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.

Dark Matter Cosmology and Astrophysics

Hypersphere World-Universe Model (WUM) envisions Matter carried from Universe into World from fourth spatial dimension by Dark Matter Particles (DMPs). Luminous Matter is byproduct of Dark Matter (DM) annihilation. WUM introduces Dark Epoch (spanning from Beginning of World for 0.4 billion years) when only DMPs existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in standard cosmological model is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning DM Supercluster’s Cores and annihilation of DMPs. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Mysterious Star KIC 8462852 with irregular dimmings;Coronal Heating problem in solar physics—temperature of Sun’s corona exceeding that of photosphere by millions of degrees;Cores of Sun and Earth rotating faster than their surfaces;Diversity of Gravitationally-Rounded Objects in Solar system and their Internal Heat;Lightning Initiation problem—electric fields observed inside thunderstorms are not sufficient to initiate sparks;Terrestrial Gamma-Ray Flashes—bursts of high energy X-rays and gamma rays emanating from Earth. Model makes predictions pertaining to Masses of DMPs, proposes New Types of their Interactions. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.

The Monty Hall Problem and beyond: Digital-Mathematical and Cognitive Analysis in Boole’s Algebra, Including an Extension and Generalization to Related Cases

The Monty Hall problem has received its fair share of attention in mathematics. Recently, an entire monograph has been devoted to its history. There has been a multiplicity of approaches to the problem. These approaches are not necessarily mutually exclusive. The design of the present paper is to add one more approach by analyzing the mathematical structure of the Monty Hall problem in digital terms. The structure of the problem is described as much as possible in the tradition and the spirit—and as much as possible by means of the algebraic conventions—of George Boole’s Investigation of the Laws of Thought (1854), the Magna Charta of the digital age, and of John Venn’s Symbolic Logic (second edition, 1894), which is squarely based on Boole’s Investigation and elucidates it in many ways. The focus is not only on the digital-mathematical structure itself but also on its relation to the presumed digital nature of cognition as expressed in rational thought and language. The digital approach is outlined in part 1. In part 2, the Monty Hall problem is analyzed digitally. To ensure the generality of the digital approach and demonstrate its reliability and productivity, the Monty Hall problem is extended and generalized in parts 3 and 4 to related cases in light of the axioms of probability theory. In the full mapping of the mathematical structure of the Monty Hall problem and any extensions thereof, a digital or non-quantitative skeleton is fleshed out by a quantitative component. The pertinent mathematical equations are developed and presented and illustrated by means of examples.

Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part II. A New Geometric Theory of Phyllotaxis (Bodnar’s Geometry)

This article refers to the “Mathematics of Harmony” by Alexey Stakhov in 2009, a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries–New Geometric Theory of Phyllotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci λ-Goniometry (λ > 0 is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scientific ideas-the “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—the “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.

Hyperbolic Fibonacci and Lucas Functions, “Golden” Fibonacci Goniometry, Bodnar’s Geometry, and Hilbert’s Fourth Problem—Part III. An Original Solution of Hilbert’s Fourth Problem

This article refers to the “Mathematics of Harmony” by Alexey Stakhov [1], a new interdisciplinary direction of modern science. The main goal of the article is to describe two modern scientific discoveries—New Geometric Theory of Phyl-lotaxis (Bodnar’s Geometry) and Hilbert’s Fourth Problem based on the Hyperbolic Fibonacci and Lucas Functions and “Golden” Fibonacci -Goniometry ( is a given positive real number). Although these discoveries refer to different areas of science (mathematics and theoretical botany), however they are based on one and the same scien-tific ideas—The “golden mean,” which had been introduced by Euclid in his Elements, and its generalization—The “metallic means,” which have been studied recently by Argentinian mathematician Vera Spinadel. The article is a confirmation of interdisciplinary character of the “Mathematics of Harmony”, which originates from Euclid’s Elements.

Pathway and Countermeasure of Farmers Livelihood Transformation in the Ecological Development Area of Northern Guangdong Province from the Perspective of Ecological Protection

[Objectives]To explore pathways and countermeasures for transforming farmers livelihoods in the way of reducing their dependence on land while promoting sustainable development and alleviating ecological degradation.[Methods]A combination of field research,literature review,and policy analysis was employed to identify key factors affecting farmers livelihoods and potential strategies for transformation.[Results]The study found that developing ecological agriculture and modern agriculture,promoting agricultural transformation and upgrading,cultivating alternative industries,strengthening ecological engineering construction,and establishing diversified ecological compensation methods and supporting policies are effective strategies for transforming farmers livelihoods.[Conclusions]Implementing these strategies can help alleviate the contradiction between ecological protection and farmers livelihood development,promoting coordinated development of both.This approach not only benefits farmers but also contributes to sustainable environmental management and biodiversity conservation.

Problem and Countermeasure Analysis of Popularization Mode for Rural Residential Demonstration Project

Popularization mode of government-dominated rural residential demonstration projects and its features were introduced.It was proposed that such a popularization mode still remained at the primary development stage and was still suffering from many problems such as guiding role of government not fully played,lack of assessment standards,unitary funding channels,ineffective popularization effects and unpractical management regulations.In view of these problems,popularization strategies for rural residential demonstration projects were given from the perspective of establishing authorized coordination and supervision agencies,improving incentive policies of demonstration projects and also regulation system for these projects,expanding funding channels,and building information platforms.The study was to provide practical references for the future development of rural residential demonstration projects.

Current Development Situation,Problem and Countermeasures on Tilapia Seed Industry in Fujian Province

As one of the four main production areas of China's tilapia farming,Fujian province plays a critical role in China's tilapia industry development."Quality seed makes the industry a half success",therefore,the study on seed industry has a very important significance for the development of tilapia industry.Based on the field survey,study and analysis,we found that there is abroad prospect of the seed industry development in Fujian province.However,in recent years,some problems has emerged during the development process,such as the serious germplasm degeneration,frequent disease occurrence,etc.,which to some extent has restricted its further development.Establishment of tilapia seed production base,financial support and quality and security system should be strengthened,so that the tilapia seed industry in Fujian province will get better development.

Work Effectiveness,Problems and Countermeasures of Third-Party Assessment Teams from Colleges and Universities for Targeted Poverty Alleviation

Conducting a third-party assessment on targeted poverty alleviation can effectively avoid the disadvantage that local government plays as both athlete(i.e.performer of poverty alleviation work)and referee(i.e.referee for poverty alleviation effect)in poverty alleviation to ensure the truth of poverty alleviation,and therefore,it is an important part of the work to win the battle against poverty.Since 2016,the thirdparty assessment teams from colleges and universities for targeted poverty alleviation have achieved good results and performance in the assessment on both the effectiveness of targeted poverty alleviation work and the exit of poor counties in China,and they have made due contributions to the cause of poverty alleviation.However,as a new thing,third-party assessment obviously has some problems,mainly including the following:subjective understanding on the long-term nature of rural poverty alleviation is insufficient,and there is a lack of long-term considerations and related mechanism for third-party assessment;affected by policies and institutions,most of the existing third-party assessment teams from colleges and universities have not regarded third-party assessment of targeted poverty alleviation as a cause,and they lack the motivation to actively study the assessment business;and the third-party assessment staff from colleges and universities for targeted poverty alleviation have low stability and high mobility,not conducive to the long-term construction of assessment teams.In order to establish long-term poverty alleviation and prevention mechanisms,these issues must be addressed squarely and relevant countermeasures need to be taken actively to effectively build a long-term mechanism for building third-party assessment teams from colleges and universities for targeted poverty alleviation.

Problems and Countermeasures in the Training of Master of Translation and Interpreting Talents in the Context of Technological Empowerment

This paper aims to explore the problems and countermeasures in the training of Master of Translation and Interpreting(MTI)talents in the context of technological empowerment.Through methods such as questionnaires and literature review,the study analyzes the problems in the training of MTI talents under technological empowerment and,by examining the feasibility and applicability of technologies,proposes countermeasures to these problems.The research finds that there are still problems in four areas:training concept,teaching content,research in the current training of MTI talents,and mutual empowerment of technology and education.Four countermeasures are suggested to address these problems,including utilizing technology to promote personalized training and optimize teaching content.This study provides valuable references for future educators to leverage technology in the training of MTI talents.

Numerical Exploration of Asymmetrical Impact Dynamics: Unveiling Nonlinearities in Collision Problems and Resilience of Reinforced Concrete Structures

This study provides a comprehensive analysis of collision and impact problems’ numerical solutions, focusing ongeometric, contact, and material nonlinearities, all essential in solving large deformation problems during a collision.The initial discussion revolves around the stress and strain of large deformation during a collision, followedby explanations of the fundamental finite element solution method for addressing such issues. The hourglassmode’s control methods, such as single-point reduced integration and contact-collision algorithms are detailedand implemented within the finite element framework. The paper further investigates the dynamic responseand failure modes of Reinforced Concrete (RC) members under asymmetrical impact using a 3D discrete modelin ABAQUS that treats steel bars and concrete connections as bond slips. The model’s validity was confirmedthrough comparisons with the node-sharing algorithm and system energy relations. Experimental parameterswere varied, including the rigid hammer’s mass and initial velocity, concrete strength, and longitudinal and stirrupreinforcement ratios. Findings indicated that increased hammer mass and velocity escalated RC member damage,while increased reinforcement ratios improved impact resistance. Contrarily, increased concrete strength did notsignificantly reduce lateral displacement when considering strain rate effects. The study also explores materialnonlinearity, examining different materials’ responses to collision-induced forces and stresses, demonstratedthrough an elastic rod impact case study. The paper proposes a damage criterion based on the residual axialload-bearing capacity for assessing damage under the asymmetrical impact, showing a correlation betweendamage degree hammer mass and initial velocity. The results, validated through comparison with theoreticaland analytical solutions, verify the ABAQUS program’s accuracy and reliability in analyzing impact problems,offering valuable insights into collision and impact problems’ nonlinearities and practical strategies for enhancingRC structures’ resilience under dynamic stress.

The Forward and Inverse Problem Based on Magneto-Acoustic Tomography with Current Injection

The Magneto-acoustic Tomography with Current Injection (MAT-CI) is a new biological electrical impedance imaging technique that combines Electrical Impedance Tomography (EIT) with Ultrasonic Imaging (UI), which possesses the non-invasive and high-contrast of the EIT and the high-resolution of the UI. The MAT-CI is expected to acquire high quality image and embraces a wide application. Its principle is to put the conductive sample in the Static Magnetic Field(SMF) and inject a time-varying current, during which the SMF and the current interact and generate the Lorentz Force that inspire ultrasonic signal received by the ultrasonic transducers positioned around the sample. And then according to related reconstruction algorithm and ultrasonic signal, electrical conductivity image is obtained. In this paper, a forward problem mathematical model of the MAT-CI has been set up to deduce the theoretical equation of the electromagnetic field and solve the sound source distribution by Green’s function. Secondly, a sound field restoration by Wiener filtering and reconstruction of current density by time-rotating method have deduced the Laplace’s equation that caters to the current density to further acquire the electrical conductivity distribution image of the sample through iteration method. In the end, double-loop coils experiments have been conducted to verify its feasibility.

The Problems and Countermeasures in the Teaching of Graphic Design Majors in Universities

As a cradle for cultivating and delivering graphic design professionals,the graphic design major in universities should keep up with the times,guided by the“Opinions on Deepening Undergraduate Education and Teaching Reform,and Comprehensively Improving the Quality of Talent Cultivation,”deepen teaching reform,and enhance the quality of talent cultivation.Based on this,this article analyzes the existing problems in the teaching of graphic design major and actively explores its teaching reform path,in order to promote the in-depth implementation of graphic design major teaching and even the entire graphic design teaching reform,comprehensively improve the quality of graphic design talent cultivation,and promote the great reform and development of higher education.

The Cost Functional and Its Gradient in Optimal Boundary Control Problem for Parabolic Systems

The problems of optimal control (OCPs) related to PDEs are a very active area of research. These problems deal with the processes of mechanical engineering, heat aeronautics, physics, hydro and gas dynamics, the physics of plasma and other real life problems. In this paper, we deal with a class of the constrained OCP for parabolic systems. It is converted to new unconstrained OCP by adding a penalty function to the cost functional. The existence solution of the considering system of parabolic optimal control problem (POCP) is introduced. In this way, the uniqueness theorem for the solving POCP is introduced. Therefore, a theorem for the sufficient differentiability conditions has been proved.

Problem and Countermeasure of Rural Domestic Sewage Treatment

With the development of rural economy, pollutions of rural sewage are in- creasingly serious. This paper introduces the characteristics of rural domestic sewage and the rural sewage treatment situation, and according to the problems of funds, management, process selection, policy and weak awareness of environmental protection in the rural domestic sewage treatment, puts forward relevant countermea- sures to ensure long-term operation of sewage treatment system, and achieve the purpose of improving rural water environment and protect the ecological environment in rural areas.

Consistency and Stability Issues in the Numerical Integration of the First and Second Order Initial Value Problem

In this note we consider some basic, yet unusual, issues pertaining to the accuracy and stability of numerical integration methods to follow the solution of first order and second order initial value problems (IVP). Included are remarks on multiple solutions, multi-step methods, effect of initial value perturbations, as well as slowing and advancing the computed motion in second order problems.

Exact Distributions of Waiting Time Problems of Mixed Frequencies and Runs in Markov Dependent Trials

We study waiting time problems for first-order Markov dependent trials via conditional probability generating functions. Our models involve α frequency cells and β run cells with prescribed quotas and an additional γ slack cells without quotas. For any given and , in our Model I we determine the waiting time until at least frequency cells and at least run cells reach their quotas. For any given τ ≤ α + β, in our Model II we determine the waiting time until τ cells reach their quotas. Computer algorithms are developed to calculate the distributions, expectations and standard deviations of the waiting time random variables of the two models. Numerical results demonstrate the efficiency of the algorithms.

World-Universe Model—Alternative to Big Bang Model

This manuscript provides a comparison of the Hypersphere World-Universe Model (WUM) with the prevailing Big Bang Model (BBM) of the Standard Cosmology. The performed analysis of BBM shows that the Four Pillars of the Standard Cosmology are model-dependent and not strong enough to support the model. The angular momentum problem is one of the most critical problems in BBM. Standard Cosmology cannot explain how Galaxies and Extra Solar systems obtained their substantial orbital and rotational angular momenta, and why the orbital momentum of Jupiter is considerably larger than the rotational momentum of the Sun. WUM is the only cosmological model in existence that is consistent with the Law of Conservation of Angular Momentum. To be consistent with this Fundamental Law, WUM discusses in detail the Beginning of the World. The Model introduces Dark Epoch (spanning from the Beginning of the World for 0.4 billion years) when only Dark Matter Particles (DMPs) existed, and Luminous Epoch (ever since for 13.8 billion years). Big Bang discussed in Standard Cosmology is, in our view, transition from Dark Epoch to Luminous Epoch due to Rotational Fission of Overspinning Dark Matter (DM) Supercluster’s Cores. WUM envisions Matter carried from the Universe into the World from the fourth spatial dimension by DMPs. Ordinary Matter is a byproduct of DM annihilation. WUM solves a number of physical problems in contemporary Cosmology and Astrophysics through DMPs and their interactions: Angular Momentum problem in birth and subsequent evolution of Galaxies and Extrasolar systems—how do they obtain it;Fermi Bubbles—two large structures in gamma-rays and X-rays above and below Galactic center;Diversity of Gravitationally-Rounded Objects in Solar system;some problems in Solar and Geophysics [1]. WUM reveals Inter-Connectivity of Primary Cosmological Parameters and calculates their values, which are in good agreement with the latest results of their measurements.

Optimal Shape Factor and Fictitious Radius in the MQ-RBF:Solving Ill-Posed Laplacian Problems

To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).

Einstein’s Gravitational Field Approach to Dark Matter and Dark Energy—Geometric Particle Decay into the Vacuum Energy Generating Higgs Boson and Heavy Quark Mass

During an interview at the Niels Bohr Institute David Bohm stated, “according to Einstein, particles should eventually emerge … as singularities, or very strong regions of stable pulses of (the gravitational) field” [1]. Starting from this premise, we show spacetime, indeed, manifests stable pulses (n-valued gravitons) that decay into the vacuum energy to generate all three boson masses (including Higgs), as well as heavy-quark mass;and all in precise agreement with the 2010 CODATA report on fundamental constants. Furthermore, our relativized quantum physics approach (RQP) answers to the mystery surrounding dark energy, dark matter, accelerated spacetime, and why ordinary matter dominates over antimatter.