Search results for "Mathematica"
showing 10 items of 7971 documents
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.
Characteristics of participation - A mathematician and a mathematics educator collaborating on a developmental research project
2018
International audience; In this paper, a developmental research project involving offering mathematical modelling (MM) activities to university biology students is presented, and a particular aspect is studied, namely the project as a collaboration between mathematicians and mathematics educators. The aim of the paper is to investigate what characterizes their participation in the project, and how the characteristics of the project and its development might influence this participation. Interview data as well as observation data from the MM sessions are analysed, and findings show that the mathematics educator served as a broker influencing the practice of the mathematician. It is hoped tha…
A Completeness Proof for a Regular Predicate Logic with Undefined Truth Value
2023
We provide a sound and complete proof system for an extension of Kleene's ternary logic to predicates. The concept of theory is extended with, for each function symbol, a formula that specifies when the function is defined. The notion of "is defined" is extended to terms and formulas via a straightforward recursive algorithm. The "is defined" formulas are constructed so that they themselves are always defined. The completeness proof relies on the Henkin construction. For each formula, precisely one of the formula, its negation, and the negation of its "is defined" formula is true on the constructed model. Many other ternary logics in the literature can be reduced to ours. Partial functions …
Hölder regularity for stochastic processes with bounded and measurable increments
2022
We obtain an asymptotic Hölder estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size $\varepsilon$ has some crucial effects compared to the PDE setting. The proof combines analytic and probabilistic arguments.
Improving Estimates Accuracy of Voter Transitions. Two New Algorithms for Ecological Inference Based on Linear Programming
2022
The estimation of RxC ecological inference contingency tables from aggregate data is one of the most salient and challenging problems in the field of quantitative social sciences, with major solutions proposed from both the ecological regression and the mathematical programming frameworks. In recent decades, there has been a drive to find solutions stemming from the former, with the latter being less active. From the mathematical programming framework, this paper suggests a new direction for tackling this problem. For the first time in the literature, a procedure based on linear programming is proposed to attain estimates of local contingency tables. Based on this and the homogeneity hypot…
Husserl's Transcendentalization of Mathematical Naturalism
2020
Abstract The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic (1929). It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach t…
Understanding tungsten erosion during inter/intra-ELM periods in He-dominated JET-ILW plasmas
2021
Tungsten erosion was quantified during inter/intra-ELM periods in He-dominated JET-ILW plasmas by optical emission spectroscopy. The intra-ELM tungsten sputtering in helium plasmas, which dominates the total W source, prevails by a factor of about 4 over inter-ELM sputtering in the investigated ELM frequency range from 90 Hz-120 Hz. He ions are mainly responsible for the W erosion during the ELMs in He plasmas. The strong in/out asymmetry of the ELM-induced W erosion is observed in He plasmas even at high ELM frequencies beyond 100 Hz. In Ohmic/L-mode plasmas and during the H-mode inter-ELM plasma phases both He2+ and Be2+ ionic species are major contributors to the W erosion. Their contrib…
Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations
2021
We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.
Evaluation of biogas production and usage potential
2016
The aim of the research is the development of theoretical and methodical bases for determining the feasibility of plant raw materials growing for its further bioconversion into energy resources and tec hnological materials to maximize profit from business activities. Monograph, statistics, modelling and abstract logical methods have been used during the research. Directions of biogas usage have been examined. Biogas yields from different crops have been analyzed. It has been determined that high methane yields can be provided from root crops, grain crops, and several green forage plants. So, forage beet and maize can provide more than 5,500 m3 of biogas per hectare. Attention is paid to the…
Teaching and Learning of Geometry as a process of Objectification: conditions and obstacles to argumentation and proof. The role of natural language,…
2021
This paper examines some examples (taken from research conducted over the years) that show students’ linguistic attitudes in geometry tasks. The examples are framed within the Theory of Objectification with reference to the notion of sensuous cognition, semiotic means of objectification and levels of generality. We show the struggle students live, at higher levels of generality, in intertwining natural language, specific language and the spontaneous use of geometrical figures, bound to perception and kinaesthetic activity. Within the networking paradigm, we coordinate the Theory of Objectification and Duval’s semio-cognitive approach to frame the interplay between the ideal and the material…