小学珠心算数学

第四章进位加法第一节进位加法的意义与加数有9一、进位加法的意义两个加数相加,某一位上的和有等于10或大于10的加法,我们称进位加法。两个一位数相加有可能出现进位加。     

小朋友学习珠心算

第二节 进位加法 一、20以内的进位加法 两个一位数相加,和等于10或大于10的加法。我们称进位加法。如图所示:     

“两位数加一位数进位加”教学设计及思考

正【课前思考】"两位数加一位数进位加"是在学生掌握了"两位数加一位数不进位加"的珠心算方法后进行教学的,通过本课学习后,要让学生理清两位数加一位数的进位加的算理和方法。本课主要让学生重点掌握三种类型的进位加:个位上直减进位加(如19+8)、个位上破五进位加(如27+7)和个位破五进位后同时十位满五的进位加(如47+6)的拨珠方法。考虑到一年级学生的年龄特征,为了让学生在掌握珠算方法、获得对数学理解的同时,也能在心算技能上得以初步尝试,进而让他们在能力和思维上     

乘方的指数与其幂的位数的关系

为了探究乘方的指数与其幂的位数的关系,定义了几个有关的新概念,并且证明了两个关于乘方以及进制进位的定理,由此建立起关于乘方以及进制进位的理论体系,其中包括进位理论中判定乘方的指数与其幂的位数是否存在周期规律的判别法,以及进位规律的求解法和四条相关的性质.     

“连续进位加”教学设计

【教学内容】《珠心算》第四册“连续进位加”。【教材分析】连续进位加这节课是在学生已学过简单加法计算的基础上进行教学的,通过本课学习,使学生进一步理解加法计算法则,会用算盘计算两位数的连续进位加法,为后面学习连续退位减作好铺垫。     

简化口诀 提升速度 优化结构——基于心理学的珠算口诀教学建议

传统的珠算加减法的口诀共52句,本人在实验的过程中发现,进位加与破五进位加、退位减与满五退位减的口诀学生容易混淆,于是减掉破五进位加与满五退位减的口诀,将52句口诀变成44句。本文在心理学分析的基础上,理论结合实践,共同验证此举的可行性。     

“破五进位加、满五退位减”教学设计

<正>【教学内容】破五进位加、满五退位减。【教学目标】一、通过复习,巩固以往所学知识,使学生进一步理解破五进位加、满五退位减的计算方法,培养学生的观察能力。二、使学生进一步熟练运用双手拨珠法进行破五进位加、满五退位减的珠算,并掌握破五进位加、满五退位减的珠心算方法。三、使学生体验与同伴相互交流学习的乐趣,增强用心算计算的自豪感。     

《实用珠算式心算讲座》(续)

七、7乘 7的排积用认字法学习效果最好。 为了更好记忆,我们引进辅助进位律。我们简称辅助进位律是辅进或说辅律。     

进位返加与逐位模2加及模2n加的相容程度分析

深入分析了进位返加运算与逐位模2加运算及模2^n加运算的相容程度,给出了它们的相容概率的计算公式．结论表明,进位返加运算与逐位模2加运算的相容概率尽管很小,但远大于理想值2^-n;进位返加运算与模2^n加运算的相容概率很大,近似为2／3．     

小朋友学习珠心算

七、多位数加法 (一)进位与不进位 若从高位计算,两同位数相加的和小于9,我们合称作不进位数,简称“不进”;两同位数相加的和等于9,     

Synthesis of basic elements of multidimensional multirate systems Part. 1. Nonseparable decimation matrices

A synthesis method is developed for multidimensional decimation matrices of given dimension for a specified number of channels which are used in multidimensional multirate systems. The method is based on application of eigenvalues and Gröbner bases techniques. A full parametrization of decimation matrices is effected for two-and three-dimensional cases. Peculiarities of a four-dimensional case are considered.     

Construction of compactp-wavelets

In [D1] the method for construction of compact wavelets, based on a decimation by 2, was introduced. In [CW] and [A] decimation by an integer different from 2 is discussed but construction for a generalp is not completely treated. Here we review some of the elements of that construction and give an approach that generalizes to thep>2 case in a concrete fashion which requires some new ideas.     

Sampling Theory with Average Values on the Sierpinski Gasket

In the case of some fractals, sampling with average values on cells is more natural than sampling on points. In this paper we investigate this method of sampling on SG and SG\(_{3}\). In the former, we show that the cell graph approximations have the spectral decimation property and prove an analog of the Shannon sampling theorem. We also investigate the numerical properties of these sampling functions and make conjectures that allow us to look at sampling on infinite blowups of SG. In the case of SG\(_{3}\), we show that the cell graphs have the spectral decimation property but show that it is not useful for proving an analogous sampling theorem.     

Criteria for Spectral Gaps of Laplacians on Fractals

Surprisingly, Fourier series on certain fractals can have better convergence properties than classical Fourier series. This is a result of the existence of gaps in the spectrum of the Laplacian. In this work we prove general criteria for the existence of gaps when the Laplacian admits spectral decimation. The known examples, including the Sierpinski gasket and the level-3 Sierpinski gasket, and the new examples including the fractal-3 tree, the Hexagasket and the infinite family of tree-like fractals satisfy the criteria.     

A centrosymmetric matrix based technique for the interpolation of a Hermitian signal

This work is concerned with the signal interpolation problem, i.e. given only samples of a signal, a method is derived for evaluating its samples on finer grids. The derivation is based on a discrete‐time decimation formula. In the special case where the known samples have the Hermitian property, two schemes are presented and mathematically proved to result in interpolated points having the same property. The first scheme does not utilize the known sample at the origin and results in a square system of equations to be solved for the unknown interpolated points of the signal. The second scheme has the merit of utilizing all the known samples, but it results in an overdetermined system of equations to be solved by the least squares method. The exploitation of the elegant properties of the involved centrosymmetric matrices is central to the treatment presented here. Copyright © 2002 John Wiley & Sons, Ltd.     

Counting the decimation classes of binary vectors with relatively prime length and density

Journal of Algebraic Combinatorics - We present a method for determining the number of decimation classes of density $$\delta $$ binary vectors indexed by a finite abelian group G of size $$\ell $$...     

A Counterexample to the “Hot Spots” Conjecture on Nested Fractals

Although the “hot spots” conjecture was proved to be false on some classical domains, the problem still generates a lot of interests on identifying the domains that the conjecture hold. The question can also be asked on fractal sets that admit Laplacians. It is known that the conjecture holds on the Sierpinski gasket and its variants. In this note, we show surprisingly that the “hot spots” conjecture fails on the hexagasket, a typical nested fractal set. The technique we use is the spectral decimation method of eigenvalues of Laplacian on fractals.     

Central limit theorems for arrays of decimated linear processes

Linear processes are defined as a discrete-time convolution between a kernel and an infinite sequence of i.i.d. random variables. We modify this convolution by introducing decimation, that is, by stretching time accordingly. We then establish central limit theorems for arrays of squares of such decimated processes. These theorems are used to obtain the asymptotic behavior of estimators of the spectral density at specific frequencies. Another application, treated elsewhere, concerns the estimation of the long-memory parameter in time series, using wavelets.     

Wave Equation on One-Dimensional Fractals with Spectral Decimation and the Complex Dynamics of Polynomials

We study the wave equation on one-dimensional self-similar fractal structures that can be analyzed by the spectral decimation method. We develop efficient numerical approximation techniques and also provide uniform estimates obtained by analytical methods.