提高找寻“算律”意识,愉快破解“创新”试题

破解难题的常用思路是特例探路,然后沿着由特殊到一般的思维规律,找寻试题中的“算理算律”,即基本原理,其实枚举法本身也不失为一种有效的学习探究路径,尤其适用于求解组合数学方面的问题.而一些创新类压轴考题的第(1)问往往也会透露出一定的解题信息,大家一定要认真捕捉,如果还发现不了明显的可用信息,那么可继续利用特例探路,往往就能看出端倪,进而找到解题方向,必要时可以给出证明.本文主要以2024年新课标Ⅰ卷高考压轴题和近期部分省市高考模拟创新类压轴题为例,引领大家探究,以期有所启发,学有所获.

着眼“意义” 建构“算律”——“乘法分配律”教学实践与思考

运算律是计算发展的必然需要，是基本运算在算法执行中产生的简约规则。为此，运算律教学时，需要在运算意义支持下，基于算法这个根基去建立认知。乘法分配律的教学，需要建立在“学生已经掌握计算方法”的基础上，借助乘法意义，把乘法分配律与乘法意义联系起来，使知识的本质与核心展现出来，构建以“数学理解”为中心的课堂。

谈基于算理、算法和算律的三类计算课

计算教学中要让学生理解算理、探寻算法和寻求合理简洁的运算途径以解决问题，不以技能的掌握作为唯一目标，既要重视学生掌握算法，形成技能，又要在感悟算理、建立联系的过程中发展思维，提升能力，还要注意运算速度以及灵活性。教学中，教师要充分理解计算教学的基本类型，上好算理型、算法型和算律型三类计算课，做到“量体裁衣”，各有侧重。

论算力时代的三定律

从日益增长的算力需求角度出发,指出了建设泛在多样、绿色安全、智能敏捷的算力设施是企业、区域乃至国家的必然选择。以算力为核心的数字信息基础设施直接影响着数字经济的发展速度和社会智能的发展高度。在政策和需求的双重驱动下,将“算力三定律”作为底层运行法则的算力时代正在加速到来,算力与电力、热力一样会成为新型生产力,推动数字经济高质量发展,推动社会、生活、科研发生前所未有的巨变。

大圆航线导航与控制律设计

随着无人机(UAV)应用范围的扩大,要求无人机能精确跟踪预定航线。预定的飞行任务可以有两种规划方式,一是近似在当地切平面上的直线或曲线;二是飞行距离较长时在地球表面的大圆航线。第二种规划相对复杂,研究较少,因此,介绍了某型无人机的动力学模型,提出了一种全新的大圆航线导航解算算法,设计了大圆导航控制律,此外,还分析了常值风及突风干扰对导航的影响。经计算机仿真验证和部分的实际飞行试验结果表明:与预定航线的距离偏差较小,航迹精度较高,新算法及设计较好地满足了实际大圆航线飞行要求。

初中学生数学运算能力培养策略新探

从加强基础知识的教学,加强算法、算理、算律的教学等四个方面详细论述了初中学生数学运算能力的培养策略。

借直观 巧融通——“两位数乘两位数的计算”教学例谈

两位数乘两位数的计算既是计算教学的重点,又是计算教学的难点。教学中将内容进行合理整合,借助直条图帮助学生搭建思维支架,能够促进学生对算理的深入理解,实现运算律的有效孕伏,建构算理、算法、算律三位一体的认知结构。

指导简便计算培养学生数感探微

简便计算是数学教学中的重要内容之一,是培养学生数感、提高学生数学思维能力的有效途径。文章从体验过程、认知算律,对比辨析、建构系统,联系生活、加强估算三个方面,对指导简便计算、培养学生数感进行研究。

An optimized hardness model for carburizing-quenching of low carbon alloy steel

Research has been conducted about the hardness prediction for the carburizing and quenching process based on an optimized hardness simulation model,in accordance with the calculation rule of mixed phases.The coupling field model incorporates carburizing field analysis,temperature field analysis,phase transformation kinetics analysis and a modified hardness calculation model.In determination of the calculation model for hardness,calculation equations are given to be applied to low carbon content(x(C)<0.5%) for the child phases and the martensite hardness is calculated for high carbon content(x(C)>0.5%) in alloy.Then,the complete carburizing-quenching hardness calculation model is built,and the hardness simulation data are corrected considering the influence of residual austenite(RA) on hardness.Hardness simulations of the carburizing and quenching process of 17CrNiMo6 samples have been performed using DEFORM-HT_V10.2 and MATLAB R2013 a.Finally,a series of comparisons of simulation results and measured values show a good agreement between them,which validates the accuracy of the proposed mathematical model.

Benford's Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.

楔入正统:经学教育的五次冲击

经学教育自汉确立,直至清末,始终占据中国古代教育的主流和主导地位,但是在中国古代教育史上依然先后出现了五次有悖于经学教育的教育思想与实践,它们分别是:东汉末年倡导文学技艺的鸿都门学;南北朝时期要求儒、玄、文、史并重的四馆;隋唐创办的具备“专科”性质的新型学校;宋初强调实用的“分斋教学”;以及清初试图颠覆经学教育的“六斋设教”。这些教育思想与实践虽然没有颠覆经学教育的地位,却在一定程度上反映了经学教育对人才以及知识认识的局限,反映了特定历史时期社会发展对教育的需求,日益丰富了中国古代的人才观与知识观,在一定程度上影响了经学教育乃至整个中国传统教育的发展走向。审视中国古代教育史上对经学教育的这五次冲击,有助于全面、深入地认识中国传统教育的发展特点与动因,亦可引起当下教育改革中对人才、知识价值以及课程整合等方面的再思考。

A Maple Package on Symbolic Computation of Conserved Densities for （1＋l）-Dimensional Nonlinear Evolution Systems

A new algorithm for symbolic computation of polynomial-type conserved densities for nonlinear evolution systems is presented. The algorithm is implemented in Maple. The improved algorithm is more efficient not only in removing the redundant terms of the genera/form of the conserved densities but also in solving the conserved densities with the associated flux synchronously without using Euler operator. Furthermore, the program conslaw.mpl can be used to determine the preferences for a given parameterized nonlinear evolution systems. The code is tested on several well-known nonlinear evolution equations from the soliton theory.

Space luminous environment adaptability of missile-borne star sensor

To solve the problem of stray interference to star point target identification while a star sensor imaging to the sky, a study on space luminous environment adaptability of missile-borne star sensor was carried out. By Plank blackbody radiation law and some astronomic knowledge, irradiancies of the stray at the star sensor working height were estimated. By relative astrophysical and mathematics knowledge, included angles between the star sensor optical axis point and the stray at any moment were calculated. The calculation correctness was verified with the star map software of Stellarium. By combining the upper analysis with the baffle suppression effect, a real-time model for space luminous environment of missile-borne star sensor was proposed. By signal-noise rate （SNR） criterion, the adaptability of missile-borne star sensor to space luminous environment was studied. As an example, a certain type of star sensor was considered when imaging to the starry sky on June 22, 2011 （the Summer Solstice） and September 20, 2011 （August 23 of the lunar year, last quarter moon） in Beijing. The space luminous environment and the adaptability to it were simulated and analyzed at the star sensor working height. In each period of time, the stray suppression of the baffle is analyzed by comparing the calculated included angle between the star sensor optical axis point and the stray with the shielded provided by system index. When the included angle is larger than the shielded angle and less than 90~, the stray is restrained by the baffle. The stray effect on star point target identification is analyzed by comparing the irradiancy of 6 magnitude star with that of the stray on star sensor sensitization surface. When the irradiancy of 6 magnitude star is 5 times more than that of the stray, there is no effect on the star point target identification. The simulation results are identicat with the actual situation. The space luminous environment of the missile-borne star sensor can be estimated real-timely by this model. The adaptability of the star sensor to space luminous environment can be analyzed conveniently. A basis for determining the relative star sensor indexes, the navigation star chosen strategy and the missile launch window can be provided.

A Graphic Algorithm of＂Track＂ Effect in 3D Games

In 3D games, a lot of weapons in the movement will drag a ＂follow the shadow＂ effect, which is called the ＂track＂. In this paper, we first analyze the change rule of the ＂track＂, and then put forward a kind of algorithm to realize the ＂track＂. The calculation of this algorithm is small, but the effect is very real, has been successfully applied to a variety of 3D games.

Ethics and the Financial and Budgetary Discipline in the Ministry of Defence

This article deals with the relation between ethics and financial and budgetary discipline during economic and social recession in the Czech Republic. We find causes of economic and social recession in the Czech Republic in the loss of democratic and human values. Czech Republic was ranked the 57th place in the Corruption Perceptions index 2013 out of the 177 countries assessed, which is the same result achieved by Bahrain, Croatia, and Namibia. Among the 31 European Union （EU） member states and Norway, Switzerland, and Iceland, the Czech Republic is on the 25th site. Market as well as public sector and public finances should follow unwritten rules of ethics and ethical behavior. Such rules should be followed especially by politicians, officials, soldiers, and businessmen. Do we need ethics in present time？ How is the role of the code of ethics in increasing financial and budgetary discipline in the defence sector？ Is it possible to measure efficiency of the code of ethics for financial and budgetary discipline？ We explain the importance of codes of ethics and formulate essential elements that each code of ethics must contain. Next, we deal with the main rules of both financial and budgetary disciplines. Furthermore, this article offers a comparison of several codes of ethics and describes the main problems in our implementation. In the end, we introduce our draft of Code of Ethics for Economic Service Officer in the Ministry of Defence and talk about possible influences of these codes on the quality of employee＇s performance.

Enhancement of Voice Quality and Bit-rate Reduction by Prosodic Control in G.723.1 Vocoder

Speech coding techniques have been studied not truly to reduce the complexity and bit rate but also to improve the sound quality. CELP type vocoder, used as standard, supports the great stead quality even low bit rate. In this paper, the preprocessing of input speech to reduce the bit rate is different from the conventional vocoder. Different kinds of parameter are used for the preprocessing compared with the other parameters to t＇md the more appropriate parameter for the vocoder. The Parameters are used to synthesize the speech not to encode or decode for coding technique so we proposed the simple algorithm not to have the influence on the processing time or the computation time. The parameters in the preprocessing step are speaking rate, duration, and PSOLA technique.

Conservation Laws and Analytic Soliton Solutions for Coupled Integrable Dispersionless Equations with Symbolic Computation

Under investigation in this paper are two coupled integrable dispersionless (CID) equations modelingthe dynamics of the current-fed string within an external magnetic field.Through a set of the dependent variabletransformations, the bilinear forms for the CID equations are derived.Based on the Hirota method and symboliccomputation, the analytic N-soliton solutions are presented.Infinitely many conservation laws for the CID equationsare given through the known spectral problem.Propagation characteristics and interaction behaviors of the solitons areanalyzed graphically.

Noether-Type Symmetries and Associated Conservation Laws of Some Systems of Nonlinear PDEs

The algorithm for constructing conservation laws of Euler Lagvange type equations via Noether-type symmetry operators associated with partial Lagrangian has been presented. As applications, many new conservation laws of some important systems of nonlinear partial differential equations have been obtained.

A General Thermal Equilibrium Discharge Flow Model

Based on isentropic flow and thermal equilibrium assumptions, a model was derived to calculate discharge flow rate, which unified the rules of room temperature water discharge, high temperature and high pressure water discharge, two-phase critical flow, saturated steam and superheated steam critical flow, and gave a method to calculate critical condition. Because of the influence of friction, the entropy is increased in the actual discharge process, and the discharge flow rate in thermal equilibrium condition can be obtained by the original model multiplied by an appropriate correction coefficient. The model calculated results agreed well with the experiment data of long nozzle critical flow.