The Experts below are selected from a list of 33 Experts worldwide ranked by ideXlab platform
Alex Lebedinsky - One of the best experts on this subject based on the ideXlab platform.
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cagan type rational expectation model on complex discrete time domains
European Journal of Operational Research, 2014Co-Authors: Ferhan M Atici, Funda Ekiz, Alex LebedinskyAbstract:In this article, we derive a solution for a Linear stochastic model on a complex time domain. In this type of models, the time domain can be any collection of points along the Real Number Line, so these models are suitable for problems where events do not occur at evenly-spaced time intervals. We present examples based on well-known results from economics and finance to illustrate how our model generalizes and extends conventional dynamic models.
Douglas S Bridges - One of the best experts on this subject based on the ideXlab platform.
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a constructive look at the Real Number Line
1994Co-Authors: Douglas S BridgesAbstract:Our aim in writing this paper is to present some of the distinctive features of the Real Number Line ℝ as it appears to the constructive mathematician. Throughout this presentation we shall pay particular attention to constructive notions and proofs that differ from their classical counterparts, or whose classical analogues are insubstantial (in the case of notions) or trivial (in the case of proofs). For example, we explain why one classical definition of ‘closed subset of ℝ’ is inappropriate in the constructive setting (6.2); and we devote a considerable amount of space to the property of locatedness, which plays no role whatsoever in traditional analysis (Section 12).
Ferhan M Atici - One of the best experts on this subject based on the ideXlab platform.
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cagan type rational expectation model on complex discrete time domains
European Journal of Operational Research, 2014Co-Authors: Ferhan M Atici, Funda Ekiz, Alex LebedinskyAbstract:In this article, we derive a solution for a Linear stochastic model on a complex time domain. In this type of models, the time domain can be any collection of points along the Real Number Line, so these models are suitable for problems where events do not occur at evenly-spaced time intervals. We present examples based on well-known results from economics and finance to illustrate how our model generalizes and extends conventional dynamic models.
Hyman Bass - One of the best experts on this subject based on the ideXlab platform.
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quantities Numbers Number names and the Real Number Line
2018Co-Authors: Hyman BassAbstract:This paper describes an approach to developing concepts of Number using general notions of quantity and their measurement. This approach, most prominently articulated by Davydov and his colleagues, is discussed, and some arguments favouring this approach are offered. First is that it provides a coherent development of both whole Numbers and fractions. Second, it makes the geometric Number Line continuum present from the start of the school curriculum as a useful mathematical object and concept into which Real Numbers can eventually take up residence. Third, in the Davydov approach, there are some significant opportunities for some early algebraic thinking. I further present an instructional context and approach to place value that simulates a hypothetical invention of a place value system of Number representation.
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is the Real Number Line something to be built or occupied
Advances in STEM Education, 2018Co-Authors: Hyman BassAbstract:Klein emphasized geometry and intuition, and made the concept of function central to mathematics education. In fact, Number and operations form the backbone of the school mathematics curriculum. A high school graduate should comfortably and capably meet an expression like, “Let y = f(x) be a function of a Real variable x,” implying that the student has a robust sense of the Real Number continuum, the home of x. This understanding is a central objective of the school mathematics curriculum, taken as a whole. Yet there are reasons to doubt whether typical (U.S.) high school graduates fully achieve this understanding. Why? And what can be done about this? I argue that there are obstacles already at the very foundations of Number in the first grades. The construction narrative of the Number Line, characteristic of the prevailing curriculum, starts with cardinal counting and whole Numbers and then builds the Real Number Line through successive enlargements of the Number systems studied. An alternative, based on ideas advanced by V. Davydov, the occupation narrative, begins with pre-numerical ideas of quantity and measurement, from which the geometric (Number) Line, as the environment of Linear measure, can be made present from the beginning, and wherein new Numbers progressively take up residence. I will compare these two approaches, including their cognitive premises, and suggest some advantages of the occupation narrative.
Funda Ekiz - One of the best experts on this subject based on the ideXlab platform.
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cagan type rational expectation model on complex discrete time domains
European Journal of Operational Research, 2014Co-Authors: Ferhan M Atici, Funda Ekiz, Alex LebedinskyAbstract:In this article, we derive a solution for a Linear stochastic model on a complex time domain. In this type of models, the time domain can be any collection of points along the Real Number Line, so these models are suitable for problems where events do not occur at evenly-spaced time intervals. We present examples based on well-known results from economics and finance to illustrate how our model generalizes and extends conventional dynamic models.
