Search results for "410"
showing 10 items of 567 documents
Improving Performance of Evolutionary Algorithms with Application to Fuzzy Control of Truck Backer-Upper System
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/709027 Open access We propose a method to improve the performance of evolutionary algorithms (EA). The proposed approach defines operators which can modify the performance of EA, including Levy distribution function as a strategy parameters adaptation, calculating mean point for finding proper region of breeding offspring, and shifting strategy parameters to change the sequence of these parameters. Thereafter, a set of benchmark cost functions is utilized to compare the results of the proposed method with some other well-known algorithms.…
The sine anecdote in Kovalevskaya’s memoirs; British Journal for the History of Mathematics
2022
In Sofya Vasilyevna Kovalevskaya’s memoirs there is a rather ambiguous story about how she came to understand trigonometric functions on her own as a teenager by reading the chapter on optics in Tyrtov’s elementary physics textbook. Furthermore, she claims that in so doing, she happened to follow ‘the same road that had been taken historically: that is, instead of a sine I used a chord’. We examine Tyrtov’s textbook in search of sources for such inspiration and quote hitherto unknown critical reactions to her autobiographical reflections by Kovalevskaya’s teacher I I Malevich. We conclude that Kovalevskaya’s memoirs may well be marred by personal interests and/or faltering memory. By adding…
Another look at the two Egyptian pyramid volume ‘formulas’ of 1850 BCE
2022
Paid Open Access
A collaboratively-derived research agenda for e-assessment in undergraduate mathematics
2022
AbstractThis paper describes the collaborative development of an agenda for research on e-assessment in undergraduate mathematics. We built on an established approach to develop the agenda from the contributions of 22 mathematics education researchers, university teachers and learning technologists interested in this topic. The resulting set of 55 research questions are grouped into 5 broad themes: errors and feedback, student interactions with e-assessment, design and implementation choices, affordances offered by e-assessment tools, and mathematical skills. This agenda gives a framework for a programme of research aligned with practical concerns that will contribute to both theoretical an…
The Limit Notion at Three Educational Levels in Three Countries
2022
AbstractThis paper documents how the limit concept is treated in high school, at a university and in teacher education in England, France and Sweden. To this end we make use of vignettes, data-grounded accounts of the situation at the three levels in the three countries. These are analysed using the Anthropological Theory of the Didactic (ATD). While university praxeologies are relatively similar across the three countries, greater differences manifest themselves in high school and teacher education. For instance, at the high school level, in France a local praxeology on the limits of sequences is taught, which is not the case in England or Sweden. Results from the analysis of limits are ex…
Asymptotic geometry and Delta-points
2022
We study Daugavet- and $\Delta$-points in Banach spaces. A norm one element $x$ is a Daugavet-point (respectively a $\Delta$-point) if in every slice of the unit ball (respectively in every slice of the unit ball containing $x$) you can find another element of distance as close to $2$ from $x$ as desired. In this paper we look for criteria and properties ensuring that a norm one element is not a Daugavet- or $\Delta$-point. We show that asymptotically uniformly smooth spaces and reflexive asymptotically uniformly convex spaces do not contain $\Delta$-points. We also show that the same conclusion holds true for the James tree space as well as for its predual. Finally we prove that there exis…
How are proof and proving conceptualized in mathematics curriculum documents in the USA and Japan?
2022
Only a few international comparative studies have reported on proof and proving in curriculum documents. This report proposes a method of comparing the meaning of proof-related words in two specific countries’ curriculum documents (the USA and Japan) through quantitative and interpretative analyses. Using a text mining approach to explore text data, we found that the co-occurrence network of the words “proof” and “prove” in curriculum documents from the two countries is quite different. In the USA, the word “proof” is concerned with justification and “prove” is used as a general process, while in Japan “proof” is more related to discovery and “prove” is more associated with specific theorem…
Isometric factorization of vector measures and applications to spaces of integrable functions
2022
Let $X$ be a Banach space, $\Sigma$ be a $\sigma$-algebra, and $m:\Sigma\to X$ be a (countably additive) vector measure. It is a well known consequence of the Davis-Figiel-Johnson-Pelczýnski factorization procedure that there exist a reflexive Banach space $Y$, a vector measure $\tilde{m}:\Sigma \to Y$ and an injective operator $J:Y \to X$ such that $m$ factors as $m=J\circ \tilde{m}$. We elaborate some theory of factoring vector measures and their integration operators with the help of the isometric version of the Davis-Figiel-Johnson-Pelczýnski factorization procedure. Along this way, we sharpen a result of Okada and Ricker that if the integration operator on $L_1(m)$ is weakly compact, t…
Mapping properties for the Bargmann transform on modulation spaces
2010
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.
Teaching and learning for mathematical literacy
2020
This dissertation reports from research that investigates the nature of teaching and learning for mathematical literacy in three lower secondary schools in Norway. Mathematical literacy is a notion used to denote the competences required to meet the mathematical demands of life in modern society. The importance of education for mathematical literacy is emphasised by The Organisation for Economic Cooperation and Development (OECD), and mathematical literacy has become increasingly prominent in national curricula around the world. In the Norwegian curriculum, mathematical literacy is considered a basic skill that should be developed across school subjects. This study of teaching and learning …