Related papers: Geometric visualizations of $b^{e}<e^{b}$ when $e<…
Although general relativity underlies modern cosmology, its applicability on cosmological length scales has yet to be stringently tested. Such a test has recently been proposed, using a quantity, EG, that combines measures of large-scale…
In this paper, we extend the concept of \( b \)-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results…
Irrational numbers are introduced usually already introduced in lower secondary level schools. But typically, maybe with the exception of $\sqrt{2}$, no mathematical proof of irrationality is provided. In particular it is not proven that…
In this note we prove the existence of two proper biharmonic maps between the Euclidean ball of dimension bigger than four and Euclidean spheres of appropriate dimensions. We will also show that, in low dimensions, both maps are unstable…
We prove an analogue of the classical Bernstein polynomial inequality on a compact subset $E$ of the real line. The Lipschitz continuity of the Green function for the complement of $E$ with respect to the extended complex plane and the…
From the beginning of quantum mechanics, there has been a discussion about the concept of reality, as exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell…
Inspired by a didactic experience in an academic environment, and following the idea given by M. Villa in \cite{Villa}, we illustrate two different proofs of an important result in Euclidean geometry studied in the first two years of…
We present a new proof of the sphere covering inequality in the spirit of comparison geometry, and as a byproduct we find another sphere covering inequality which can be viewed as the dual of the original one. We also prove sphere covering…
The traditional optical concept for the object does not provide an experimental feasibility to speak for itself, due to the fact that no measuring instrument catches up with the fluctuation of light fields. Using the theory of coherence, we…
In each of the last five years, a few dozen empirical studies appeared in visualization journals and conferences. The existing empirical studies have already featured a large number of variables. There are many more variables yet to be…
In the classroom, we traditionally visualize inferential concepts using static graphics or interactive apps. For example, there is a long history of using apps to visualize sampling distributions. Recent developments in statistical graphics…
Measurements in quantum theory can fail to be jointly measurable. Like entanglement, this incompatibility of measurements is necessary but not sufficient for violating Bell inequalities. The (in)compatibility relations among a set of…
The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…
We discuss the validity of general relativity at low-energy and relate the threshold below which the theory breaks down with the observed value of the cosmological constant. This suggests the existence of a mass scale of ${\cal O}(10^{-3})…
We developed and validated a rating scale to assess the aesthetic pleasure (or beauty) of a visual data representation: the BeauVis scale. With our work we offer researchers and practitioners a simple instrument to compare the visual…
We describe three methods to determine the structure of (sufficiently continuous) representations of the algebra B^a(E) of all adjointable operators on a Hilbert B-module E by operators on a Hilbert C-module. While the last and latest proof…
We study mappings that satisfy the inverse modulus inequality of Poletsky type with respect to $p$-modulus. Given $n-1<p\leqslant n,$ we show that, the image of some ball contains a fixed ball under mappings mentioned above. This statement…
We introduce the E-measure: a measure-like generalization of the E-value to a class of hypotheses. Unlike classical measures, E-measures are closed under infimums instead of addition. They arise from a compatibility axiom with logical…
The status of experimental tests of general relativity and of theoretical frameworks for analysing them are reviewed. Einstein's equivalence principle (EEP) is well supported by experiments such as the E\"otv\"os experiment, tests of…
A visibility representation of a graph $G$ is an assignment of the vertices of $G$ to geometric objects such that vertices are adjacent if and only if their corresponding objects are "visible" each other, that is, there is an uninterrupted…