We describe a system, called nViZn, that implements a language for quantitative graphics. The structure of this system differs from existing statistical graphics, visualization, and mapping systems. Instead of treating a graphics display as a viewer for underlying data, nViZn treats data as an accessory to viewing a graph. nViZn is based on the mathematical definition of the graph of a function...

We begin with defining the ubiquitous concept of a vector space and several properties associated with them, as well as mathematical operations defined on them. The concept of a vector space is, in general, defined over an arbitrary field of scalars. However, we shall restrict ourselves to real vector spaces, i.e. those defined over the field of reals. Definition 2.1 (Vector Space). A real vect...

We present here three different approaches to the problem of modeling mathematically the concept of a nondeterministic mechanism. Each of these three approaches leads to a mathematical definition. We then show that all the three mathematical concepts are equivalent to one another. This insight gives us the option of approaching the wp formalism of Dijkstra from a different viewpoint that is eas...

M.A. Roytberg, Institute of Mathematical Problems in Biology, Pushchino, Russia, Higher School of Economics, Moscow, Russia, [email protected] We propose a new definition of the loop, which on the one hand is a generalization of the definition of Mathews-Turner [1], and on the other hand allows to divide into loops an arbitrary secondary structure, not only the pseudoknot-free structure. Bas...

Relational lattice is a formal mathematical model for Relational algebra. It reduces the set of six classic relational algebra operators to two: natural join and inner union. We continue to investigate Relational lattice properties with emphasis onto axiomatic definition. New results include additional axioms, equational definition for set difference (more generally anti-join), and case study d...

MathML is a complex XML application that can, in fact, benefit from a schema definition. One problem in defining such a schema is to develop an architecture that captures the logical structure of MathML. The MathML definition provides two sorts of markup, presentation markup which captures the notational aspects of mathematics, and content markup which captures the meaning of mathematical expre...

Although many work have been done on corner detection, no generally accepted mathematical definition exists. This paper gives an explicit definition of corner which is based on the multi-orientation nature of corner and presents an algorithm for corner detection based on orientation estimation. Experimental results show that the proposed algorithm is more accurate and noise-robust compared with...

This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...

The widespread use of high level mathematical functions to solve problems in the mathematical and physical sciences has led the National Institute of Standards and Technology to engage in a massive project to update and expand the National Bureau of Standards Handbook of Mathematical Functions [1]. The handbook, which discusses the definition and computations of “special functions”, will be dis...