高考数学“思想实验”中的若干关键词

除有形实验(physical experi ments)外,还有在较高理智水平上使用的其他实验,即思想实验(thought experi ments).而在数学中的实验是在想象中做的,是设想着做的,是在思想中进行的实验[1].显然,这种实验乃是在头脑中进行的抽象     

利用位似图形解作图题一例

位似图形所有对应点的连线所在直线相交于一点,这一交点或在两图形的同侧,或在两图形之间,或在图形之内,或在图形的边上及顶点上,利用这一性质可以解决某些作图问题.     

浅谈高中数学的类比方法

世界万物总在不断变化、完善着,数学知识亦不例外.对诸多数学知识的理解在深化,应用在优化,有诸多数学命题在延伸、拓广,在这些变化过程中“类比”有着它独特的功效.     

看书要细 思考要慎

同学们在平时阅读教材时,因为教材经过老师在课堂中的解读,自己好像已全然明白,所以,读起来很粗糙,不作慎思.因此,在做题时常范些莫名其妙的错误.现举两例.     

关注数学活动 提升数学素养——以《勾股定理》应用为例

在新课程的指导下,数学教学中越来越关注学生数学综合实践能力的培养,基于此,在教学中可以开展一些拓展性课程,多让学生参加一些数学活动,让学生在活动中发现,在发现中探究,在探究中解决,在解决中积累,进而培养学生发现问题、提出问题、分析问题和解决问题的能力,以此促进学生综合能力和数学素养不断提升.     

让数学课堂教学行走在生活的道路上——《向量加法》教学案的设计示例

新课程改革的背景下,学生想要的是:自由遨游在数学的天空中,自由呼吸在数学的花园里,自由徜徉在数学的长廊里.在数学的天空里,飞翔着生动,闪烁着鲜活,蕴育着智慧,然而,数学的抽象与逻辑就像一堵墙,在定格数学的同时,也凝固了人们对数学的兴趣.怎么办?……答案无他:实现数学的生活化,让数学课堂教学行走在生活的道路上.一、导入新课要实现"生活化"很多老师在教学过程中对导入新课环节不是很重视,其实中学课堂教学的导入新课环节,是整个课堂教学中不可缺少的     

读者心声

张老师:您好!请允许我这样称呼。听了您去年5月份在兰州和前天在西安的培训、讲座,改变了原来不切合实际的、盲目追求成绩的做法,顶着领导的质疑,我回来后一直在尝试,在我们一个农村学校,在我的班级也收效很好,学生受益匪浅,我将继续坚持下去,真的很感谢您!     

另类《守株待兔》

正欢迎来到另类世界,在这个世界里,一切常规都可以被打破,鱼儿可以在天上飞,汽车可以在水里行,故事也可以另类发展。发散思维,激荡脑力,一起另类地笑吧!     

揭示问题内隐谨防以假乱真

在数学问题中,或在解决数学问题的过程中,如果包含了没有直接言明但又确实存在的事实,那么我们称这个事实为问题内隐．在教学中经常发现,同学们在解决某些数学问题时,由于忽视问题内隐的存在,从而导致解题过程的失误．本文拟例举此类失误的几种常见情形,以资同学们在学习中参考．     

基于学科素养的思辨教学策略

数学作为基础学科,其地位不言而喻.要充分发挥其学科价值就要在数学教学中打破“照本宣科”的“灌输”式讲授,引导学生站在更高的角度去审视问题,审视数学,为此,在教学中要努力提高学生的思辨能力,以此活跃思维,发展思维,让思维在发展中优化,在优化中完善,促进数学素养全面提升.     

Singular Fibers in Elliptic Fibrations on the Rational Elliptic Surface

We determine the combinations of singular fibers a locally holomorphic elliptic fibration on the rational elliptic surface can admit. This problem has been answered for globally holomorphic elliptic fibrations by Persson and Miranda [12], [9]; we compare our methods and results to theirs. In particular, we find combinations of singular fibers which can be realized by locally holomorphic fibrations but not by globally holomorphic ones.     

复Banach空间中C-R方程的全纯解

二重复数是复数的一种推广，在其上的全纯映照族对应于Ｃ２上满足复Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯映照族．可以证明，这样的映照族本质上是由二个单复变数的全纯函数的直乘积所组成的族．本文证明：即使在Ｂａｎａｃｈ空间中，Ｃａｕｃｈｙ－Ｒｉｅｍａｎｎ方程的全纯解，具有同样的性质．     

Transverse Lie jets and holomorphic geometric objects on transverse bundles

Two holomorphic fields of geometric objects on a transverse Weil bundle are called equivalent if there exists a holomorphic diffeomorphism of this bundle onto itself which induces the identity transformation of the base manifold and maps one of these fields into the other. In terms of transverse Lie jets, we establish necessary and sufficient conditions for a holomorphic field of geometric objects on a transverse Weil bundle to be equivalent to the prolongation of a field of foliated geometric objects given on the base manifold. As an example, we consider a holomorphic linear connection on a transverse bundle.     

On holomorphic immersions into K(a)hler manifolds of constant holomorphic sectional curvature

We study holomorphic immersions f: X → M from a complex manifold X into a Kahler manifold of constant holomorphic sectional curvature M, i.e. a complex hyperbolic space form, a complex Euclidean space form, or the complex projective space equipped with the Fubini-Study metric. For X compact we show that the tangent sequence splits holomorphically if and only if f is a totally geodesic immersion. For X not necessarily compact we relate an intrinsic cohomological invariant p(X) on X, viz. the invariant defined by Gunning measuring the obstruction to the existence of holomorphic projective connections, to an extrinsic cohomological invariant v(f)measuring the obstruction to the holomorphic splitting of the tangent sequence. The two invariants p(X) and v(f) are related by a linear map on cohomology groups induced by the second fundamental form.In some cases, especially when X is a complex surface and M is of complex dimension 4, under the assumption that X admits a holomorphic projective connection we obtain a sufficient condition for the holomorphic splitting of the tangent sequence in terms of the second fundamental form.     

Totally geodesic holomorphic subspaces

In [G. Munteanu, Complex Spaces in Finsler, Lagrange and Hamilton Geometries, vol. 141, Kluwer Academic Publishers, Dordrecht, FTPH, 2004.] we underlined the motifs of a remarkable class of complex Finsler subspaces, namely the holomorphic subspaces. With respect to the Chern–Finsler complex connection (see [M. Abate, G. Patrizio, Finsler Metrics—A Global Approach, Lecture Notes in Mathematics, vol. 1591, Springer, Berlin, 1994.]) we studied in [G. Munteanu, The equations of a holomorphic subspace in a complex Finsler space, Publicationes Math. Debrecen, submitted for publication.] the Gauss, Codazzi and Ricci equations of a holomorphic subspace, the aim being to determine the interrelation between the holomorphic sectional curvature of the Chern–Finsler connection and that of its induced tangent connection.In the present paper, by means of the complex Berwald connection, we study totally geodesic holomorphic subspaces. With respect to complex Berwald connection the equations of the holomorphic subspace have simplified expressions. The totally geodesic subspace request is characterized by using the second fundamental form of complex Berwald connection.     

The equations of a holomorphic subspace in a complex Finsler space

In [Mu1] we underlined the motifs of holomorphic subspaces in a complex Finsler space: induced nonlinear connection, coupling connections, and the induced tangent and normal connections. In the present paper we investigate the equations of Gauss, H-and A-Codazzi, and Ricci equations of a holomorphic subspace. We deduce the link between the holomorphic curvatures of the Chern-Finsler connection and its induced tangent connection. Conditions for totally geodesic holomorphic subspaces are obtained. Communicated by János Szenthe     

多复变数全纯映射精细的Bohr定理

本文首先建立不依赖自同构从复Banach空间平衡域到Cn单位多圆柱上一定限制条件下全纯映射精细的范数型Bohr定理及复Banach空间X上单位球到复Banach空间Y上单位球全纯映射精细的泛函型Bohr定理.其次,给出有界对称域上全纯映射精细的Bohr定理.最后,得到J*代数单位球上全纯映射精细的Bohr定理.所得结果将一维的Bohr定理推广至高维.     

Higher dimensional tautological inequalities and applications

We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifolds. Using Ahlfors currents in higher dimension, we obtain several strong degeneracy statements such as the proof of a generalized Green-Griffiths–Lang conjecture for threefolds with holomorphic foliations of codimension one.     

Some new results on domains in complex space with non-compact automorphism group

We provide a new proof of the Wong-Rosay theorem, using the structure of the ring of holomorphic functions. As a byproduct, we provide an analogous theorem for classical bounded symmetric domains. The second main result of this article concerns a new existence theorem for holomorphic peaking functions at a hyperbolic orbit accumulation boundary point. Finally, we give a proof of a version of the Greene-Krantz conjecture using holomorphic vector fields and a strengthened Hopf lemma.     

Hecke operators for weakly holomorphic modular forms and supersingular congruences

We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.