Mathematical Terms Research Articles

Review of Problems with a Point

Many readers will be familiar with the Computational Complexity blog, started in 2003 by Lance Fortnow and, since 2007, co-blogged by Bill Gasarch. Professor Gasarch is also the first author of Problems with a Point, which is based on 24 of Gasarch's Computational Complexity blog posts, most of them significantly expanded or reworked with contributions from co-author Clyde Kruskal. The book presents us with 24 stories, problems, or theorems ?with a point." Indeed, most chapters have an opening subsection with the pleasingly succinct title ?Point," in which the point of the chapter is summarized, implicitly justifying the selection of the corresponding blog post for inclusion in the book. The Computational Complexity blog is known for the surprisingly wide ambit of its topics (officially ?fun stuff in math and computer science"). This breadth is reflected in the book, which features chapters on a variety of topics, including: the usage of mathematical terms in mainstream publications; what makes a good math competition problem?; what makes a math problem interesting?; what constitutes an elegant proof?; discussion of natural (?sane") reductions; and some healthy lessons about when and how to apply mathematical skepticism and intuition. The accessibility of the selection is admirable: most chapters can be appreciated by a strong high school mathematician, while a few require elementary knowledge of complexity or computability theory.

Analysis of mathematical critical thinking ability in student learning style

This article aims to analyze mathematical critical thinking skills on student learning styles. Mathematical critical thinking skills can be developed through the character of the learning styles possessed by each student in learning mathematics. Learning can be maximized by knowing the learning styles of students and continued with the learning process by means of one way communication but must go through a process of interaction that is two way communication. This research was carried out at SMP Negeri 3 Jekulo in the odd semester 2019/2020 school year using the comparative-associative explanative research method. From the research results obtained that: 1) There are differences in learning outcomes in terms of mathematics learning styles of students. 2) There are differences in mathematics learning outcomes in terms of students’ mathematical critical thinking skills. 3) student learning styles do not affect students’ mathematical critical thinking abilities From the results of these studies indicate that every student, both those who have auditory, visual, or kinesthetic learning styles have different mathematical critical thinking abilities.

El logro de los aprendizajes en matemáticas en PISA, ENLACE y PLANEA en adolescentes mexicanos. Un análisis retrospectivo

En el presente artículo se ofrece un análisis histórico del nivel de logro de aprendizaje en matemáticas en adolescentes mexicanos de 15 años que cursan último año de secundaria. El análisis se focaliza en los resultados de las pruebas PISA, ENLACE y PLANEA en el logro de la competencia matemática para ese nivel, dada la relevancia de ésta asignatura en el desarrollo de competencias útiles para generar tecnología, de cara a la 4ta Revolución Industrial. A nivel internacional, los resultados de la prueba PISA dan cuenta de la importante distancia que existe entre los adolescentes evaluados de los países punteros (sobre todo los asiáticos), en comparación con los adolescentes mexicanos. Es innegable el rotundo fracaso que enfrenta el sistema educativo nacional en cuanto al logro de los aprendizajes en matemáticas en tercer grado de secundaria, ya que los resultados se han mantenido en los niveles más bajos de la escala, por más de diez años tanto en PISA como en las pruebas nacionales (ENLACE y PLANEA), estas últimas además están alineadas al currículo, lo que refleja que no se están alcanzando los aprendizajes planeados. Estos resultados reflejan las grandes carencias que tendrán nuestros jóvenes en el futuro y los escasos conocimientos con los que los estamos equipando para trabajar en un contexto globalizado y para competir con los ciudadanos de las grandes potencias mundiales. Gobiernos que, por cierto, dedican un alto presupuesto de su Producto Interno Bruto a la educación, lo que a su vez se traduce en una inserción desventajosa al mundo del trabajo y en los espacios de participación social, así como en limitadas oportunidades para proseguir con su educación formal. El logro de los aprendizajes en matemáticas es la gran asignatura pendiente en la agenda de política educativa mexicana.

Random Branching of Polymer Chains with Schulz–Zimm Distribution. 1. Bivariate Distribution and Related Formulae

AbstractAnalytical solution for the bivariate distribution W(r,k) of the degree of polymerization r and the number of branch points k is obtained for the random branching of polymer chains that follow the Schulz–Zimm distribution, or in mathematical term, the gamma distribution. It is found that when the bivariate distribution is normalized to make the total area unity, the normalized distribution follows another gamma distribution. The bivariate distribution function enables one to determine various useful properties of the branched polymer system, including full weight fraction distribution W(r), the number‐ and weight‐average degree of polymerization having k branch points, the expected branching density ρ for a given degree of polymerization r or a given number of branch points k. The branching density at large r limit, ρr → ∞ is an important property to represent the branched polymer system, rather than the average branching density of the whole system, and the value of ρr → ∞ can be determined for the present random branched system. The effect of the distribution breadth of the primary chains can be investigated by using the formulae developed in this article.

Multiplicity of clines for systems of indefinite differential equations arising from a multilocus population genetics model

We investigate sufficient conditions for the presence of coexistence states for different genotypes in a diploid diallelic population with dominance distributed on a heterogeneous habitat, considering also the interaction between genes at multiple loci. In mathematical terms, this corresponds to the study of the Neumann boundary value problem p1′′+λ1w1(x,p2)f1(p1)=0,in Ω,p2′′+λ2w2(x,p1)f2(p2)=0,in Ω,p1′=p2′=0,on ∂Ω,where the coupling-weights wi are sign-changing in the first variable, and the nonlinearities fi:[0,1]→[0,+∞[ satisfy fi(0)=fi(1)=0, fi(s)>0 for all s∈]0,1[, and a superlinear growth condition at zero. Using a topological degree approach, we prove existence of 2N positive fully nontrivial solutions when the real positive parameters λ1 and λ2 are sufficiently large.

Profil Kemampuan Penalaran Kreatif Matematis Mahasiswa Calon Guru

This study aims to obtain an overview of the mathematical creative reasoning abilities of the prospective teacher. The ability of mathematical creative reasoning in this study is the ability of students to justify a statement on the grounds of the truth of a statement that is based on novelty, plausible, and mathematical foundation. This research approach is qualitative using Grounded Theory. The population in this study were all students participating in the Calculus class of the Study Program Mathematics Education at one of the universities in West Java. In a while, the sample of 55 students was selected by a cluster random sampling technique. The results showed that students' mathematical creative reasoning abilities were categorized into three levels of ability based on the quality of the four categories, namely the initial step, the flow of completion, the related concepts, and the mathematical term errors.

Why Physicalism Seems to Be (and Is) Incompatible with Intentionality

There is a long history of philosophical intuition that the human mind must be more than physical or mechanical. I argue that this intuition arises from the perfect “transparency” of physical and mechanical states, in the sense that such states have no obscure or occult elements, but are fully intelligible in (usually) mathematical terms. In the paper, I derive a contradiction from the claim that such a physical system has genuine intentionality, comparable with an intelligent human. The contradiction arises from the fact that, according to physicalism, the physical properties of a brain state determine the narrow propositional content of any conscious thought occurring in that state. This fact allows a physical property of brain states to be defined using Cantor’s diagonal construction, and then a contradiction results if a physical system is assumed to form thoughts involving that property.

Why is Cantor’s Absolute Inherently Inaccessible?

In this article, as implied by the title, I intend to argue for the unattainability of Cantor’s Absolute at least in terms of the proof-theoretical means of set-theory and of the theory of large cardinals. For this reason a significant part of the article is a critical review of the progress of set-theory and of mathematical foundations toward resolving problems which to the one or the other degree are associated with the concept of infinity especially the one beyond that of the natural intuition of natural numbers. Naturally the review includes the foundation and development of the theory of large cardinals, especially after Cohen’s revolutionary introduction of the forcing method, insofar as it paved the way toward a transcendence of the delimitative character of Godel’s constructible universe L and further toward ever stronger infinity assumptions. Given that Cantor in his theory of transfinite numbers defined the mathematical absolute in ontological rather than concrete mathematical terms, I proceed in the last section to a philosophical discussion with certain prompts from phenomenology regarding the transposability of the formal conception of the infinite to the level of subjective constitution and argue in these terms on the infeasibility of acceding to an ‘absolute’ infinite cardinality. Of course the argumentation is strongly based on a view of the set-theoretical universe V of von Neumann’s cumulative hierarchy as a formal representative of the essential traits one would seek from a model of Cantor’s Absolute. It is also based on the conclusions reached from the whole discussion within the context of formal-theoretical structures as such.

Mathematical languages shape our understanding of time in physics

Physics is formulated in terms of timeless classical mathematics. A formulation on the basis of intuitionist mathematics, built on time-evolving processes, would offer a perspective that is closer to our experience of physical reality.

On Some Possible Explanations for the Continuing Denial of the Existence of Keynes’s IS-LM Model in Section 4 of Chapter 21 of the General Theory: Propaganda (from Joan Robinson), Ignorance (of the Keynes-Harrod Correspondence in Volume 13 Of the CWJMK in Late 1935), Anchoring (on Keynes’s Mention of Robinson’s Name in the Preface to the General Theory), Groupthink, and Cognitive

On Some Possible Explanations for the Continuing Denial of the Existence of Keynes’s IS-LM Model in Section 4 of Chapter 21 of the General Theory: Propaganda (from Joan Robinson), Ignorance (of the Keynes-Harrod Correspondence in Volume 13 Of the CWJMK in Late 1935), Anchoring (on Keynes’s Mention of Robinson’s Name in the Preface to the General Theory), Groupthink, and Cognitive

Big Data Investigation into the Causes and Treatment of Caries in Kindergarteners

It has been thousands of years that tooth decay is a health problem among human beings (the Chu, 2000). The disease is like our common daily influenza. The aim of this paper is to use the heated topic big data analysis and its related statistical mathematics to predict the possible behavior behind kindergarten children tooth-care response — a predictive medicine for the prevention. Moreover, the paper also develops a thought experiment from the Bayes’ Decision tree. The aim is to determine some suitable strategies in the case of kindergarten tooth-caries — for regenerative medicine. During the research process, I have found that the Butterfly Effect can be a kind of predictive philosophy. Then I rationale the philosophy with Bayes Theory and map each outcome with the corresponding Domino effects (Heinrich Theorem). While in the middle part between these two well-known theorems, I insert random variables respectively as the connection. This event forms a completely new theory which can catch the chaos and dominos of the Butterfly Effects (philosophy) or the so-called Lorenz system. I propose the name should be the (HKLam’s) Net-Seizing Theory. When my theory is expressed in terms of mathematics (linear algebra) and statistics (random matrix and linear regression), one may use it in the prediction of human behavior etc. Furthermore, with the help of decision-making theory such as the Savage one, one can apply the machine learning technique to generate the necessary policy for handling the social problem which is just like the child’s tooth care shown in this research paper.

НЕКОТОРЫЕ АСПЕКТЫ ОЦЕНИВАНИЯ КОГНИТИВНОЙ СЛОЖНОСТИ МАТЕМАТИЧЕСКИХ ПОНЯТИЙ

The article is devoted to the development of a method for assessing the cognitive complexity of mathematical concepts by summing the complexities of the terms included in their definitions. A measure of the concept complexity is the number of words that need to be pronounced to define a concept using terms included in a fifth-grader’s thesaurus. The amount of information contained in an ordinary word is taken as a conventional unit of information. Difficulty equations were compiled for the evaluated concepts. As a result of the analysis of definitions, the complexity of mathematical concepts was estimated and it was found that it varies from 1–3 (add, multiply) to 100–200 (gradient, divergence, rotor). The resulting comparison base can be used to assess the complexity of other mathematical terms.

The Effects of Training that Aims to Promote the Use of Mathematics Textbooks for Deepening Understanding on Mathematics Terms

The Effects of Training that Aims to Promote the Use of Mathematics Textbooks for Deepening Understanding on Mathematics Terms

Profit Maximization in a Product Mix Bakery Using Linear Programming Technique

Linear Programming is one of the optimization techniques in finding solutions to managerial decisions making. Linear Programming is a widely used mathematical modelling technique designed to help managers in planning and decisions making relative to resource allocation. This study applied linear programming technique to decision making problem in university of Benin Bakery, Benin city, Edo state, Nigeria, and intended to determine the quantity of Bread that the firm should produce in a day to maximize profit, subject to constraints in the production process. Data on quantity of major raw material used in production of large, medium and small size bread per day were collected from the extract of the financial record of the bakery. The problem was formulated in mathematical term and solved using computer software known as Linear Programming Solver (LIPS). The solution obtained from a single iteration showed that 667 units of extra- large bread should be produced daily for the firm to achieve a maximum daily profit of #100,000. It is therefore recommended that the firm should concentrate more on production of extra- large bread to obtain maximum profit of #100,000 per day.

Modelling of transient behaviour of roughness reduction in ball end magnetorheological finishing process

Ball end magnetorheological finishing (BEMRF) process provides nano level of surface finish for materials which are magnetic as well as non-magnetic in nature. The available literature on this process has been vastly limited to establishing its finishing capabilities on materials of different nature. This research work deals with theoretical investigations into surface roughness reduction in BEMRF process, performance of machining parameters during long time periods and providing their representation in mathematical terms. Starting with the mechanism of abrasive wear in BEMRF process, this work advances to find out prolonged effect of abrasive rubbing on a ferromagnetic workpiece surface. The study finds out a phenomenon termed as transient roughness reduction in which the material removal by abrasive wear in BEMRF process is diminished with time and a particular combination of machining parameters and fluid composition reduce roughness only up to a critical value, beyond which no further reduction is achieved. A mathematical model is developed to depict this transient roughness reduction phenomenon, the model is then experimentally verified and the close proximity of the experimental results with the theoretical ones validates the model and the transient roughness reduction phenomenon in BEMRF process.

WSGF — Time for a change part 1: Damped Harmonic Oscillators and the Vibrator/Ground model

In land seismic exploration a vibrator is used to generate a controlled wave-train of seismic energy into the earth by the forced oscillations of the ground surface over several seconds in what is known as a vibroseis sweep. Usually, these oscillations are sinusoidal in character and are generated by a hydraulic force acting on two masses, a baseplate (BP) that is in firm contact with the ground and a reaction mass (RM) positioned above the baseplate via a hydraulic actuator connecting both masses. The oscillations generated by the vibrator mechanism propagate away from the vibrator location through the subsurface in the form of seismic waves and are reflected/refracted back to the surface and recorded electronically by multiple sensors laid out on the surface or in a borehole. The energy received at each sensor is the result of the seismic signal generated by the vibrator (its signature) modified by the earth’s geology and the travel paths taken by the propagating wave. In mathematical terms, the signal received at the sensor is the seismic signal convolved by the earth. Unlike impulsive seismic sources, such as dynamite, the raw vibroseis field records are generally uninterpretable because of the relatively low energy output of the source and the multiple overlapping seismic signals that are reflected and refracted during the transmission of the sweep. In addition, the vibroseis signal is contaminated with undesirable environmental and source-generated noise and must be ‘deconvolved’ with the sweep signal to produce an interpretable record that resembles the wavelet generated by an impulsive source. Obviously, the more accurate the deconvolution operator is in replicating the source signature, the greater the resolution obtained in the processing of the seismic data.

Статистический анализ и оценка клинического эффекта на основе фактора Байеса в оториноларингологии

The article discusses the use of Bayesian methods for statistical inference as an alternative to the traditional method of testing hypotheses based on the significance level. Illustrative examples of solving traditional statistical problems of hypothesis testing in otorhinolaryngology based on the calculation and interpretation of the Bayes factor are presented. As two tasks for illustration, we used the tasks of assessing the impact of sauna visits on indicators of nasal flow in patients with allergic rhinitis and the task of assessing the association of the season of the year and the frequency of birth of children with hearing impairment. Although in the form of an article it is impossible to fully describe and explain all the mathematical terms and their origin for understanding the logic of Bayesian methods, we tried to explain what they mean without reference to the mathematical manuals. As Bayesian methods are increasingly used in statistical applications, a basic understanding of how to calculate them should be part of the toolkit of every medical researcher, and how to interpret it, of every practitioner who is interested in modern results of clinical trials. All calculations used in the article are accompanied by an R-code, so they can easily be reproduced, the text of the article can be used as step-by-step instructions for their implementation.

Surrogate Leadership Model for Digital Organizational Systems

The increase of investigations regarding digital systems for the social structure mapping leads to dynamizing previously rigidly recorded processes or deliberately ignored ones. Such processes include, among others, matters with a social context, which have been difficult to describe in mathematical terms. This investigation is an integral part of explanatory research on the digital representation of an organization. The main purpose of the study is to investigate the literary sources and approaches to find the determinants of a general surrogate model, to identify the required parameters and their mathematical contents as well, as to design a surrogate model construct capable of application to different digital organizational systems, independent of the dominant behavioral and decision-making pattern of the lead unit. The relevance of this scientific problem decision is that recently, an increasingly vast number of research investigations on the digitization of anthropological systems is being done. The modeling of the leadership surrogate model is a part of our research on the digitization of organizational systems. Investigation of the topic is carried out in the following logical sequence: analysis of scientific publications on the researched subject and model creation. This part consists of successive steps: abstraction of a real system of management units and the delimitation of the indicated topics, definition of constraints for further simplification of the surrogate model, model construction, establishment of model-describing formalism, and obtaining the exact surrogate model based on the dataset. Since our surrogate model has a general character, the last step was described only indicatively. Nevertheless, we consider this to be a tremendous potential extension for the following investigations on different scenarios. The research results can be useful for other scientists searching for research on the mathematical representations of the leadership model, the surrogate model for the leadership unit, and practitioners who intend to implement the leadership model in the digital organization system. The additional parameters can complement the created surrogate model; respectively the considered parameters can be calculated or measured by other methods. Keywords: Digital Organizational Systems, Leadership Model, Surrogate Model, Mathematical Model.

Modelling of transient behaviour of roughness reduction in ball end magnetorheological finishing process

Ball end magnetorheological finishing (BEMRF) process provides nano level of surface finish for materials which are magnetic as well as non-magnetic in nature. The available literature on this process has been vastly limited to establishing its finishing capabilities on materials of different nature. This research work deals with theoretical investigations into surface roughness reduction in BEMRF process, performance of machining parameters during long time periods and providing their representation in mathematical terms. Starting with the mechanism of abrasive wear in BEMRF process, this work advances to find out prolonged effect of abrasive rubbing on a ferromagnetic workpiece surface. The study finds out a phenomenon termed as transient roughness reduction in which the material removal by abrasive wear in BEMRF process is diminished with time and a particular combination of machining parameters and fluid composition reduce roughness only up to a critical value, beyond which no further reduction is achieved. A mathematical model is developed to depict this transient roughness reduction phenomenon, the model is then experimentally verified and the close proximity of the experimental results with the theoretical ones validates the model and the transient roughness reduction phenomenon in BEMRF process.

Approximate factorization of positive matrices by using methods of tropical optimization

The problem of rank-one factorization of positive matrices with missing (unspecified) entries is considered where a matrix is approximated by a product of column and row vectors that are subject to box constraints. The problem is reduced to the constrained approximation of the matrix, using the Chebyshev metric in logarithmic scale, by a matrix of unit rank. Furthermore, the approximation problem is formulated in terms of tropical mathematics that deals with the theory and applications of algebraic systems with idempotent addition. By using methods of tropical optimization, direct analytical solutions to the problem are derived for the case of an arbitrary positive matrix and for the case when the matrix does not contain columns (rows) with all entries missing. The results obtained allow one to find the vectors of the factor decomposition by using expressions in a parametric form which is ready for further analysis and immediate calculation. In conclusion, an example of approximate rank-one factorization of a matrix with missing entries is provided.