例析高考中数表问题的几种类型

所谓数表就是指满足一定的生成规则并按一定的顺序排列成的一个表．数表问题常与数列知识联手，在高考中奏出一曲曲优美的“乐章”．本文试就数表问题考查的几种常见类型及变化趋势作一阐述，以馈读者．

例谈数表问题的解法

2003年全国高考数学(理科)卷第22题是一道'数表题'.对于数表问题,在前些年的高考试卷中从未出现过,对绝大多数同学来说,题型是陌生的.又因这类题目不仅考查学生对等差(等比)数列的通项、前 n 项和等基础知识的掌握程度,往往还对学生的观察能力、归纳能力、探索能力、合情推理能力、创造能力及直觉思维提出了较高的要求,考查学生的思维灵活性,敏捷性.一般来说,题目综合性强.因此,不少同学在具体解题中感到困难多多.为了方便广大同学更好地复习、掌握,笔者特整理了几个例题如下,供师生参考.一、给出数表,求某个数的位置,某个位置上的数或某组数的和、通项等等.这是数表问题的一种主要形式.通过观察。

数阵与数表问题解题策略

课标课程强调学生能力的形成与提高，与之相适应的教材命制了很多新情境、新定义和新背景的问题，数阵与数表就是其中较典型的一类．由于这类问题可以较好地考查学生的观察能力、归纳推理能力和综合应用能力，非常适应高考命题以能力立意的要求，因而为高考命题留下了广阔的空间，这类题也就时常在高考题中出现．下面就谈一谈本人在平时教学过程中对数阵与数表问题所作的一些解题策略的探究，供各位同仁参考．

从棋子计数看一类数表型创新题

本文中,我们基于一道棋子计数趣题解题过程介绍“有序化”和“极端原理”等解题策略,并借助这些策略解决几道高中数学数表型创新题,其中包括2021年和2022年北京市海淀区高三期末数学第21题.

Analysis of radial basis function interpolation approach

The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.

On Univalent Functions in Multiply Connected Domains

The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.

Diagrams Produced by Secondary Students in Multiplicative Comparison Word Problems

We investigated the use of diagrams in multiplicative comparison word problems. The diagrams have been considered as one of the effective heuristic strategies or solving math problems. However, how students use during their school and the degree development that shows in their performance when applied to specific fields of knowledge is a task to be elucidated. We place our study in the school stage in which it makes the transition from arithmetic to algebra and arithmetic problems we focus on in the underlying multiplicative comparison scheme. In this paper, we analyzed the responses of high school students to the translation of multiplicative comparison word problems to representation graphs. We have used the responses of 12 -14 year old students （freshman year of secondary school） to represent multiplicative comparison word problems to identify and categorize the students responses, which allowed us identify categories for each type of representation and hypothesize priority order and subordination between the categories. Results show that students are not familiar with building diagrams that integrate existing relations in word problems. Most of the students do not use all the quantitative information contained in the word problem, therefore draw diagrams referring to the subject or context of the problem without relating to the data in it. We describe in detail the quantitative diagram types produced by these students. We have identified four kinds of quantitative diagrams that the students used to represent the multiplicative comparison problems with inconsistent statements, and these diagrams correspond to the four strategies for tackling the construction of the diagram.

Vortex-Source Method for the 3D Incompressible Irrotational Flow

The weighted residuals method was used for obtaining the boundary integral representation of the velocity of the three-dimensional inviscid irrotational flow. It is shown that velocity in an arbitrary point of domain can be expressed through its values on the boundary. Boundary integral equations of the second kind for solving boundary-valued problems of the first and second kinds are developed. The result has been also generalised to the case of solenoidal vector fields with potential vorticity. It is shown that the resulting integral equations are Fredholm integral equations of the second kind and allow effective numerical solving of corresponding boundary-valued problems. Examples of numerical solutions for a sphere and an ellipsoid are given for demonstration of efficiency of the offered method.

Algebraic solution of differential geometric guidance command and time delay control

According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.

Identifiability and Stability of an Inverse Problem Involving a Fredholm Equation

The authors study a linear inverse problem with a biological interpretation,which is modelled by a Fredholm integral equation of the first kind, where the kernel is represented by step functions. Based on different assumptions, identifiability, stability and reconstruction results are obtained.

A NOTE ON THE NESTEDNESS PROPERTY FOR ORDERED MEDIAN PROBLEMS IN TREE NETWORKS

The nestedness property has become an increasingly important means for devising efficient algorithms for network location problems.There have been attempts to explore the nestedness property of network location problems with some special cases of the convex ordered median objectives.However,there is little research on the nestedness property for those problems with the concave ordered median objectives.This paper constructs a tree network T and shows that the nestedness property cannot hold for the concave ordered median problem,which fills a gap in the research on the nestedness property.Finally,the authors pose an open problem on identifying the nestedness property for the continuous strategic ordered median problem.