This essay begins with a quotation from Carl Schmitt in which he quotes Søren Kierkegaard on the significance of the exception in political theology. The essay is an extended reflection on this quotation within a quotation. Through a comparison of Kierkegaard and Schmitt, the author presents two readings of the state of exception: the first centers on the figure of the sovereign, while the second centers on the figure of the martyr. The sovereign suspends the law from above, while the martyr suspends it from below. In the political sphere, there are two ways of becoming the exception: the sovereign versus the martyr.

We introduce the notions of returns and well-aligned sets for closed relations on compact metric spaces and then use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition, we give a characterization of finite relations with non-zero entropy in terms of Li–Yorke and DC2 chaos.

If we talk about the centre of a triangle, what might we be referring to? Any triangle has many different points that could regarded as its centre; in fact, Encyclopedia of Triangle Centres lists over 70 000 possibilities. Three of the most famous centres, that every triangle will possess (although they may coincide), are the incentre (where the three angle bisectors meet), the centroid (where the three medians meet) and the orthocentre (where the three altitudes meet). Proofs that these centres are well-defined and exist for every triangle are simple and satisfying, good examples of reasoning (if we are teachers) for our students. Proving the three altitudes of a triangle share a point using the scalar product of vectors is a wonderful demonstration of the power of this idea.

There are various combinatorial questions on rectangular arrays consisting of points, numbers, fields or, in general, of symbols such as chessboards, lattices, and graphs. Many such problems in enumerative combinatorics come from other branches of science and technology like physics, chemistry, computer sciences and engineering; for example the following two very challenging problems from chemistry:Problem 1: Dimer problem (Domino tiling)In chemistry, a large molecule composed repeatedly from monomers as a long chain is called a polymer and a dimer is composed of two monomers (where: mono = 1, di = 2, poly = many and mer = part).

The Greek architect Kostas Vittas published in 2006 a beautiful theorem ([1]) on the cyclic quadrilateral as follows:

Theorem 1 (Kostas Vittas, 2006): If ABCD is a cyclic quadrilateral with P being the intersection of two diagonals AC and BD, then the four Euler lines of the triangles PAB, PBC, PCD and PDA are concurrent.

According to Candomblé, axé is present in every living being and is necessary to life. To develop and maintain a sense of well-being, one must maintain a balanced level of axé which is linked to a reciprocal relationship between human beings and orixás (African deities). This article will explore the link between the spiritual force axé and well-being (bem estar) within Candomblé philosophy. Starting with explaining axé within the context of Candomblé and its concept of personhood, the article will reflect in the latter part on the concept of well-being from the perspective of axé and put forward an argument for the inclusion of Candomblé in philosophy of religion.

Archaeologists in the Canary Islands have gathered substantial quantitative data from radiocarbon measurements and aDNA analyses. While undeniably helpful and necessary for apprehending past human activity, their interpretation, based on theories underpinning models developed for island chains, has lagged, leaving a gap in our understanding of processes of occupation and social network systems. The decontextualized nature of the archaeological landscape of the Canaries and a lack of consensus about proper radiocarbon methodologies are some of the factors contributing to heated scholarly debate. Here, for the Canary Islands, the author reviews the current literature on aDNA and discusses settlement theories, the chronological evidence used for occupation models, and how such perspectives align with current thinking on island colonization.

Cointegrating polynomial regressions (CPRs) include deterministic variables, integrated variables, and their powers as explanatory variables. Based on a novel kernel-weighted limit result and a novel functional central limit theorem, this paper shows that the fully modified ordinary least squares (FM-OLS) estimator of Phillips and Hansen (1990, Review of Economic Studies 57, 99–125) is robust to being used in CPRs. Being used in CPRs refers to a widespread empirical practice that treats the integrated variables and their powers, incorrectly, as a vector of integrated variables and uses textbook FM-OLS. Robustness means that this “formal” FM-OLS practice leads to a zero mean Gaussian mixture limiting distribution that coincides with the limiting distribution of the Wagner and Hong (2016, Econometric Theory 32, 1289–1315) application of the FM estimation principle to the CPR case. The only restriction for this result to hold is that all integrated variables to power one are included as regressors. Even though simulation results indicate performance advantages of the Wagner and Hong (2016, Econometric Theory 32, 1289–1315) estimator, partly even in large samples, the results of the paper give an asymptotic foundation to “formal” FM-OLS and thus enlarge the usability of the Phillips and Hansen (1990, Review of Economic Studies 57, 99–125) estimator implemented in many software packages.

The following equations relate y only implicitly to x:(1)(2) In both equations, y is a function of x for a continuous range of (x, y) values in the real x-y plane. (1) represents an ellipse. (2) has been designed by the author to have a solution in the real x-y plane at (−1, 2), and because the function on the left-hand side of (2) meets certain conditions regarding continuity and partial differentiability there must be a line of points in the real x-y plane satisfying (2) and passing continuously through (−1, 2) [1, pp. 23-28].