Higher Variations of the Monty Hall Problem (3.0, 4.0) and Empirical Definition of the Phenomenon of Mathematics, in Boole’s Footsteps, as Something the Brain Does

In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.

R(D) Definition Domain Deriving of Limited Distortion Source Coding With Different Sources

For limited distortion source coding, it is generally considered that the minimum value of the coding average distortion is 0, and the maximum value is the minimum distortion value of making R(D) = 0. This is the definition domain of the information rate distortion function. In this paper, the upper and lower bounds of the information rate distortion function R(D) are derived and computed for the typical sources. The results show that the lower bound of the coding average distortion D is related to the symbol distortion function, which can further improve the theory of limited distortion source coding.

A Study on Defining of Metaphoric Competence: Problems and Strategies

With the deepening of studies on metaphoric competence, the problematic definition of metaphoric competence hasincreasingly been becoming a barrier in the development of metaphoric competence studies. It is discovered that therelevant studies on the definition of metaphoric competence have ignored the essential differences betweenmetaphoric thinking way and metaphoric competence. For the solution of the problem, the corresponding measuresare proposed and the metaphoric competence is redefined as the ability that the cognitive subjects with metaphoricthinking way apply their theoretical knowledge on this thinking model into the better identification, understanding,and production of metaphor.

SEMI-DEFINITE RELAXATION ALGORITHM OF MULTIPLE KNAPSACK PROBLEM

The multiple knapsack problem denoted by MKP (B,S,m,n) can be defined as fol- lows.A set B of n items and a set Sof m knapsacks are given such thateach item j has a profit pjand weightwj,and each knapsack i has a capacity Ci.The goal is to find a subset of items of maximum profit such that they have a feasible packing in the knapsacks.MKP(B,S,m,n) is strongly NP- Complete and no polynomial- time approximation algorithm can have an approxima- tion ratio better than0 .5 .In the last ten years,semi- definite programming has been empolyed to solve some combinatorial problems successfully.This paper firstly presents a semi- definite re- laxation algorithm (MKPS) for MKP (B,S,m,n) .It is proved that MKPS have a approxima- tion ratio better than 0 .5 for a subclass of MKP (B,S,m,n) with n≤ 1 0 0 ,m≤ 5 and maxnj=1{ wj} minmi=1{ Ci} ≤ 2 3 .

Left-definite boundary conditions of Sturm-Liouville problems when the interval shrinks to a point

On the condition that the interval of the problem shrinks to a point, we investigated the separated boundary conditions Sα,β of left-definite Sturm-Liouville problem, and answered the following question： Is there a co ∈ J such that Sα,β is always left-definite or semi-left-definite for the Sturm-Liouville equation for each c ∈ （a, co）？

Modulus-Based Matrix Splitting Iteration Methods for a Class of Stochastic Linear Complementarity Problem

For the expected value formulation of stochastic linear complementarity problem, we establish modulus-based matrix splitting iteration methods. The convergence of the new methods is discussed when the coefficient matrix is a positive definite matrix or a positive semi-definite matrix, respectively. The advantages of the new methods are that they can solve the large scale stochastic linear complementarity problem, and spend less computational time. Numerical results show that the new methods are efficient and suitable for solving the large scale problems.

Applying the disciplinary relation matrix to multidisciplinary design optimization modeling and solving

A new efficient coupling relationship description method has been developed to provide an automated and visualized way to multidisciplinary design optimization (MDO) modeling and solving. The disciplinary relation matrix (DRM) is proposed to describe the coupling relationship according to disciplinary input/output variables, and the MDO definition has been reformulated to adopt the new interfaces. Based on these, a universal MDO solving procedure is proposed to establish an automated and efficient way for MDO modeling and solving. Through a simple and convenient initial configuration, MDO problems can be solved using any of available MDO architectures with no further effort. Several examples are used to verify the proposed MDO modeling and solving process. Result shows that the DRM method has the ability to simplify and automate the MDO procedure, and the related MDO framework can evaluate the MDO problem automatically and efficiently.

Simplified Iterative Tikhonov Regularization and Posteriori Parameter Choice Rules

In this paper, a simplified iterative regnlarization method was used to solve the operator equations of the first kind involving semi-positive definite operators, the convergence rates of regularized solutions were obtained and a posteriori parametr choice strategy was given.

“复变函数与数理方程”课程思政教学探索

课程思政是全面提升人才培养质量、落实立德树人根本任务的重要途径。对电子类专业的专业课程“复变函数与数理方程”的思想政治教学进行了探索,并选取课程中的复变函数的积分、傅里叶变换、定解问题等主要教学内容,通过对教学内容的剖析,挖掘知识点中所蕴含的科学元素和思政元素,将思想政治教育融入知识传授中。在激发学生学习兴趣、培养其学习主动性的同时,帮助学生树立正确的世界观、人生观、价值观,以达到教书育人的目的。

基于五维模型的雷达装备质量问题分类方法研究

雷达装备是现代武器系统的重要组成部分且应用广泛,当前对雷达装备的质量和可靠性要求越来越高。雷达装备具有组成功能复杂、服役环境严苛、多品类、小批量、研制生产交叉等特点,使得质量问题表现形式多样化且存在区别和交叉,给雷达装备质量问题的准确分类带来极大挑战。为此,本文以雷达装备为研究对象,研究了雷达装备质量问题的定义和分类,并提出一种基于五维模型的雷达装备质量问题分类判定方法,为实现质量问题分级分类处理模式转型升级、提高雷达装备质量问题处理成效、增强雷达装备使用可靠性及作战效能提供有益指导。

图形化PDDL语言编译系统的设计与应用

针对当前PDDL开发存在的编辑复杂和文本可读性差等问题,设计一个图形化PDDL在线编辑工具和相应的编译系统Graph Compiler。Graph Compiler结合领域专用编译技术和ChatGPT模型,实现从自然语言到图形化PDDL的自动化生成。系统支持编译不同版本的PDDL语言,提供相应版本的语法分析,将PDDL规划结果转换为ROS的话题消息,为机器人行动提供具体的动作指令。实验结果表明,Graph Compiler在多届IPC的多版本PDDL测试用例上,编译成功率达到100%;也可以应用在ROS项目中,通过具体的动作序列指导机器人行动。

ADOPT问题解决模式联合饮食护理对糖尿病患者并发症发生率的影响

目的探究在对糖尿病患者护理时开展ADOPT问题解决模式联合饮食护理对患者并发症以及血糖水平的影响。方法在2021年10月至2023年11月本院糖尿病患者中抽选60例,通过随机数字表法划分2个小组,将30例开展常规护理支持的患者归入对照组,将30例开展ADOPT问题解决模式联合饮食护理的患者归入观察组。针对两组并发症发生率、血糖水平以及生活质量、自我管理能力进行对比。结果针对患者血糖水平对比,护理后观察组空腹血糖、餐后2 h血糖水平以及糖化血红蛋白水平较对照组低(均P<0.05)。针对患者生活质量对比,护理后观察组世界卫生组织生存质量测定量表(WHOQOL-BREF)中生理、环境因子、社会关系以及心理评分均较对照组高(均P<0.05)。针对患者自我管理能力对比,护理后观察组自我护理能力量表(ESCA)中自我护理技能、健康知识水、自护责任评分相比对照组均增加(均P<0.05)。统计患者恢复期间糖尿病足、糖尿病肾病、糖尿病脑血管病变等并发症发生率,观察组较对照组低(P<0.05)。结论在对糖尿病患者护理时开展ADOPT问题解决模式联合饮食护理,有助于降低患者并发症发生率,改善患者血糖水平,提升患者生活质量以及自我管理能力。

CRITERION OF POSITIVE DEFINITENESS OF MATRICES AND SOLUTION OF INVERSE PROBLEM FOR SYSTEM OF LINEAR EQUATIONS

The class of symmetric definitely positive matrices is extremely important in the matrix theory. At present, positive definiteness of a symmetric matrix can be shown by determining the signs of its all ordered principal minors or the signs

基于PDDL的成像卫星任务规划建模

基于对成像卫星任务规划问题的特点的深入分析,提出一种基于状态-动作模型的任务规划建模的方法:采用PDDL语言对成像卫星的领域知识进行描述,解决动作的持续时间约束、复杂的资源约束和一类特殊的外部事件约束的表达问题,最终建立成像卫星任务规划模型。通过对该建模方法的模型描述能力分析,表明该建模方法较传统规划建模方法具有较好的描述能力,能满足描述成像卫星任务规划问题的要求。

线性互补问题与绝对值方程的转化

给出线性互补问题与绝对值方程解存在的条件及线性互补问题与绝对值方程间的转化:包括无条件的转化和有条件的转化,并给出了线性互补问题与绝对值方程的求解方法.

谐波情况下电网无功补偿器容量算法的研究

非线性电网中传统功率定义不再适用于无功补偿电容器的容量计算,为此分析了谐波条件下频域和时域功率定义,但频域功率定义存在不足,因此从时域功率定义的角度,推导了一种基于非线性电流正交分解的补偿电容器容量算法。该方法将电网非线性负载侧的电流正交分解,确定补偿系统所需的无功电流,利用无功电流与电容器容量的关系,获得能准确补偿系统无功功率的电容器电容值。Matlab仿真表明,该方法更能针对性地补偿系统无功功率,有效改善电网无功功率欠补偿的现状,提高系统的功率因数,从而保障电网供电质量。

空间故障树的径集域与割集域的定义与认识

为从系统工作环境的角度分析条件因素对系统可靠性的影响,找出适合系统运行的环境条件,基于已有空间故障树的定义,提出空间故障树的径集域与割集域的定义。从关注于基本事件的组合转移到关注于系统运行条件的组合,进而达到从工作环境角度定义系统的故障情况和可靠性。以某电气系统为例,考虑使用时间t和使用温度c等2个因素,构建单一基本事件和系统的径集域、割集域和域边界。结果表明:研究区域可划分为径集域、割集域和域边界。实施合理的更换方案后的系统径集域不断扩大,割集域不断减小,所以可根据径集域占整个区域的比例判断更换方案的优劣程度。

JBI循证卫生保健中心关于不同类型研究的质量评价工具——系统评价的方法学质量评价

澳大利亚JBI循证卫生保健中心作为全球最大的循证协作中心之一,一直致力于推动循证资源的整合、传播和应用。2016年11月,JBI推出了针对不同类型研究的质量评价工具,以帮助研究者科学评价研究的方法学质量。本文旨在对JBI关于系统评价的质量评价工具进行详细解读,该工具包括11个条目,从循证问题界定、检索策略、文献质量评价、资料提取及合成、发表偏倚等方面评价系统评价的方法学质量。

地理信息科学学科领域界定再思考

地理信息科学形成与发展已十多年,该文介绍、分析、论证了Goodchild关于地理信息科学是"信息科学有关地理信息的一个分支学科"定义的准确性;通过对地理信息科学的发展,信息科学的学科界定、认知问题、研究主题等国内外的一些研究工作与成果的重新思考、分析与研究,较为详细地讨论了地理信息科学的重要研究主题,界定了地理信息科学的学科领域,旨在为推动地理信息学科的发展做贡献。

3D瞬变电磁场的有限差分正演计算

文中研究的 3D地电介质时间域电磁场的有限差分计算方法 ,激发源为水平电偶极子 ,并且向地下供以交变电流。经分析研究和不同模型的试算表明 ,其结果稳定、可靠 ,精度较高 ,计算速度快。该计算结果为