4-5岁幼儿数量守恒概念发展的干预研究

数量守恒是幼儿数学认知发展中的重要概念。研究采用个别测查法与实验干预法,对30名尚未形成数量守恒概念的4-5岁幼儿进行三种不同方式的干预。结果表明,＂正误反馈＂、＂正误反馈＋幼儿对自我判断推理＂和＂正误反馈＋幼儿对主试判断推理＂等三种干预方法均可有效提升幼儿的数量守恒能力,后两种干预方法的效果显著好于第一种干预方法。

一个探索恒河猴和熊猴数量守恒的实验研究

本实验对三只恒河猴和一只熊猴在一系列判断与数量有关的问题上进行训练,继而让动物对呈现数多少的刺激对进行“同”和“异”的判断。刺激物是画在白色卡片上的黑点,在设计上排除使动物利用黑点累加面积和卡片亮度作为线索的可能性,也使动物不可能记住黑点排列的特定模式。本实验共有六项实验程序,在最后一项中,把数从2到6的所有“同”和“异”的刺激对全部呈现给动物。实验结果表明有两只恒河猴和一只熊猴达到所有六项实验程序的预定标准。本文讨论了实验结果在皮亚杰关于数量守恒观点上的含义,以及据以解释数多少判断的可能的内部过程。

大班幼儿守恒能力的发展现状及教育对策——以莆田市A幼儿园大四班为例

守恒是大班数学教育活动中的一项重要内容,对幼儿的发展具有重要意义。本研究在参考皮亚杰守恒实验和以往文献基础上,自编数量守恒和长度守恒测量工具,采用量化研究的方法对福建省莆田市A幼儿园大四班35位幼儿的数量守恒和长度能力发展现状展开调查。调查发现:1) 该班幼儿数量守恒和长度守恒发展偏低。2) 该班幼儿数量守恒发展优于长度守恒的发展。3) 该班幼儿数量和长度守恒能力的发展不存在性别差异。4) 幼儿数量守恒与长度守恒能力呈显著正相关,但无法预测长度守恒能力;并在此基础上提出了相应的教育对策。

例谈小学生数学守恒观念的培养

守恒是皮亚杰儿童认知发展阶段论中的核心概念之一,是获得数和量概念的重要条件。发展和培养学生守恒观念,强化学生对数学知识本质的理解,达成知识的融会贯通,在现阶段教师应重视提高学生的数学素养。教师可从培养学生的数量守恒、长度守恒、面积守恒、体积守恒观念四个方面开展教学实践,培养数学守恒观念。

Lie Symmetrical Hojman Conserved Quantity of Relativistic Mechanical System

In this paper, we study the Lie symmetrical Hojman conserved quantity of a relativistic mechanical system under general infinitesimal transformations of groups in which the time parameter is variable. The determining equation of Lie symmetry of the system is established. The theorem of the Lie symmetrical Hojman conserved quantity of the system is presented. The above results are generalization to Hojman's conclusions, in which the time parameter is not variable and the system is non-relativistic. An example is given to illustrate the application of the results in the last.

A numerical simulation of seepage structure surface and its feasibility

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P（Dfi｜ Ri） is established. The index, P（Dfi｜ Ri）, shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Fractional Birkhoffian Dynamics Based on Quasi-fractional Dynamics Models and Its Lie Symmetry

In order to investigate the dynamic behavior of non-conservative systems,the Lie symmetries and conserved quantities of fractional Birkhoffian dynamics based on quasi-fractional dynamics model are proposed and studied.The quasi-fractional dynamics model here refers to the variational problem based on the definition of RiemannLiouville fractional integral(RLFI),the variational problem based on the definition of extended exponentially fractional integral(EEFI),and the variational problem based on the definition of fractional integral extended by periodic laws(FIEPL).First,the fractional Pfaff-Birkhoff principles based on quasi-fractional dynamics models are established,and the corresponding Birkhoff’s equations and the determining equations of Lie symmetry are obtained.Second,for fractional Birkhoffian systems based on quasi-fractional models,the conditions and forms of conserved quantities are given,and Lie symmetry theorems are proved.The Pfaff-Birkhoff principles,Birkhoff’s equations and Lie symmetry theorems of quasi-fractional Birkhoffian systems and classical Birkhoffian systems are special cases of this article.Finally,some examples are given.

Form Invariance of Raitzin＇s Canonical Equations of Relativistic Mechanical System

A form invariance of Raitzin's canonical equations of relativistie mechanical system is studied. First, the Raitzin's canonical equations of the system are established. Next, the definition and criterion of the form invariance in the system under infinitesimal transformations of groups are given. Finally,the relation between the form invariance and the conserved quantity of the system is obtained and an example is given to illustrate the application of the result.

Mathematical model for coupled reactive flow and solute transport during heap bioleaching of copper sulfide

Based on the momentum and mass conservation equations, a comprehensive model of heap bioleaching process is developed to investigate the interaction between chemical reactions, solution flow, gas flow, and solute transport within the leaching system. The governing equations are solved numerically using the COMSOL Multiphysics software for the coupled reactive flow and solute transport at micro-scale, meso-scale and macro-scale levels. At or near the surface of ore particle, the acid concentration is relatively higher than that in the central area, while the concentration gradient decreases after 72 d of leaching. The flow simulation between ore particles by combining X-ray CT technology shows that the highest velocity in narrow pore reaches 0.375 m/s. The air velocity within the dump shows that the velocity near the top and side surface is relatively high, which leads to the high oxygen concentration in that area. The coupled heat transfer and liquid flow process shows that the solution can act as an effective remover from the heap, dropping the highest temperature from 60 to 38 ℃. The reagent transfer coupled with solution flow is also analyzed. The results obtained allow us to obtain a better understanding of the fundamental physical phenomenon of the bioleaching process.

Pseudopotential generation

Different classes of first-principle pseudopotentials are compared and various schemes for pseudopotential generation based on norm conservation are discussed in this paper. BHS (Bachelet, Hamann, and Schlüter)-scheme and V (Vanderbilt)-modifications are used to derive the KB (Kleinman and Bylander)-pseudopotentials and pseudo wave functions of bismuth. Quality test of pseudopotentials shows that no ghost states occur in the logarithmic der ivatives of pseudo wave functions of Bismuth. The obtained bond length of bismuth dimer with this type of pseudopotentials is in good agreement with previous accurately calculate d ab initio quantum chemical result.

A Redemptive Analysis of Suffering

The notion of suffering carries with it aspects which are private and individual on the one hand, and social and lingual on the other. I would pay attention to the latter part of the suffering notion, where the notion of suffering is recognized to be primitive by almost all the theories of human values. This primitive character allows a commensurable basis on the basis of which most plural theories share something in common to talk objectively to each other. In this paper, I would like to offer three arguments in order to advance a thesis that one＇s suffering is redemptive of others. First, the conservation law of mass says that matter of a closed system can neither be created nor destroyed, although it may be differently rearranged. This may be applied to the experience of suffering, to allow the conservation law of suffering： My unjust self-interest costs pains in others to the level of the same amount but if I voluntarily suffer a sacrifice, others will have their pains lightened to the analogous level. Second, notion of yin-yang helps to support the redemptive thesis of suffering. The notion says that all things in the reality consist of two complementary opposite Capacities that interact within a greater whole, as part of a dynamic system. Then, my acceptance of suffering and the decrease of other＇s pain are two complementary capacities of one reality. Third, any person is responsible for his own act, so is a society as a whole. Then, as an individual restores his damaged person, when he commits a crime, by being suffered or punished, a society restores itself to its own proper state, when any member of the society is wronged, by suffering communally in one way or other.

A Super Extension of Kaup-Newell Hierarchy

With the help of the zero-curvature equation and the super trace identity, we derive a super extensionof the Kaup-Newell hierarchy associated with a 3×3 matrix spectral problem and establish its super bi-Hamiltonianstructures.Furthermore, infinite conservation laws of the super Kaup-Newell equation are obtained by using spectralparameter expansions.

A Free Surface Sharpening Strategy Using Optimization Method

VOF method which consists in transporting a discontinuous marker variable is widely used to capture the free surface in computational fluid dynamics.There is numerical dissipation in simulations involving the transport of the marker.Numerical dissipation makes the free surface lose its physical nature.A free surface sharpening strategy based on optimization method is presented in the paper.The strategy can keep the location of the free surface and local mass conservation at both time,and can also keep free surface in a constant width.It is independent on the types of solvers and meshes.Two famous cases were chosen for verifying the free surface sharpening strategy performance.Results show that the strategy has a very good performance on keeping local mass conservation.The efficiency of prediction of the free surface is improved by applying the strategy.Accurate modeling of flow details such as drops can also be captured by this method.