Proposition Research Articles

АНИМАЦИОННЫЕ РИСУНКИ КАК СРЕДСТВО ЦИФРОВЫХ ТЕХНОЛОГИЙ ОБУЧЕНИЯ МАТЕМАТИКЕ

Statement of the problem. Universal digitalization of economy and public relations is a reality of today, and a school teacher is faced with the task of forming a personality ready to reveal his/her creative potential in the digital economy. The problem is to outline the ways of digitalization of teaching mathematics that meets the needs of society, and contribute to the understanding and assimilation of mathematical knowledge based on digital educational resources using the animation capabilities of computer environments. The purpose of the article is to present animated images in the GeoGebra environment as new means of digital technologies for teaching mathematics. Research methodology. Analysis of scientific, educational and methodological literature, synthesis of the authors’ work experience at school and university in approbation of elements of the mathematics teaching system using animated images. Research results. Specific types of animated images are presented and the expediency of their use as effective means of digital technologies for teaching mathematics in the lessons of arithmetic, algebra, trigonometry and the beginnings of mathematical analysis is substantiated. Conclusion. The use of new technology with the use of animated images in mathematics lessons at school increases the level of understanding and assimilation of mathematical knowledge by providing clarity of mathematical concepts and statements. In addition, animated images are used to eliminate computational difficulties, to generate tasks of the same type, and to organize self-testing of students’ knowledge. The creation of digital educational content using the animation capabilities of computer environments increases the technological equipment of a modern mathematics teacher, which will allow him/her to achieve better educational results.

Comparing Student Proofs to Explore a Structural Property in Abstract Algebra

ABSTRACT Connecting and comparing across student strategies has been shown to be productive for students in elementary and secondary classrooms. We have recently been working on a project converting such practices from the K–12 level to the undergraduate classroom. In this paper, we share a particular instantiation of this practice in an abstract algebra setting. Students compare across two common proof approaches to showing that the Abelian property is preserved by isomorphism. We share a complete sample lesson where students make sense of the theorem and the two proof approaches, then leverage the differences between them in order to modify both proofs and mathematical statements. We conclude with the students' reflections on the activities, and share our learnings from adapting best practices from K–12 to this new setting.

Analysis of non-Newtonian fluid flow over fine rotating thin needle for variable viscosity and activation energy

The main motive of this work is to study the effects of nonlinear radiation and mixed convection for the Casson nanofluid through the thin needle. Mass transfer is further characterized by activation energy. Temperature-dependent viscosity and a variable magnetic field are assumed for the current problem. The consequences of the physical framework on the velocity, temperature and species including the impact of radiative heat flux are discussed. The partial differential equations of the physical model are achieved using the concept of boundary layer approximation and are remolded into the ordinary differential mathematical statement which is coupled nonlinear, by substituting specific similarity transformations. By making the use of built-in MATLAB bvp4c function, the results are calculated and arranged in the manner of graphs and tables. The effects of different physical parameters of our interest such as the Casson fluid parameter, Brownian motion, Prandtl number, buoyancy ratio parameter, thermal radiation, thermophoresis parameter, Schmidt number and relaxation time are examined for the velocity, concentration and temperature profiles.

A Review of IPO Underpricing: Evidences from Developed, Developing and Emerging Markets

The empirical evidence of high initial return from Initial Public Offerings (IPO) phenomena known as underpricing. From last three decades, it is an ongoing issue of every financial market throughout the world. We review underpricing research in developed, developing and emerging markets. In this regard, a thorough review of existing literature has been done. In result, higher underpricing of IPOs is found in emerging markets than developing and developed market because in emerging market issuer of IPOs takes underpricing as a signal of their quality IPOs, where information asymmetry is a significant element. Furthermore, based on the review, we managed to pinpoint significant factors that influenced the initial return. However, scale of underpricing among different countries varies depending on the factors, discussed in detail. Various theories and proposition have developed in these three markets to elucidate the phenomena of underpricing. We believe that there exist few factors that could be used as the primary determinants of IPO underpricing in future. These factors are country specific environment, micro and macro-economic factors, quality of legal framework based on listing regulations, and socio-political factors and marketing of IPO, which could provide a promising area of research.

Why Aboutness Matters: Meta-Fictionalism as a Case Study

Recent work in the philosophy of language attempts to elucidate the elusive notion of aboutness (Berto 2018; Lewis 1988; Fine 2017a, b; Hawke 2017; Moltmann 2018; Yablo 2014). A natural question concerning such a project has to do with its motivation: why is the notion of aboutness important? Stephen Yablo (2014) offers an interesting answer: taking into consideration not only the conditions under which a sentence is true, but also what a sentence is about opens the door to a new style of criticism of certain philosophical analyses. We might criticize the analysis of a given notion not because it fails to assign the right truth conditions to a class of sentences, but because it characterizes those sentences as being about something they are not about. In this paper, I apply Yablo’s suggestion to a case study. I consider meta-fictionalism, the view that the content of a mathematical claim S is ‘according to standard mathematics, S’. I argue, following Woodward (2013), that, on certain assumptions, meta-fictionalism assigns the right truth-conditions to typical assertoric utterances of mathematical statements. However, I also argue that meta-fictionalism assigns the wrong aboutness conditions to typical assertoric utterances of mathematical statements.

TCT CONNECT-453 Risk of Coronary Obstruction and Feasibility of Coronary Access After Repeat Transcatheter Aortic Valve Replacement With Self-Expanding Prostheses

The supra-annular leaflet position and tall stent frame of the self-expanding Evolut PRO or Evolut PRO+ THV transcatheter heart valves (THVs) may cause coronary occlusion during transcatheter aortic valve replacement (TAVR)-in-TAVR and present challenges for future coronary access. We sought to

Maths in the time of social media: conceptualizing the Internet phenomenon of mathematical memes

ABSTRACT Mathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an empirical base, elucidating its educational potential. To pursue this goal, a two-year ethnographic research study has been conducted in a selection of social media communities that exchange mathematical memes. In the paper, a twofold theoretical lens is used to investigate the phenomenon from a memetic perspective focused on the general characteristics of Internet memes, and from a cultural perspective considering the Web 2.0 environment. Analysis tools derived from the memetic and cultural theoretical background are applied to an instrumental case study, to reconstruct how mathematical memes activate the interaction among members of an online community. The investigation elicits key characteristics of the phenomenon, provides grounds to conceptualize mathematical memes as hybrid representations of mathematical statements, and sheds light on the traits of the epistemic culture they establish in the community.

Formation of basic skills of students when learning to search for proof of mathematical statements

Formation of basic skills of students when learning to search for proof of mathematical statements

Proposition of Issues in Curriculum Studies Concerning Spread of Competency-Based Educational Reforms in African Countries

Due to the rapid progress of globalization in recent years, the knowledge-based society is progressing not only in developed countries but also throughout the world, and the wave is spreading to African countries. Kusaka (2020) gave specific examples of competency-based educational reforms in African countries and analysed facing issues. In this article, we discuss the challenges in developing and implementing competency-based curricula in African countries and propose the role of future curriculum research to address these issues. Keywords: Mathematics curriculum, competency-based, curriculum reform, Curriculum research, Comparative studies, African countries

Modeling of a Catalytic Cracking in the Gasoline Production Installation with a Fuzzy Environment

The article offers a systematic approach to the method of developing mathematical models of a chemical-technological system (CTS) in conditions of deficit and fuzziness of initial information using available data of various types. Based on the results of research and processing of the collected quantitative and qualitative information, mathematical models of the reactor are constructed. Formalized and obtained mathematical statements of the control problem for choosing effective modes of operation of technological systems are based on mathematical modeling. Based on the obtained expert information, linguistic variables were described and a database of rules describing the operation of the input parameters of the reactor unit of the catalytic cracking unit was obtained.

A graduação na área da saúde em tempos de pandemia da COVID-19: o ensino da disciplina de Prática de Promoção da Saúde e Prevenção de doenças

Objetivo: apresentar as estratégias adotadas na graduação da área da saúde de uma instituição privada do Município do Rio de Janeiro para o ensino da disciplina de Prática de Promoção da Saúde e Prevenção de doenças no contexto da pandemia por COVID-19. Metodologia: Trata-se de um relato de experiência sobre o ensino remoto na graduação da saúde de uma instituição privada do Município do Rio de Janeiro que foi delineado por dois docentes e envolveu a disciplina de práticas de promoção da saúde e prevenção de doenças, componente da estrutura curricular dos cursos da área da saúde, com exceção do curso de medicina. Resultados: Foram abordadas em sequência a estrutura da disciplina e sua relevância para a formação dos discentes, a metodologia proposta para o ensino durante a pandemia da COVID-19 e as estratégias adotadas pelos docentes para orientar o processo de ensino-aprendizagem e para avaliar o desempenho dos discentes. Conclusão: A disposição dos docentes em inovar para tornar o ensino da graduação da saúde mais fluído em tempos de pandemia da COVID-19 mostrou-se necessária. Para além de partilha entre os docentes no que tange a elaboração de material didático e diálogos propositivos que envolveram a disciplina, observou-se esforço significativo voltado para a construção de estratégias múltiplas de aprendizagem com a finalidade de gerar nos discentes maior interesse, envolvimento e participação.

Self-equilibration theorem in quantum-point contacts of interacting electrons: Time-dependent quantum fluctuations of tunnel transport beyond the Levitov–Lesovik scattering approach

Equilibration to the steady state for a wide class of Luttinger liquid ballistic weakly linked tunnel contacts is extensively studied. Quantum fluctuations of tunnel current are considered in all orders in tunnel coupling and out of the equilibrium in the time domain. Especially, two important mathematical statements: Self-equilibration (SE-)theorem and Self-equilibration (SE-)lemma on the exact re-exponentiation of thermal average from the Keldysh-contour-ordered evolution operator for arbitrary weakly linked Luttinger liquid tunnel contact are proven. Demonstrated proof of SE-theorem and SE-lemma represents first evidence of a novel emergent phenomenon of ”self-equilibration” in the dynamics of quantum fluctuations of electron transport through ballistic tunnel junctions. This phenomenon and all related real-time full counting statistics are shown to be much more general as compared to the usual Levitov–Lesovik scattering approach for the non-interacting electrons, though SE-theorem also contains known results obtained within the Levitov–Lesovik scattering approach as corresponding limiting case for lowest order cumulants at g=1. As the result, corresponding differential equation of ”self-equilibration” for time-dependent Keldysh partition function of tunnel contact is derived and explained. It is shown that proven SE-theorem can be considered also as the dynamical version of well-known Jarzynski equality for the tunnel electron transport out of the equilibrium. As the result, for arbitrary weakly linked tunnel junction model of interest the exact time-dependent cumulant generating functional is derived being valid at arbitrary electron–electron repulsion in the Luttinger liquid leads of the junction, arbitrary temperature and arbitrary bias voltage. Respective general formula in its long-time asymptote turns into a non-perturbative Luttinger liquid generalization of the Levitov–Lesovik type of detailed balance formula for cumulant generating function. As the consequence of obtained results, a universal character of self-equilibration of tunnel current in one-dimensional weakly linked tunnel junctions is revealed and studied on the level of non-equilibrium Fano factor. As well, a new measure of disequilibrium in such systems – the ”steady flow” rate – is also introduced and discussed.

Elaboração de uma sequência didática no ensino de Química estruturada em uma metodologia ativa com tema gerador: o café

O uso das Metodologias Ativas no ensino é caracterizado por inserir o aluno como centro do processo de aprendizagem, dando autonomia para que ele consiga solucionar problemas a partir das discussões, interações e atividades que exigem que ele se torne agente ativo nesse processo, buscando estratégias, como as tecnologias digitais, para solução de problemas. Nesse contexto, o objetivo deste trabalho foi elaborar por meio de uma metodologia ativa, uma sequência didática composta por atividades planejadas para lecionar alguns conteúdos no ensino de química básica por meio de um tema gerador, o café. As propostas didáticas foram estruturadas em: *Principiar a História do Café no ensino com a promulgação da Lei 10.639 de 2003; *Inserir temas para a contextualização do Ensino de Química com outras disciplinas, como por exemplo: Geografia, Biologia, História e Matemática; *Despertar nos alunos o interesse do tema gerador como produto para pesquisas em artigos; *Estudar sobre a composição química do café e *Análise Sensorial de diferentes tipos de café. Nessa analogia, de modo a contribuir conceitos para o ensino, compreende-se que as referências históricas e tecnológicas permitem identificar grandes possibilidades de contextualização que podem ser construídas por meio de conceitos e metodologias ativas aplicadas no tema gerador escolhido. Ou seja, este texto busca desenvolver um estímulo em torno dos conceitos e proposições sobre sequência didática, que consiste em propostas metodológicas para a organização e planejamento do ensino, com diferentes aspectos e ênfases.

Students’ Achievement Levels, Gender, and Learning Styles on Abstract Algebra: A Profile of Evidence Developing Ability

Mathematics education students’ ability on developing evidence needs to be reviewed by lecturers. 50% of the subjects in the mathematics education departement require students' accuracy in analyzing mathematical statements. This is increasingly important because the Indonesian National Qualifications Framework (KKNI) for the Bachelor level requires graduates to become technicians / analysts. The diversity of levels of students’ ability, gender, and learning styles are assumsed to be the discrepancy abilities to develop evidence. This study aims to describe the evidence developing ability based on the levels of achievement, gender, and student learning styles. The subjects of this study were abstact algebra students in the mathematics education department. Type of this research was descriptive qualitative with data collection techniques using test and non-test techniques. Students were given five questions about abstact algebra that demanded the evidence developing ability. The achivement levels and gender were obtained from students’ academic achievement data. The learning styles were attained from questionnaires. The results of the study is higher the students’ academic achievement, better the evidence developing ability on Abstract Algebra. The gender does not affect the evidence developing ability on Abstact Algebra. Students with visual learning styles have the ability to develop evidence better than students with other learning styles.

Proposição de um instrumento de mensuração do desenvolvimento de capacidades dinâmicas

Objetivo: este estudo objetiva construir e validar uma escala de mensuração dos elementos componentes e dos mecanismos organizacionais de desenvolvimento de capacidades dinâmicas (CD) em organizações.Método: a metodologia da pesquisa baseou-se na abordagem quantitativa e descritiva, com coleta de dados bibliográfica e por meio de e-survey em 137 organizações do Sul do Brasil. A validação da escala foi realizada pela modelagem de equações estruturais (MEE) com o software SmartPLS 3.2.8.Originalidade/Relevância: ainda que existam esforços no desenvolvimento de escalas sobre CD, há uma lacuna teórica quanto à criação de escalas e instrumentos de medição, uma vez que tais capacidades estão ligadas aos processos internos das organizações. Diante disso, este estudo se mostra relevante ao se direcionar à proposição e validação de uma escala baseada no desenvolvimento das CD que possibilite novas investigações empíricas e discussões teóricas.Resultados: a escala final proposta para mensuração dos elementos componentes e dos mecanismos organizacionais de desenvolvimento de CD apresentou três dimensões e vinte indicadores. Os achados demonstram que a articulação dos indicadores dos elementos componentes e dos mecanismos de desenvolvimento das capacidades dinâmicas resulta em uma escala que pondera vários aspectos relacionados à existência do desenvolvimento de CD em organizações.Contribuições teóricas/metodológicas: esta pesquisa proporciona um recurso acadêmico para a utilização da escala proposta em futuras pesquisas e amplia a possibilidade de desenvolvimento da temática das capacidades dinâmicas nos estudos organizacionais.

Hierarchical model form uncertainty quantification for turbulent combustion modeling

All models invoke assumptions that result in model errors. The objective of model form uncertainty quantification is to translate these assumptions into mathematical statements of uncertainty. If each assumption in a model can be isolated, then the uncertainties associated with each assumption can be independently assessed. In situations where a series of assumptions leads to a hierarchy of models with nested assumptions, physical principles from a higher-fidelity model can be used to directly estimate a physics-based uncertainty in a lower-fidelity model. Turbulent nonpremixed combustion models fall into a natural hierarchy from the full governing equations to Conditional Moment Closure to flamelet-like models to thermodynamic equilibrium, and, at each stage of the hierarchy, a single assumption can be isolated. In this work, estimates are developed for the uncertainties associated with each assumption in the hierarchy. The general method identifies a trigger parameter that can be obtained with information only from the lower-fidelity model that is used to estimate the error in the lower-fidelity model using only physical principles from the higher-fidelity model. Starting from the lowest fidelity model, the trigger parameters identified in this work are the product of a chemical time scale and the scalar dissipation rate for the equilibrium chemistry model, which characterizes the errors associated with neglecting finite-rate chemistry and transport; the reciprocal of the product of a generalized Lagrangian flow time and the scalar dissipation rate for the steady flamelet model, which characterizes the errors associated with neglecting flow history effects; and the relative magnitude of the conditional fluctuations for Conditional Moment Closure. The approach is applied in LES to a turbulent nonpremixed simple jet flame to quantify the errors associated with the equilibrium chemistry model and the steady flamelet model. The results indicate that errors associated with neglecting finite-rate chemistry and transport in the equilibrium chemistry model are dominant upstream while errors associated with neglecting flow history in the steady flamelet model become more important downstream.

Nonlinear subspace system identification based on output-only measurements

In this paper a new deterministic subspace approach is introduced for multi-dimensional nonlinear system identification based on output-only measurements. The strategy is to excite an arbitrary degree of freedom (DOF) and estimate linear and nonlinear parameters of other DOFs within continuous-time state space models. The nonlinearity is characterized in terms of the measured response and its derivatives in locations away from the excitation. Then, basis functions are assigned to predict the nonlinear restoring force and exploited instead of the input data in the identification process. It is demonstrated that projecting the output row space onto these functions, cancels the subspace corresponding to the nonlinear dynamics and the remaining space contains the dynamics of the underlying linear system as well as the contributions of unmeasured input and noise data to the system response. The recent concept and required assumptions are presented through a few mathematical statements and proofs. To ensure the validity of the proposed approach, several discrete and continuous systems with different structural nonlinearities are studied. The estimated parameters are compared with those obtained from traditional subspace identification algorithms and the direct parameter estimation method. The results highlight the robustness of the proposed approach in dealing with noise contaminated measurements.

Optimization of transmission capacity of energy water pipeline networks with a tree-shaped configuration and multiple sources

The problem of pipeline network transmission capacity optimization is solved during network design, optimization, and development. It consists in determining the optimal pipeline diameters, installation sites, and parameters of pumps and valves. This study proposes a methodology for optimizing the transmission capacity of tree-shaped water pipeline networks of energy systems that serve various purposes and have multiple sources. A method for constructing a network model that ensures the versatility of its representation regardless of the purpose of the network and the composition of its equipment is proposed. A method for modeling of the branch that enables one to flexibly alter the configuration of the branch in the process of running the optimization algorithm without changing the network topology is presented. The mathematical statement of the problem is formulated as the discrete-continuous optimization problem. This statement is based on the proposed methods of representing the network model and its elements. An algorithm based on dynamic programming is proposed, which implements a new approach to setting up the computational procedure and is versatile enough for calculating networks that serve various purposes. The results obtained during real network optimization are presented.

Mathematical reasoning through the application of solid geometry

This study aims to find out how the process and results of students’ reasoning abilities are faced with the problems of applying solid geometry. This research was conducted on 10 students of class VIII SMP in the even semester of the 2018/2019 school year. Data collection techniques using purposive sampling. Data triangulation process is carried out to confirm the results of the test and interview. The results of this study indicate that students’ mathematical reasoning abilities measured by reasoning indicators have different results. Indicator of the ability to present mathematical statements verbally, in writing, drawings, diagrams, get good results because students have been able to write the information requested and find solutions to problems. Indicator of the ability to do mathematical manipulation to get enough results, because students in the process of working on mathematical manipulation are incomplete and inaccurate. Indicators compile evidence and give reasons to get bad results because students cannot give reasons precisely because the preparation of evidence is incomplete. The indicator draws conclusions from a statement getting bad results because students cannot deduce the questions given correctly due to a lack of understanding. Based on the results it was concluded that the student’s reasoning ability was still lacking at the stage of giving reasons for the evidence compiled and inferring from a statement.

Methods of mathematical modeling for predicting university entry into TOP-100 world university rankings

Subject. The article focuses on mathematical methods for predicting university entry into TOP-100 World University Rankings. Objectives. The purpose of the study is to develop mathematical modeling techniques for predicting university entry into TOP-100 World University Rankings. Methods. We consider two approaches in mathematical simulation for the said purpose. The first approach employs population dynamics equations, including the Verhulst and the Lotka-Volterra equations. The second approach uses linear algebraic equation in three variables together with the variables constraints. Results. Population dynamics equations enable to model improvement in university performance expressed by Total Score or Overall Score indicator, to define intra-university competition and competition between universities of the World University Rankings. Linear algebraic equations provide projections of a university's specified position in the world rankings. We made clear mathematical statement of the problems; solved the problem that relates to entering TOP-100 of three global rankings (ARWU, THE, QS) by the Moscow State University and St. Petersburg University. Conclusions. We assume that the offered approaches will be useful for university managers who monitor and guide their university positioning.