Search results for "Algebra"

Visualization in the integrated SimPhoNy multiscale simulation framework

2018

Abstract We describe three distinct approaches to visualization for multiscale materials modelling research. These have been developed with the framework of the SimPhoNy FP7 EU-project, and complement each other in their requirements and possibilities. All have been integrated via wrappers to one or more of the simulation approaches within the SimPhoNy project. In this manuscript we describe and contrast their features. Together they cover visualization needs from electronic to macroscopic scales and are suited to simulations made on personal computers, workstations or advanced High Performance parallel computers. Examples as well as recommendations for future calculations are presented.

Fostering Heuristic Strategies in Mathematics Teacher Education

2018

International audience; The “double discontinuity” stated by Felix Klein 1908 is still relevant in the mathematics teacher education at German universities. We are developing a course approach, which is intended to bridge the double discontinuity in a didactic dimension. We offer additional learning opportunities for teacher students, which are characterized by clarifications of mathematical methods that are fundamental to the regular lecture contents. We focus especially on reflections on heuristic strategies, which are the core part of mathematical methods according to George Pólya. Feedback shows that students consider our approach as helpful in the transition from school to university.

New Insights into Segmental Packing, Chain Dynamics and Thermomechanical Performance of Aliphatic Polyurea Composites: Comparison between Silica Oxid…

2021

Polyurea (PU) is intrinsically reinforced by its microphase-separated morphology, giving its excellent mechanical properties. In this study, it is shown how a high-index PU formulation applies easy diffusion of hard segments into the soft phase of the PU matrix and tune its chain mobility. Moreover, the interaction of micro (>100 nm), nano (<100 nm) fillers with the microdomains and their thermomechanical properties are unraveled. Herein, nanosilica oxide (NS) and micro titanium (III) oxide (Ti2O3) are incorporated at low loadings into a solvent-free two-component aliphatic PU via insitu polymerization. While NS achieves an interfacial interaction with urea groups and forms a tight ha…

A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

Students' problems in the identification of subspaces in Linear Algebra

2018

International audience; The goal of the study presented in this paper is the investigation of students' problems with exercises concerning central topics of linear algebra courses at university level. We present the results of our analysis of students' work on an exercise about subspaces of . We evaluated the written solutions of the task as well as transcripts based on videos taken of student groups working on the problem. We identified and classified descriptions of vector spaces and subspaces that varied widely and demonstrated highly different skills in working with geometric or formal algebraic objects. We analyzed how far students could progress in a complex reasoning process, and ide…

Ordered fuzzy rules generation based on incremental dataset

2021

This paper proposes a novel approach for building transparent knowledge-based systems by generating interpretable fuzzy rules that allow for present dependences between quantitative variables by accounting for uncertainty and the dynamics of their values. In the approach, IF-THEN rules are used to show the conditional relationship between the ordered fuzzy numbers, which contain additional information about the tendencies of variables' value changes. This paper elaborates an approach of mining ordered fuzzy rules from numerical data included in an incremental database. This approach develops the ability to record uncertainty and its change in the context of rapidly changing data. In additio…

Ungdomsskoleelevers bruk av symboler i algebra

2016

Masteroppgave matematikkdidaktikk – Universitetet i Agder 2016 The thesis investigates the challenges students in 10th grade face while learning algebra, algebraic symbols and how they assess the subject. With the use of a theoretical test and semistructured interviews, the thesis aims to answer the following research questions: 1. What challenges do students from lower secondary education encounter while learning algebra? 2. How do these students engage with algebra and what are their views and aspects towards the subject? The thesis serves primarily as a qualitative case study, of three students from lower secondary school. In addition, quantitative research methods have been undertaken b…

Extensions of representable linear functionals to unitized quasi *-algebras

2013

This paper starts from noting that, under certain conditions, *-representability and extensibility to the unitized *-algebra of a positive linear functional, defined on a *-algebra without unit, are equivalent. Here some conditions for the equivalence of the same concepts for a hermitian linear functional defined on a quasi *-algebra $(\A,\Ao)$ without unit are given. The approach is twofold: on the one hand, conditions for the equivalence are exhibited by introducing a condition for the *- representability of the extension of a *-representable functional to the unitized quasi *-algebra, on the other hand a *-representable extension to the unitization of a hermitian linear functional by mea…

La corrispondenza Giovanni Novi - Enrico Betti

2011

Regularity for nonlinear stochastic games

2015

We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations. peerReviewed