您知道什么是人工智能吗? 介绍一个最简单的人工智能系统

在人工智能系统中广泛地应用了计算机功能,利用计算机处理符号,这些符号不是代表数学方程和数字而是直接代表某种事物,诸如方案、人员、过程等。把一些属性附于对象并预先确定好它们之间的关系,以便产生一个解决问题的合理方法。用定则和符号所代表的事实可繁可简。最简单的例子,如用符号代表各种泵、阀门以及其连接件,然后就可回答一些有关泵与阀的问题。     

三次PH曲线偶的C1 Hermite插值

对计算机图形中一类特殊的多项式曲线——Pythagorean hodograph(PH)曲线的C1Hermite插值问题进行研究.PH曲线具有诸如有精确的有理Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质.基于复分析方法,避免了实分析讨论中出现的复杂表示及繁琐计算,构造了满足给定C1 Hermite插值条件且以C1拼接连续的三次PH曲线偶.该曲线偶可灵活处理拐点,从而克服了一般三次PH曲线因恒凸而无法处理拐点的缺陷.相应的两条Bézier曲线表示及其控制顶点的计算简单方便.所得4条插值曲线中,通常有1条曲线具有很好的几何形状特征.结果可直接应用于各工业产品设计及加工领域中.     

三次PH曲线偶的C1 Hermite插值

对计算机图形中一类特殊的多项式曲线—— Pythagorean hodograph(PH )曲线的 C1 Herm ite插值问题进行研究 .PH曲线具有诸如有精确的有理 Offset、弧长函数可由多项式函数表示以及几何解释优美等一系列优良性质 .基于复分析方法 ,避免了实分析讨论中出现的复杂表示及繁琐计算 ,构造了满足给定 C1 Hermite插值条件且以C1拼接连续的三次 PH曲线偶 .该曲线偶可灵活处理拐点 ,从而克服了一般三次 PH曲线因恒凸而无法处理拐点的缺陷 .相应的两条 Bézier曲线表示及其控制顶点的计算简单方便 .所得 4条插值曲线中 ,通常有 1条曲线具有很好的几何形状特征 .结果可直接应用于各工业产品设计及加工领域中 .     

计算机代数与符号演算语言CASC

计算机代数与符号演算语言CASC是一种高级程序设计语言,它可用于编制推演数学公式的程序。它是我们设计并用PASCAL在IBM-PC/XT上实现的。CASC还是一个数学专家系统,可解四十多类数学问题。本文阐述了CASC语言、并研究了公式推演语言的特点。阐述了自由变量和受束变量、表达式的原形、原值和当前值等概念,并研究了它们在实现自动公式推演中所起的关键作用。CASC的运行方式有会话式和批量式两种。     

一种实时手写数学方程编辑器

该文所述的数学方程编辑器,用户可用笔和书写板输入手写的数学公式,系统通过实时字符、符号识别和图形语法分析软件产生与输入相对应的语法分析树,并由此转换成诸如Latex、数学的或LISP-like符号等输出形式,与基于特殊方程描述语言的编辑系统相比,该手写方程编辑器相对简单且使用方便。     

将缩短网址打回原形

之前PCD介绍过一些可以将冗长链接缩短为简短网址的网站,减缩网址链接可以方便记忆或是方便与朋友共享。不过,被缩短了的网址一般都与原网址大相径庭,虽然可以通过打开链接的方式将其显回原形,但如果这个缩短了的网址是个恶意网站地址,打开时后果可就不堪设想了。那么,有没有什么方法可以直接将这些缩短了的网址打回原形呢？答案是肯定的。     

网络搜索引擎技术与优化策略

搜索引擎是通过计算机联网,为用户提供查询所需信息的搜索工具,按其搜集信息的方式及不同服务方式可分为目录式搜索引擎、机器人搜索引擎、元搜索引擎三类.搜索引擎在为用户带来方便的同时,还存在着诸如技术受限、规则复杂、覆盖范围有限、准确度不高等局限性,因此应从网站的结构、内容、关键字、链接等方面进行搜索引擎技术优化.     

高维数据特征提取算法的研究及比较

1 引言近年来随着科技的发展,出现了越来越多的复杂数据,如多媒体数据、蛋白质数据等。直接对这些高维数据进行诸如聚类、最近邻搜索及可视化等操作,其代价十分昂贵,需要的运算量往往超出机器的容许范围。特征提取的目的旨在对这些数据进行降维,从而大大降低对它们进行各种操作的计算复杂度。     

感受张景中院士的信息化教学理念

计算机的发展影响了整个世界,更深刻地改变了数学世界.数学需要数学实验,计算机使当今数学实验变得更加现实,使数学模型思想发展到了前所未有的水平.在计算机的支持下,数学家可把头脑中的"数学实验"变成现实,对精深的数学概念、过程进行模拟;再难的计算、复杂的方程,只要给出算法就能得到解决;复杂多变的几何关系,利用多媒体动态的作图功能就可以得到表示.     

大学水平的“数学分析知识”的获取和分析研究

在过去的几十年里,数学软件系统变得越来越强大和复杂.各种数学系统的集成变得非常有意义.基于Web的分布式数学平台使得与数学相关的活动（称之为数学服务）都可以在Web上得以实现.所有这些都需要一个底层的、可共享的、面向内容的知识库作为支撑.本文介绍一个大学水平的、可共享的数学分析知识库的获取和分析方法.NKIMath采用基于本体、框架、逻辑和类型的形式表示,采用面向概念的知识获取方法,从一套大学本科数学分析课本（2本）中获取了所有主要概念和定理.本文还总结和分析了知识获取过程中出现的错误.     

A Jump Inversion Theorem for the Degree Spectra

In the present article, we continue the study of the propertiesof the spectra of structures as sets of degrees initiated in[11]. Here, we consider the relationships between the spectraand the jump spectra. Our first result is that every jump spectrumis also a spectrum. The main result sounds like a Jump inversiontheorem. Namely, we show that if a spectrum is contained inthe set of the jumps of the degrees in some spectrum then thereexists a spectrum such that and is equal to the set of thejumps of the degrees in .     

On the parameterized complexity of multiple-interval graph problems

Multiple-interval graphs are a natural generalization of interval graphs where each vertex may have more than one interval associated with it. Many applications of interval graphs also generalize to multiple-interval graphs, often allowing for more robustness in the modeling of the specific application. With this motivation in mind, a recent systematic study of optimization problems in multiple-interval graphs was initiated. In this sequel, we study multiple-interval graph problems from the perspective of parameterized complexity. The problems under consideration are k$k$-Independent Set, k$k$-Dominating Set, and k$k$-Clique, which are all known to be W[1]-hard for general graphs, and NP-complete for multiple-interval graphs. We prove that k$k$-Clique is in FPT, while k$k$-Independent Set and k$k$-Dominating Set are both W[1]-hard. We also prove that k$k$-Independent Dominating Set, a hybrid of the two above problems, is also W[1]-hard. Our hardness results hold even when each vertex is associated with at most two intervals, and all intervals have unit length. Furthermore, as an interesting byproduct of our hardness results, we develop a useful technique for showing W[1]-hardness via a reduction from the k$k$-Multicolored Clique problem, a variant of k$k$-Clique. We believe this technique has interest in its own right, as it should help in simplifying W[1]-hardness results which are notoriously hard to construct and technically tedious.     

Parameterized graph separation problems

We consider parameterized problems where some separation property has to be achieved by deleting as few vertices as possible. The following five problems are studied: delete k   vertices such that (a) each of the given ?$?$ terminals is separated from the others, (b) each of the given ?$?$ pairs of terminals is separated, (c) exactly ?$?$ vertices are cut away from the graph, (d) exactly ?$?$ connected vertices are cut away from the graph, (e) the graph is separated into at least ?$?$ components. We show that if both k   and ?$?$ are parameters, then (a), (b) and (d) are fixed-parameter tractable, while (c) and (e) are W[1]-hard.     

On Representing Sentential Connectives of Lesniewski's Elementary Protothetic

After a brief presentation of Leniewski's notation for 1- and2-place sentential connectives of protothetic, the article discussesa method of extending this method to n 3-place sentential connectives.Such a method has been hinted at by Luschei, but in fact, nogeneral effective method of defining such functors has beenclearly and explicitly given. The purpose of this article isto provide such a method.     

激光测量轮廓中的数学方法应用

针对激光测距仪测量火车轮对踏面形状中出现激光装置定位难和测量误差问题,采用最小二乘法解决激光装置定位问题,确定激光测距仪在坐标系中的坐标,以及采用正交多项式曲线拟合方法过滤掉测量数据中的发散点,得到准确的踏面形状曲线数据;应用结果表明,该数学方法是可靠的和有效的;同时说明计算机在工业控制和数控加工的应用中,合理使用数学方法的必要性和优点,并为相关问题处理提供借鉴。     

Gröbner bases with respect to several orderings and multivariable dimension polynomials

Let D=K[X]$D=K\left[X\right]$ be a ring of Ore polynomials over a field K$K$ and let a partition of the set of indeterminates into p$p$ disjoint subsets be fixed. Considering D$D$ as a filtered ring with the natural p$p$-dimensional filtration, we introduce a special type of reduction in a free D$D$-module and develop the corresponding Gröbner basis technique (in particular, we obtain a generalization of the Buchberger Algorithm). Using such a modification of the Gröbner basis method, we prove the existence of a Hilbert-type dimension polynomial in p$p$ variables associated with a finitely generated filtered D$D$-module, give a method of computation and describe invariants of such a polynomial. The results obtained are applied in differential algebra where the classical theorems on differential dimension polynomials are generalized to the case of differential structures with several basic sets of derivation operators.     

基于遗传算法的直接甲醇燃料电池的数学模型及优化设计

微型直接甲醇燃料电池由于具有系统结构简单、体积小、环境友好、燃料比能量高及便于携带与储存等优点,在便携式电源,如手机、笔记本电脑等上展示出良好的应用前景。研究DMFC的数学模型可以深入了解DMFC中物质的传递过程和电化学机理,为寻找DMFC性能的最优化工作条件提供理论依据。主要依据微型直接甲醇燃料电池中物质传递的基本原理及电化学动力学机理,建立微型直接甲醇燃料电池的一维数学模型,利用遗传算法对其进行优化设计。仿真结果显示当阳极甲醇浓度为2.32mol/L,阴极氧气浓度为0.06mol/L,电流密度为545.67mA/cm2,DMFC的功率密度达到最大值为71.5mW/cm2。     

Drawing slicing graphs with face areas

We consider orthogonal drawings of a plane graph G$G$ with specified face areas. For a natural number k$k$, a k$k$-gonal drawing of G$G$ is an orthogonal drawing such that the boundary of G$G$ is drawn as a rectangle and each inner face is drawn as a polygon with at most k$k$ corners whose area is equal to the specified value. In this paper, we show that every slicing graph G$G$ with a slicing tree T$T$ and a set of specified face areas admits a 10-gonal drawing D$D$ such that the boundary of each slicing subgraph that appears in T$T$ is also drawn as a polygon with at most 10 corners. Such a drawing D$D$ can be found in linear time.