Search results for "matematiikka"

On the continuous and discontinuous maximal operators

2018

Abstract In the first part of this paper we study the regularity properties of a wide class of maximal operators. These results are used to show that the spherical maximal operator is continuous W 1 , p ( R n ) ↦ W 1 , p ( R n ) , when p > n n − 1 . Other given applications include fractional maximal operators and maximal singular integrals. On the other hand, we show that the restricted Hardy–Littlewood maximal operator M λ , where the supremum is taken over the cubes with radii greater than λ > 0 , is bounded from L p ( R n ) to W 1 , p ( R n ) but discontinuous.

Enhancing Dialogic Argumentation in Mathematics and Science

2017

This paper reports on a teacher professional development (PD) programme addressing dialogic argumentation in mathematics and science classrooms. While argumentation skills are becoming more and more important in an increasingly polarised society, the social aspect of argumentation is often neglected in secondary education. Moreover, it is agreed that genuine argumentation requires time and space in classroom dialogue. There have been calls for research delving into how teachers could be familiarised with dialogic argumentation so that they could foster such dialogue in students. The described PD programme features versatile and continuous cooperation between scholars and participating teach…

Strong BV-extension and W1,1-extension domains

2021

We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those $BV$-extension domains for which the set $\partial\Omega \setminus \bigcup_{i} \overline{\Omega}_i$ is purely $1$-unrectifiable, where $\Omega_i$ are the open connected components of $\mathbb{R}^2\setminus\overline{\Omega}$.

Trialling the 4C framework in an Indian grade 3 mathematics classroom

2017

This thesis describes an action research carried out in a Grade 3 maths classroom in a low income, English medium school in Mumbai, India. The maths teacher in the study used the 4C model proposed by Do Coyle (2010) as a framework of Content and Language Integrated Learning (CLIL) for teaching maths in English to students whose exposure to English outside the classroom was negligible. The aim of this research was to understand from a teacher’s perspective how the 4C framework contributed to this specific context and how group-work enhanced the 4C framework. The action research was carried over a period of nearly five months in three cycles. Through the entire duration of the action research…

Ahlfors-regular distances on the Heisenberg group without biLipschitz pieces

2015

We show that the Heisenberg group is not minimal in looking down. This answers Problem 11.15 in `Fractured fractals and broken dreams' by David and Semmes, or equivalently, Question 22 and hence also Question 24 in `Thirty-three yes or no questions about mappings, measures, and metrics' by Heinonen and Semmes. The non-minimality of the Heisenberg group is shown by giving an example of an Ahlfors $4$-regular metric space $X$ having big pieces of itself such that no Lipschitz map from a subset of $X$ to the Heisenberg group has image with positive measure, and by providing a Lipschitz map from the Heisenberg group to the space $X$ having as image the whole $X$. As part of proving the above re…

Mathematical Fuzzy Logic in the Emerging Fields of Engineering, Finance, and Computer Sciences

2022

With more than 50 years of literature, fuzzy logic has gradually progressed from an emerging field to a developed research domain, incorporating the sub-domain of mathematical fuzzy logic (MFL) [...]

Geometry of Quadrangles in Almqvist’s The Queen’s Tiara

2018

Quadrangles are repeatedly used in construction of scenes in Swedish author C. J. L. Almqvist’s novel The Queen’s Tiara. They limit and frame views. Repeating these structures creates connections between scenes. They form in relations between characters. Several quadrangular structures form around one main character called Tintomara, when she involuntarily attracts characters that fall in love in her. Also, quadrangles inside and beside each other are visible in scenes. Almqvist presented these forms in the elementary geometry textbook he published a year before this novel. peerReviewed

Dialogista argumentaatiota matematiikkaan ja fysiikkaan

2017

Local dimensions of measures on infinitely generated self-affine sets

2014

We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore the local dimension equals the minimum of the local Lyapunov dimension and the dimension of the space. We also give an estimate, that holds for all translation vectors, with only assuming the affine maps to be contractive.

Developing a Pedagogical Framework and Design Principles for STEM Learning Environment Design

2020

The need for effective and attractive learning environments (LEs) for science, technology, engineering, and mathematics (STEM) has been internationally recognized. Additionally, the connection between STEM learning and cross-curricular skills such as creativity, innovation, and entrepreneurship has garnered attention. A deep theoretical and empirical understanding is required when designing STEM LEs. In this study, a pedagogical framework for STEM LEs has been developed based on feedback from students, aged 10–18 years old, teachers, school directors, parents, and STEM professionals, and supported by the literature. First, representatives of key stakeholder groups in Belarus, Finland, Germa…