于概念的抽象性,对基础知识不全面或对题意理解不准确等而导致在导数单调性与极值应用中出现一些错误现象.正确的东西也往往需要在对正确与错误的鉴别中被接受,因此,采取积极的学习策略,正视错误,剖析错误,澄清错误,更能加深对概念本质的理解.     

出口对中国就业的影响分析-欧美日对比分析

欧盟、美国和日本作为中国的三大贸易伙伴,它们与中国间的贸易对中国的就业有着重要的影响,利用区分加工贸易的非竞争型投入占用产出模型,对比分析了2007年中国分别向所有地区、欧盟、美国、日本和世界其他地区出口1000美元货物对中国就业的拉动作用;并结合SDA方法分析了中国出口对就业拉动效率在时间上的变迁和地区间的差别.分析发现2002年到2007年,出口对就业的拉动效率不断下降,其中就业系数的下降是主要原因.中国对美国的出口对就业的拉动效率最低,而对日本的出口对就业的拉动效率最高.     

我国劳动力老化对劳动生产率的影响研究

人口老龄化对经济的直接影响体现为劳动力老化对劳动生产率的影响.本文在基于标准C-D生产函数的计量经济模型框架下,采用省级面板数据和固定效应估计方法,深入探究全国以及不同区域劳动力老化对劳动生产率的影响.实证结果显示,我国劳动力老化对劳动生产率有显著的消极影响,且沿海地区劳动力老化对劳动生产率的消极影响比非沿海地区更强烈.要缓解劳动力力老化对劳动生产率的消极影响,可以从以下三个方面入手:首先,稳定低生育水平,适当放宽人口政策;其次,大力发展教育事业,特别是对老年劳动力的教育和培训;第三,合理引导人口流动,实现地区间劳动力年龄结构的优势互补.     

Newton's solution to the equiangular spiral problem and a new solution using only the equiangular property

This paper is a study of Proposition IX of Book I of Newton's Principia, the problem of determining the centripetal force for an equiangular spiral. In Newton's main proof of this proposition there is an error concerning his reason for the figure SPRQT being “given in kind,” and a very interesting technique of varying things in the neighborhood of a limit. This main proof utilized Newton's formula for the limit of SP²QT²/QR given in Corollary I to Proposition VI of the Principia. Newton also gave an alternate proof which utilized his formula for SY²PV given in Corollary III to Proposition VI. The “given” of Proposition IX was “a spiral PQS, cutting all the radii SP, SQ, &c., in a given angle.” Both the main proof and the alternate proof implicitly depend on the property of the equiangular spiral that the radius of curvature at any point is proportional to the pole distance SP. We here offer a new proof of Newton's proposition which does not depend on this implicit assumption.     

Complex Hadamard matrices and equiangular tight frames

In this paper, we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al. [3] and extend the list of known equiangular tight frames. In particular, a (36, 21)-frame coming from a nontrivial cube root signature matrix is obtained for the first time.     

Numerically erasure-robust frames

Given a channel with additive noise and adversarial erasures, the task is to design a frame that allows for stable signal reconstruction from transmitted frame coefficients. To meet these specifications, we introduce numerically erasure-robust frames. We first consider a variety of constructions, including random frames, equiangular tight frames and group frames. Later, we show that arbitrarily large erasure rates necessarily induce numerical instability in signal reconstruction. We conclude with a few observations, including some implications for maximal equiangular tight frames and sparse frames.     

Equiangular Points

Apoint T is an equiangular point of a collection of localized vectors if all of them are seen from T at an equal oriented angle. It is proved that almost each planar triple of vectors with fixed origins (not all of which coincide) has an equiangular point. As a consequence, it is proved that if a planar triple of vectors has no equiangular points, then their projections to a certain axis are equal. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 299, 2003, pp. 162–168.     

矩阵代数上的局部合同变换和局部相似变换

令F表示任意域,Mn（F）表示由F上所有n×n矩阵形成的结合代数.本文的目的是研究Mn（F）上具有如下性质的两类线性映射,其中一类线性映射在Mn（F）上每一点的取值与Mn（F）的某个合同变换在该点的取值相同,另一类线性映射在Mn（F）上每一点的取值与Mn（F）的某个相似变换在该点的取值相同,随着Mn（F）上的点不同,这些合同变换和相似变换可能也不同.利用矩阵的秩、幂等阵以及幂零阵的性质,通过矩阵计算的方法证明了第一类线性映射或者是合同变换或者是合同变换与转置变换的复合,第二类线性映射或者是相似变换或者是相似变换与转置变换的复合.由这个结果可知存在真正意义上的局部合同变换和局部相似变换,从而丰富了局部映射理论的研究。     

Equiangular tight frames and fourth root seidel matrices

In this paper we construct complex equiangular tight frames (ETFs). In particular, we study the grammian associated with an ETF whose off-diagonal entries consist entirely of fourth roots of unity. These ETFs are classified, and we also provide some computational techniques which give rise to previously undiscovered ETFs.     

Type-II matrices in weighted Bose–Mesner algebras of ranks 2 and 3

Type-II matrices are nonzero complex matrices that were introduced in connection with spin models for link invariants. Type-II matrices have been found in connection with symmetric designs, sets of equiangular lines, strongly regular graphs, and some distance regular graphs. We investigate weighted complete and strongly regular graphs, and show that type-II matrices arise in this setting as well.     

Combinatorial constructions of packings in Grassmannian spaces

The problem of packing n-dimensional subspaces of m-dimensional Euclidean space such that these subspaces are as far apart as possible was introduced by Conway, Hardin and Sloane. It can be seen as a higher dimensional version of spherical codes or equiangular lines. In this paper, we first give a general construction of equiangular lines, and then present a family of equiangular lines with large size from direct product difference sets. Meanwhile, for packing higher dimensional subspaces, we give three constructions of optimal packings in Grassmannian spaces based on difference sets and Latin squares. As a consequence, we obtain many new classes of optimal Grassmannian packings.     

CLOSED LIGHT PATHS IN EQUIANGULAR SPIRAL DISKS

A new type of deformation for microscopic laser disks, the equiangular spiral deformation is proposed. First a short review of the geometry of light paths in equiangular spirals in the language of real two-dimensional geometric calculus is given. Second, the constituting equations for closed paths inside equiangular spirals are derived. Third, their numerical solution is performed and found to yield two generic types of closed light paths. Degenerate closed paths that exist over large intervals of the deformation parameter, and nondegenerate closed paths which only exist over relatively small deformation parameter intervals spanning less than 1% of the nondegenerate intervals. Fourth, amongst the nondegenerate paths a stable asymmetric bow-tie shaped light trajectory was found.