Related papers: Marching in squares
The satisfactory development of Quaternionic Analysis has indicated new solutions for physical and mathematical problems. It is worth mentioning the fact that quaternions possess four dimensions, and in this way they may be considered as…
In this paper we present an introduction to morphological calculus in which geometrical objects play the rule of generalised natural numbers.
We provide a self-contained introduction to finite extensive games with perfect information. In these games players proceed in turns having, at each stage, finitely many moves to their disposal, each play always ends, and in each play the…
We present a mathematical model to predict pedestrian motion over a finite horizon, intended for use in collision avoidance algorithms for autonomous driving. The model is based on a road map structure, and assumes a rational pedestrian…
Mathematicians judge proofs to possess, or lack, a variety of different qualities, including, for example, explanatory power, depth, purity, beauty and fit. Philosophers of mathematical practice have begun to investigate the nature of such…
The number of walks from one vertex to another in a finite graph can be counted by the adjacency matrix. In this paper, we prove two theorems that connect the graph Laplacian with two types of walks in a graph. By defining two types of…
This is a survey article on distance-squared mappings and related topics.
This is not in any way meant to be a complete survey on positive curvature. Rather it is a short essay on the fascinating changes in the landscape surrounding positive curvature. In particular, details and many results and references are…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
We define a magic square to be a square matrix whose entries are nonnegative integers and whose rows, columns, and main diagonals sum up to the same number. We prove structural results for the number of such squares as a function of the…
Remarks on mathematical proof and the practice of mathematics.
Quantum random walks have received much interest due to their non-intuitive dynamics, which may hold the key to a new generation of quantum algorithms. What remains a major challenge is a physical realization that is experimentally viable…
Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and…
In this paper we construct a geometric analogue of the Weil representation over a finite field. Our construction is principally invariant, not choosing any specific realization. This eliminates most of the unpleasant formulas that appear in…
We experimentally demonstrate that the statistical properties of distances between pedestrians which are hindered from avoiding each other are described by the Gaussian Unitary Ensemble of random matrices. The same result has recently been…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
In the field of enumeration of weighted walks confined to the quarter plane, it is known that the generating functions behave very differently depending on the chosen step set; in practice, the techniques used in the literature depend on…
In this paper, we consider the existence of a factorization of a monic, bounded motion polynomial. We prove existence of factorizations, possibly after multiplication with a real polynomial and provide algorithms for computing polynomial…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
Two-dimensional (random) walks in cones are very natural both in combinatorics and probability theory: they are interesting for themselves and also because they are strongly related to other discrete structures. While walks restricted to…