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We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...
Let R be a unital commutative ring, and let M be an R-module that is generated by k elements but not less. Let be the subgroup of generated by the elementary matrices. In this paper we study the action of by matrix multiplication on the set of unimodular r ...
Precipitation is a process wherein a solid phase forms from a solution. Precipitation is at the heart of many industries producing pharmaceuticals, catalysts, ceramics, and nanoparticles. In addition to being a material synthesis route, precipitation has i ...
Let F 2 C[x; y; z] be a constant-degree polynomial, and let A; B; C subset of C be finite sets of size n. We show that F vanishes on at most O(n(11/6))points of the Cartesian product A X B X C, unless F has a special group-related form. This improves a the ...
X-ray irradiation has been extensively used in recent years as a fabrication step for nanoparticles and nanoparticle systems. A variant of this technique, continuous-flow X-ray irradiation, has recently been developed, and offers three important advantages ...
X-ray irradiation has been extensively used in recent years as a fabrication step for nanoparticles and nanoparticle systems. A variant of this technique, continuous-flow X-ray irradiation, has recently been developed, and offers three important advantages ...
Let epsilon be a set of points in F-q(d). Bennett et al. (2016) proved that if \epsilon\ >> [GRAHICS] then epsilon determines a positive proportion of all k-simplices. In this paper, we give an improvement of this result in the case when epsilon is the Car ...
Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors v(1), ..., v(m) is an element of R-d and a constraint family B subset of 2([m]), find a set S. B that maximizes the squared volume of the sim ...
We present asymptotically sharp inequalities for the eigenvalues mu(k) of the Laplacian on a domain with Neumann boundary conditions, using the averaged variational principle introduced in [14]. For the Riesz mean R-1(z) of the eigenvalues we improve the k ...
This study aims at understanding different students approaches for solving assignments in MOOCs. It makes use of a large dataset of logs from students interaction with the MOOC platform Coursera on a course about functional programming with Scala. In total ...
