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一道以群的定义为背景的高考试题赏析 总被引:2,自引:0,他引:2
每一年的高考数学试卷中都有一些以高等数学背景立意的好题目,如2006年四川卷理科第16题,是一道以近世代数中群的定义为背景立意的填空题,这样的试题能够有效考查学生的学习能力、思维能力和数学创新意识,这为高校选拔学习潜质好的学生创造了条件.…… 相似文献
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备课是教师的一项基本功,是教师对教材进行再创造的过程,是集教学内容,教学方式,教学艺术于一体的一项关键设计.备课质量的高低,不仅影响着教学计划的实施和教育方针的落实,更潜在地制约着课堂教学的效率. 相似文献
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2011年高考已经落幕,笔者有意关注了湖北数学试卷,解读理科数学试卷,两道立体几何试题给我留下了很深的印象.小题的背景和问题设置让人耳目一新;大题的解法入口宽,方法多,涉及的知识面广,打破了单纯考查立体几何的常规,建立了立体几何与函数、三角、向量、解几的密切联系.这两道试题充分体现了源于教材,略高于教 相似文献
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在解析几何中有二次曲线与直线位置关系的讨论、二次曲面与直线位置关系的讨论,而二次曲面与平面相关位置关系的探讨较少.本文给出二次曲面a11x2+a22y2+a33z2+2a12xy+2a13xz+2a23yz+2a14x+2a24y+2a34z+a44=0(1)和平面Ax+By+Cz+D=0(2)的相对位置的判别式Δ=a11a12a13a14Aa21a22a23a24Ba31a32a33a34Ca41a42a43a44DA B C D0(aij=aji).(3)并证明了:若Δ>0,则二次曲面(1)与平面(2)相交;若Δ=0,则(1)和(2)相切;若Δ<0,则(1)和(2)相离. 相似文献
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For a convex closed bounded set in a Banach space, we study the existence and uniqueness problem for a point of this set that is the farthest point from a given point in space. In terms of the existence and uniqueness of the farthest point, as well as the Lipschitzian dependence of this point on a point in space, we obtain necessary and su.cient conditions for the strong convexity of a set in several infinite-dimensional spaces, in particular, in a Hilbert space. A set representable as the intersection of closed balls of a fixed radius is called a strongly convex set. We show that the condition “for each point in space that is sufficiently far from a set, there exists a unique farthest point of the set” is a criterion for the strong convexity of a set in a finite-dimensional normed space, where the norm ball is a strongly convex set and a generating set. 相似文献
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We demonstrate the behavior of the soliton which, while moving in non-dissipative and dispersion-constant medium encounters a finite-width barrier with varying dissipation and/or dispersion; beyond the layer dispersion is constant (but not necessarily of the same value) and dissipation is null. The transmitted wave either retains the form of a soliton (though of different parameters) or scatters a into a number of them. And a reflection wave may be negligible or absent. This models a situation similar to a light passing from a humid air to a dry one through the vapor saturation/condensation area. Some rough estimations for a prediction of an output are given using the relative decay (or accumulation) of the KdV conserved quantities in a dissipative area; in particular for a restriction for a number of solitons in the transmitted signal. 相似文献
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In this paper a barrier function method is proposed for approximating a solution of the nonconvex quadratic programming problem with box constraints. The method attempts to produce a solution of good quality by following a path as the barrier parameter decreases from a sufficiently large positive number. For a given value of the barrier parameter, the method searches for a minimum point of the barrier function in a descent direction, which has a desired property that the box constraints are always satisfied automatically if the step length is a number between zero and one. When all the diagonal entries of the objective function are negative, the method converges to at least a local minimum point of the problem if it yields a local minimum point of the barrier function for a sequence of decreasing values of the barrier parameter with zero limit. Numerical results show that the method always generates a global or near global minimum point as the barrier parameter decreases at a sufficiently slow pace. 相似文献
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B. Lemaire 《Set-Valued Analysis》2001,9(1-2):111-121
This paper deals with a variant of a dynamical selection scheme introduced by Attouch and Cominetti for ill-posed convex minimization which combines approximation with the steepest descent method by mean of a suitable parameterization of the approximation parameter as a function of the time. This variant applies to a general inclusion with a maximal monotone operator by mean of a staircase parameterization. A discrete analogue is also considered. Applications to selecting a particular zero of a maximal monotone operator or a particular fixed point of a nonexpansive mapping via regularization techniques are presented. Finally, the alternative use of well-posedness by perturbations is discussed. 相似文献
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We consider a collective insurance risk model with a compound Cox claim process, in which the evolution of a claim intensity
is described by a stochastic differential equation driven by a Brownian motion. The insurer operates in a financial market
consisting of a risk-free asset with a constant force of interest and a risky asset which price is driven by a Lévy noise.
We investigate two optimization problems. The first one is the classical mean-variance portfolio selection. In this case the
efficient frontier is derived. The second optimization problem, except the mean-variance terminal objective, includes also
a running cost penalizing deviations of the insurer’s wealth from a specified profit-solvency target which is a random process.
In order to find optimal strategies we apply techniques from the stochastic control theory. 相似文献
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研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系. 相似文献
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Lorenzo Fusi Angiolo Farina 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(5):826-847
In this paper we present a new mathematical model for Bingham-like materials in which the core behaves as a visco-elastic Maxwell fluid. We deduce the model in a general 3D framework, using a thermodynamical approach based on the theory of natural configurations. We apply the model to the case of a plane Poiseuille flow driven by a time-dependent pressure gradient. The mathematical formulation of the latter case turns out to be a free boundary problem in which a parabolic equation and a dissipative wave equation are coupled together. 相似文献
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This paper proposes a mathematical model to compare a network organization with a hierarchical organization. In order to formulate the model, we define a three-dimensional framework of the coordination structure of a network and of other typical coordination structures. In the framework, we can define a network structure by contrasting it with a hierarchy, in terms of the distribution of decision making, which is one of the main features of information processing. Based on this definition, we have developed a mathematical model for evaluating coordination structures. Using this model, we can derive two boundary conditions among the coordination structures with respect to the optimal coordination structure. The boundary conditions help us to understand why an organization changes its coordination structure from a hierarchy to a network and what factors cause this change. They enable us, for example, to find points of structural change where the optimal coordination structure shifts from a hierarchy to a hierarchy with delegation or from a hierarchy with delegation to a network, when the nature of the task changes from routine to non-routine. In conclusion, our framework and model may provide a basis for discussing the processes that occur when coordination structures change between a hierarchy and a network. 相似文献
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Molly Maxwell 《Journal of Combinatorial Theory, Series A》2009,116(2):351-378
We define involutively self-dual matroids and prove that an enumerator for their bases is the square of a related enumerator for their self-dual bases. This leads to a new proof of Tutte's theorem that the number of spanning trees of a central reflex is a perfect square, and it solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted version of the latter result.We give an algebraic analogue relating to the critical group of a graph, a finite abelian group whose order is the number of spanning trees of the graph. We prove that the critical group of a central reflex is a direct sum of two copies of an abelian group, and conclude with an analogous result in Kalai's setting. 相似文献