Some issues on the automatic computation of plane envelopes in interactive environments

This paper addresses some concerns, and describes some proposals, on the elusive concept of envelope of an algebraic family of varieties, and on its automatic computation. We describe how to use the recently developed Gröbner Cover algorithm to study envelopes of families of algebraic curves, and we give a protocol toward its implementation in dynamic geometry environments. The proposal is illustrated through some examples. A beta version of GeoGebra is used to highlight new envelope abilities in interactive environments, and limitations of our approach are discussed, since the computations are performed in an algebraically closed field

Visualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-Regression

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency

Conjuring cognition : A review of educational magic-based interventions

For hundreds of years, magic tricks have been employed within a variety of pedagogic contexts, including promoting science and mathematics, delivering educational messaging, enhancing scepticism about the paranormal, and boosting creative thinking for product design. This review examines this diverse body of work, focusing on studies that have assessed the impact of such interventions. Although the studies tended to yield positive outcomes, much of the work suffered from methodological shortcomings, including measuring the impact of interventions over a relatively short period of time, focusing on self-report measures and failing to employ control groups. The paper makes several recommendations for future study in the area, including assessing the longer-term impact of magic-based interventions, comparing these interventions to other types of pedagogic techniques, focussing on knowledge retention and behavioural outcomes, and collaborating with magicians to develop more impactful interventions.Peer reviewedFinal Published versio

Analysis of Relation between Asset Growth and Stock Return in Tehran Stock Exchange

Studying and quantifying the relationship between risk and return and identifying factors affecting the return have always been in the interest of researchers in the field of finance. Researches have shown that multi-factor models have higher power in explaining stock returns when compared with single factor models. Fama and French (1993) presented a three-factor model including market portfolio, size and the ratio of book value to market value to describe market return. The aim of this study is to add a new variable, assets growth, to this model and make a four-factor model to have a better analysis and to make a better prediction of stock market return in Tehran Stock Exchange. To accomplish this purpose, the impact of assets growth on stock return is considered under two different models which in one of them, it is not controlled for the effects of the two variables of size and the ratio of book value to market value, and in the other one, these variables are included in our model. The data are examined over a 10-year period (2000-2010) using Eviews software, and the results show that although assets growth independently does not have any significant impact on stock return, when it is added to a three-factor model that was introduced by Fama and French , it will have a negative impact on stock market return

Elements of linear space

Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given.Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices