Search results for "algebra"

Simulating Secularities: Challenges and Opportunities in the Computational Science of (Non)Religion

2021

This article provides scholars of nonreligion and secularism with an introduction to some of the major opportunities and challenges associated with the growing application of computational methods to the phenomena they study. It also illustrates these opportunities and challenges by describing several overlapping research projects and some of the models of (non)religion they have produced. Finally, the article addresses some of the significant philosophical issues surrounding the use of computer modeling and simulation, focusing on the ethical and epistemological concerns that these tools often raise. I invite scholars of nonreligion to consider adding these techniques to their methodologic…

A simulation function approach for best proximity point and variational inequality problems

2017

We study sufficient conditions for existence of solutions to the global optimization problem min(x is an element of A) d(x, fx), where A, B are nonempty subsets of a metric space (X, d) and f : A -> B belongs to the class of proximal simulative contraction mappings. Our results unify, improve and generalize various comparable results in the existing literature on this topic. As an application of the obtained theorems, we give some solvability theorems of a variational inequality problem.

Unification of Graphs and Relations in Mizar

2020

Summary A (di)graph without parallel edges can simply be represented by a binary relation of the vertices and on the other hand, any binary relation can be expressed as such a graph. In this article, this correspondence is formalized in the Mizar system [2], based on the formalization of graphs in [6] and relations in [11], [12]. Notably, a new definition of createGraph will be given, taking only a non empty set V and a binary relation E ⊆ V × V to create a (di)graph without parallel edges, which will provide to be very useful in future articles.

Cover Picture: Tumor-Associated MUC1 Tandem-Repeat Glycopeptide Microarrays to Evaluate Serum- and Monoclonal-Antibody Specificity (Angew. Chem. Int.…

2009

Cover Picture: Access to Phylogeny from Voltammetric Fingerprints of Seeds: the Asparagus Case (Electroanalysis 2/2017)

2017

An Enchanted Era Remembered: Interview with Dirk Jan Struik

2018

Dirk J. Struik was born in Rotterdam in 1894, where he attended the Hogere Burger School from 1906–1911 before entering Leiden University. At Leiden he studied algebra and analysis with J. C. Kluyver, geometry with P. Zeeman, and physics under Paul Ehrenfest. After a brief stint as a high school teacher at Alkmaar, he spent seven years at Delft as the assistant to J. A. Schouten, one of the founders of tensor analysis. Their collaboration led to Struik’s dissertation, Grundziige der mehrdimensionalen Differentialgeometrie in direkter Darstellung, published by Springer in 1922, and numerous other works in the years to follow.

Algebraic models of the real affine plane

2017

We introduce a new invariant, the real (logarithmic)-Kodaira dimension, that allows to distinguish smooth real algebraic surfaces up to birational diffeomorphism. As an application, we construct infinite families of smooth rational real algebraic surfaces with trivial homology groups, whose real loci are diffeomorphic to $\mathbb{R}^2$, but which are pairwise not birationally diffeomorphic. There are thus infinitely many non-trivial models of the real affine plane, contrary to the compact case.

Convergence Analysis of Distributed Set-Valued Information Systems

2016

This paper focuses on the convergence of information in distributed systems of agents communicating over a network. The information on which the convergence is sought is not rep- resented by real numbers, as often in the literature, rather by sets. The dynamics of the evolution of information across the net- work is accordingly described by set-valued iterative maps. While the study of convergence of set-valued iterative maps is highly complex in general, this paper focuses on Boolean maps, which are comprised of arbitrary combinations of unions, intersections, and complements of sets. For these important class of systems, we provide tools to study both global and local convergence. A distr…

Gui-driven intelligent tutoring system with affective support to help learning the algebraic method

2017

Despite many research efforts focused on the development of algebraic reasoning and the resolution of story problems, several investigations have reported that relatively advanced students experience serious difficulties in symbolizing certain meaningful relations by using algebraic equations. In this paper, we describe and justify the Graphical User Interface of an Intelligent Tutoring System that allows learning and practising the procedural aspects involved in translating the information contained in a story problem into a symbolic representation. The application design has been driven by cognitive findings from several previous investigations. First, the process of translating a word pr…

Feature extraction from remote sensing data using Kernel Orthonormalized PLS

2007

This paper presents the study of a sparse kernel-based method for non-linear feature extraction in the context of remote sensing classification and regression problems. The so-called kernel orthonormalized PLS algorithm with reduced complexity (rKOPLS) has two core parts: (i) a kernel version of OPLS (called KOPLS), and (ii) a sparse (reduced) approximation for large scale data sets, which ultimately leads to rKOPLS. The method demonstrates good capabilities in terms of expressive power of the extracted features and scalability.