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In the present paper, we study in the harmonic analysis associated to the Weinstein operator, the boundedness on Lp of the uncentered maximal function. First, we establish estimates for the Weinstein translation of characteristic function of a closed ball with radius ε centered at 0 on the upper half space Rd-1× ]0,+∞[. Second, we prove weak-type L1-estimates for the uncentered maximal function associated...
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Algorithms and algorithmic thinking are key topics in STEM Education. By using algorithms approximate solutions can be obtained for analytical unsolvable problems. Before new methods can be safely applied they have to be thoroughly tested in experiments. In this article we present a series of exercise where students can experiment with algorithms and test them using GeoGebra or the TI-Nspire. Based...
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This paper presents a theorem dealing with absolute matrix summability of infinite series. This theorem has been proved taking quasi β-power increasing sequence instead of almost increasing sequence.
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Letter to the editor
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The results of Zarzycki for the cardinality of the sets of all bijections, surjections, and injections are generalized to the case when the domains and codomains are infinite and different. The elementary proofs the cardinality of the sets of bijections and surjections are given within the framework of the Zermelo-Fraenkel set theory with the axiom of choice. The case of the set of all injections...
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Tłumaczenie
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We discuss the role of a heuristic principle known as the Principle of Permanence of Forms in the development of mathematics, especially in abstract algebra. We try to find some analogies in the development of modern formal logic. Finally, we add a few remarks on the use of the principle in question in mathematical education.
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In this paper we explore different ways of solving quadratic equations. Our main goal is to review traditional textbooks methods and offer an alternative, often side-stepped method based on the area model. We conclude that whereas traditional methods offer effective algorithms that quickly lead to the desired results, alternative methods may enhance meaningful and joyful learning.
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In this paper we present three aspects of the autonomy of geometry. (1) An argument for the geometric as opposed to the ‘geometric algebraic’ interpretation of Euclid’s Books I and II; (2) Hilbert’s successful project to axiomatize Euclid’s geometry in a first order geometric language, notably eliminating the dependence on the Archimedean axiom; (3) the independent conception of multiplication from...
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The paper presents, among others, the golden number as the limit of the quotient of neighboring terms of the Fibonacci and Fibonacci type sequence by means of a fixed point of a mapping of a certain interval with the help of Edelstein's theorem. To demonstrate the equality , where is $n$-th Fibonacci number also the formula from Corollary \ref{cor1} has been applied. It was obtained using...
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In this study, it was aimed to investigate the beliefs of mathematics teachers about mathematics instruction and their teaching self-efficacy within the scope of flow theory. Participants consists of a total of 228 mathematics teachers engaged in teaching at secondary and high school levels in Turkey; they were determined using the combinations of convenience and purposive sampling. Data from the...
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In this article, I analyze the theoretical foundations of the division with remainder in the arithmetic of natural numbers. As a result of this analysis I justify that the notation a:b=c r s, where a, b, c, s are natural numbers and r denotes, is correct at school mathematics level and does not lead to a contrediction suggested by the author of the article (Semadeni, 1978). As a generalization of...
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This paper presents some generalizations of BCI algebras (the RM, tRM, *RM, RM**, *RM**, aRM**, *aRM**, BCH**, BZ, pre-BZ and pre-BCI algebras). We investigate the p-semisimple property for algebras mentioned above; give some examples and display various conditions equivalent to p-semisimplicity. Finally, we present a model of mereology without antisymmetry (NAM) which could represent a tRM algebra.
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Tłumaczenie
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Letter to the Editor
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We present two sets of lessons on the history of mathematics designed for prospective teachers: (1) Euclid's Theory of Area, and (2) Euclid's Theory of Similar Figures. They aim to encourage students to think of mathematics by way of analysis of historical texts. Their historical content includes Euclid's Elements, Books I, II, and VI. The mathematical meaning of the discussed propositions is simple...
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Good preparation of students to the profession of teacher is very important. In my research I focus on improving the quality of teacher's preparation at the university level, and through it at school level in the future. I present the proposal of teaching mathematics with the use of algorithmisation. It is possible, because solutions to many mathematical problems can be expressed in the form of an...
