Islamophobia: With or without Islam?

Islamophobia has been a controversial concept ever since it first gained popular currency. One of the main sticking points over the term is whether or not it refers to religion. For both detractors and advocates of the term alike, religion should be or is removed from the meaning of Islamophobia, which is conceived as a form of anti-Muslim racism. Islam, we might say, is thereby removed from Islamophobia. Yet, in doing so, it falls short on two of its key objectives, i.e., identifying the particular forms of discrimination that Muslims face in society and subsequently providing a positive basis from which to address this discrimination. In this article, the question asked is if we should put Islam back into Islamophobia and, if so, on what basis? According to the existing literature as well as a study of converts to Islam, it is suggested that Islam as a religion is both an important feature of Islamophobia as well as central to the identities of many Muslims, and then it is suggested why and how we should think about including religion into the scope of thinking on Islamophobia and how it is addressed.

Lower and Upper Bounds for Positive Bases of Skein Algebras

We show that if a sequence of normalized polynomials gives rise to a positive basis of the skein algebra of a surface, then it is sandwiched between the two types of Chebyshev polynomials. For the closed torus, we show that the normalized sequence of Chebyshev polynomials of type one $(\hat{T}_n)$ is the only one that gives a positive basis.

The Underground Current of the Idealism of Problems

The article deals with the fundamental influence on Deleuze of the little-studied strain of French philosophy and epistemology from the 20th century that deals with such concepts as question, theme and problem. Some figures adjoining this lineage are known outside France (Bergson, Bachelard, Canguilhem, Althusser, Foucault), and others are just beginning to arouse intense interest (Lautman, Ruyer, Simondon); but they have rarely been seen as part of a single tradition of theorizing about problematics. And in spite of the fact (or thanks to it) that thinking about problematics has nominally entered the mainstream of the contemporary academy as a principal methodological basis, its actual current remains unknown and underground. The author offers a brief analysis of Martial Gueroult’s dianoematics. Dianoematics is a structuralist approach to the history of philosophy which consists of two parts: the history of the history of philosophy and the philosophy of the history of philosophy. Gueroult regards the latter as a transcendental science, one which takes philosophy (or, more precisely, the multiplicity of philosophies or problematics) and the conditions of its possibility as its subject. When philosophies lay claim to timeless truth about Real, this inoculates them against any reduction to the pure subjectivity of thinkers or the social circumstances of their thinking. And so Gueroult postulates that the philosophical choices which ground philosophies have their own unitary ahistorical logic. That unity of logic, however, does not reduce the multitude of philosophies to one. Therefore, in place of a single Real there is a multiplicity of Reals which are internal to philosophies — that is the so-called “radical idealism” of Gueroult. The author points out the interplay between Gueroult’s approach not only with the history of philosophy from What Is Philosophy? but also with Laruelle’s non-philosophy, with which Deleuze carries on a dialogue in his book. While Deleuze tries to “sublate” Gueroult’s idealism by taking it as a positive basis for materialist thought regarding immanence, Laruelle takes it as the clearest expression of the idealism inherent in all philosophies and uses it negatively as a building material for non-philosophy.

Shape Preserving Properties forq-Bernstein-Stancu Operators

We investigate shape preserving forq-Bernstein-Stancu polynomialsBnq,α(f;x)introduced by Nowak in 2009. Whenα=0,Bnq,α(f;x)reduces to the well-knownq-Bernstein polynomials introduced by Phillips in 1997; whenq=1,Bnq,α(f;x)reduces to Bernstein-Stancu polynomials introduced by Stancu in 1968; whenq=1,α=0, we obtain classical Bernstein polynomials. We prove that basicBnq,α(f;x)basis is a normalized totally positive basis on[0,1]andq-Bernstein-Stancu operators are variation-diminishing, monotonicity preserving and convexity preserving on[0,1].

Total Positivity of the Cubic Trigonometric Bézier Basis

Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parametersλandμgiven in Han et al. (2009) forms an optimal normalized totally positive basis forλ,μ∈(-2,1]. Moreover, we show that forλ=-2orμ=-2the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.