No abstract

Mathematical competitions feature in most developed countries as a part of the secondary school experience, but to a lesser extent in developing countries. In this paper we investigate how widespread these competitions are in Africa, both historically as well as currently, focussing both on national Olympiads and on the participation of African countries in competitions beyond their borders, such as the continent-wide Pan African Mathematical Olympiad and the global International Mathematical Olympiad. Since we could not find a consolidated source of information on African competitions, we include many details and links, hoping that this paper will serve as a valuable starting point for future investigators. Next, we present some survey findings on the attitudes towards and experiences of mathematical competitions, both from the perspective of teachers in secondary schools as well as from secondary school students, and whether these experiences have served to improve or degrade their perceptions of mathematics in general. Among other results, we find that teachers view their students’ participation in mathematics competitions as being important, with the biggest barrier to participation being that there are not enough competitions at appropriate levels available, and that students enjoy mathematics competitions and are more likely to pursue a STEM career because of them. Finally, we present some suggestions on how this research may be taken further, and on how the state of mathematical competition culture in Africa may be improved.

The oil-immersed transformer is commonly used in modern electrical power systems, and it is also a crucial component in smart grids related to power efficiency and quality. Because of its complex electromagnetic characteristics, it is not viable to establish its thermal control model simply by conventional approaches, such as thermal balance, specific heat capacity and thermal field. In this paper, a dynamic thermal control model dependent on modern control theories, especially thermal-electrical analogy, will be presented. Plus, its mathematical model will be developed and explained step by step.

No abstract

We study representations of integers as sums of the form ±a1 ± a2 ± · · · ± an, where a1, a2, . . . is a prescribed sequence of integers. Such a sequence is called an Erdős-Surányi sequence if every integer can be written in this form for some n ∈ N and choices of signs in infinitely many ways. We study the number of representations of a fixed integer, which can be written as a trigonometric integral, and obtain an asymptotic formula under a rather general scheme due to Roth and Szekeres. Our approach, which is based on Laplace's method for approximating integrals, can also be easily extended to find higher-order expansions. As a corollary, we settle a conjecture of Andrica and Ionaşcu on the number of solutions to the signum equation ±1 k ± 2 k ± · · · ± n k = 0.