scholarly journals Understanding Early Mathematical Modelling: First Steps in the Process of Translation Between Real-world Contexts and Mathematics

2021 ◽  
Author(s):  
Ángel Alsina ◽  
María Salgado
Keyword(s):  
Mathematical Modelling ◽  
Important Data ◽  
Mathematical Objects ◽  
The Real ◽  
Childhood Education ◽  
Modelling Activity ◽  
Proposed Model ◽  
And Mathematics ◽  
Concrete Model ◽  
Modelling Process

Abstract The aim of this study is to provide data to better understand the processes of early mathematical modelling. According to this, an early mathematical modelling activity carried out by 21 Spanish schoolchildren aged 5–6 years is analysed, using the validated tool “Rubric for the Evaluation of Mathematical Modelling Processes” (REMMP). The results show that children link the content of the problem with their prior knowledge (understanding); identify the important data of the problem and simplify it (structuring); show some difficulties in substituting the elements of the real context for mathematical objects (mathematizing); use progressively mathematical objects and strategies in order to propose solutions for the problem (working mathematically); compare the solution with the initial problem (interpretation); justify the proposed model via valid arguments (validation); and also communicate the decisions taken throughout the modelling process and the concrete model obtained applied to the real context (presenting). We conclude that the description of this type of activities and the tools for their analysis could be used for grading and teaching tool in order to promote mathematic modelling in early childhood education.

scholarly journals The Real Forms of the Fractional Supergroup SL(2,C)

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 933
Author(s):  
Yasemen Ucan ◽  
Resat Kosker
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
The Real ◽  
And Mathematics ◽  
Real Forms

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.

scholarly journals Learning Personalized Itemset Mapping for Cross-Domain Recommendation

2020 ◽  
Author(s):  
Yinan Zhang ◽  
Yong Liu ◽  
Peng Han ◽  
Chunyan Miao ◽  
Lizhen Cui ◽  
...  
Keyword(s):  
Single Domain ◽  
Model Parameters ◽  
The Real ◽  
Cross Domain ◽  
Proposed Model ◽  
Latent Space ◽  
Learning Parameter ◽  
Generation Procedure ◽  
Over Time

Cross-domain recommendation methods usually transfer knowledge across different domains implicitly, by sharing model parameters or learning parameter mappings in the latent space. Differing from previous studies, this paper focuses on learning explicit mapping between a user's behaviors (i.e. interaction itemsets) in different domains during the same temporal period. In this paper, we propose a novel deep cross-domain recommendation model, called Cycle Generation Networks (CGN). Specifically, CGN employs two generators to construct the dual-direction personalized itemset mapping between a user's behaviors in two different domains over time. The generators are learned by optimizing the distance between the generated itemset and the real interacted itemset, as well as the cycle-consistent loss defined based on the dual-direction generation procedure. We have performed extensive experiments on real datasets to demonstrate the effectiveness of the proposed model, comparing with existing single-domain and cross-domain recommendation methods.

scholarly journals An innovative STEM outreach model (OH-Kids) to foster the next generation of geoscientists, engineers, and technologists

2019 ◽  
Vol 2 (2) ◽  
pp. 187-199 ◽  
Author(s):  
Adrián Pedrozo-Acuña ◽  
Roberto J. Favero Jr. ◽  
Alejandra Amaro-Loza ◽  
Roberta K. Mocva-Kurek ◽  
Juan A. Sánchez-Peralta ◽  
...  
Keyword(s):  
Well Being ◽  
Next Generation ◽  
Stem Learning ◽  
Information And Communications Technologies ◽  
Research Project ◽  
Childhood Education ◽  
Communications Technologies ◽  
And Mathematics ◽  
Problem Solvers

Abstract. Childhood education programmes aiming at incorporating topics related to science, technology, engineering, and mathematics (STEM) have gained recognition as key levers in the progress of education for all students. Inspiring young people to take part in the discovery and delivery of science is of paramount importance not only for their well-being but also for their future human development. To address this need, an outreach model entitled OH-Kids was designed to empower pupils through the development of high-quality STEM learning experiences based on a research project. The model is an opportunity for primary school learners to meet geoscientists while receiving the take-home message that anyone can get involved in scientific activities. The effort is part of a research project aimed at the real-time monitoring of precipitation in Mexico City, which is a smart solution to rainfall monitoring using information and communications technologies. The argument behind this effort is that in order to produce the next generation of problem-solvers, education should ensure that learners develop an appreciation and working familiarity with a real-world project. Results show success at introducing the role of researchers and STEM topics to 6–12-year-old learners.

scholarly journals Categories as Mathematical Models

2018 ◽  
Author(s):  
David I. Spivak
Keyword(s):  
Dynamical Systems ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Category Theory ◽  
Vector Spaces ◽  
Mathematical Objects ◽  
Working Definition ◽  
Modelling Framework ◽  
Categorical Models ◽  
Definition Of

Category theory is presented as a mathematical modelling framework that highlights the relationships between objects, rather than the objects in themselves. A working definition of model is given, and several examples of mathematical objects, such as vector spaces, groups, and dynamical systems, are considered as categorical models.

scholarly journals Geometric Modelling of Octagonal Lamp Poles

2014 ◽  
Vol XL-5 ◽  
pp. 145-150 ◽  
Author(s):  
T. O. Chan ◽  
D. D. Lichti
Keyword(s):  
Point Cloud ◽  
Geometric Model ◽  
Real Data ◽  
Point Clouds ◽  
Circular Cone ◽  
Basic Point ◽  
The Real ◽  
Cone Model ◽  
Proposed Model ◽  
Pole Point

Lamp poles are one of the most abundant highway and community components in modern cities. Their supporting parts are primarily tapered octagonal cones specifically designed for wind resistance. The geometry and the positions of the lamp poles are important information for various applications. For example, they are important to monitoring deformation of aged lamp poles, maintaining an efficient highway GIS system, and also facilitating possible feature-based calibration of mobile LiDAR systems. In this paper, we present a novel geometric model for octagonal lamp poles. The model consists of seven parameters in which a rotation about the z-axis is included, and points are constrained by the trigonometric property of 2D octagons after applying the rotations. For the geometric fitting of the lamp pole point cloud captured by a terrestrial LiDAR, accurate initial parameter values are essential. They can be estimated by first fitting the points to a circular cone model and this is followed by some basic point cloud processing techniques. The model was verified by fitting both simulated and real data. The real data includes several lamp pole point clouds captured by: (1) Faro Focus 3D and (2) Velodyne HDL-32E. The fitting results using the proposed model are promising, and up to 2.9 mm improvement in fitting accuracy was realized for the real lamp pole point clouds compared to using the conventional circular cone model. The overall result suggests that the proposed model is appropriate and rigorous.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

The World Code

2008 ◽  
pp. 58-75
Author(s):  
Azamat Abdoullaev
Keyword(s):  
Big Bang ◽  
Theoretical Physics ◽  
Formal Ontology ◽  
Knowledge Domain ◽  
The Real ◽  
Black And White ◽  
The World ◽  
Theory Of Everything ◽  
And Mathematics ◽  
The Universe

Formalizing the world in rigorous mathematical terms is no less significant than its fundamental understanding and modeling in terms of ontological constructs. Like black and white, opposite sexes or polarity signs, ontology and mathematics stand complementary to each other, making up the unique and unequaled knowledge domain or knowledge base, which involves two parts: • Ontological (real) mathematics, which defines the real significance for the mathematical entities, so studying the real status of mathematical objects, functions, and relationships in terms of ontological categories and rules. • Mathematical (formal) ontology, which defines the mathematical structures of the real world features, so concerned with a meaningful representation of the universe in terms of mathematical language. The combination of ontology and mathematics and substantial knowledge of sciences is likely the only one true road to reality understanding, modeling and representation. Ontology on its own can’t specify the fabric, design, architecture, and the laws of the universe. Nor theoretical physics with its conceptual tools and models: general relativity, quantum physics, Lagrangians, Hamiltonians, conservation laws, symmetry groups, quantum field theory, string and M theory, twistor theory, loop quantum gravity, the big bang, the standard model, or theory of everything material. Nor mathematics alone with its abstract tools, complex number calculus, differential calculus, differential geometry, analytical continuation, higher algebras, Fourier series and hyperfunctions is the real path to reality (Penrose, 2005).

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