We present the formalism of sequential and asynchronous processes defined in terms of random or quantum grammars and argue that these processes have relevance in genomics. To make the article accessible to the non-mathematicians, we keep the mathematical exposition as elementary as possible, focusing on some general ideas behind the formalism and stating the implications of the known mathematic...

The availability of mathematical knowledge on the Web changes mathematical practices. In a study of professional mathematicians’ search behavior we identified ten behavioral patterns particular to mathematicians. In this paper, we present a set of design goals for mathematical search interfaces implied by these patterns and insights derived from them.

1.1. This article surveys some developments in pure mathematics which have, to varying degrees, grown out of the ideas of gauge theory in Mathematical Physics. The realisation that the gauge fields of particle physics and the connections of differential geometry are one and the same has had wide-ranging consequences, at different levels. Most directly, it has lead mathematicians to work on new ...

Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical mathematical theories. One of the challenging problems in knot distinguishing mutant knots. Mutant knots are not distinguished colored HOMFLY-PT polynomials either symmetric or antisymmetric representations $SU(N)$. Some can be simplest non-symmetric representation $[2...

Singular perturbation problems have been studied by many mathematicians. Since the approximate solutions of these problems are as the sum of internal solution (boundary layer area) and external ones, the formation or non-formation of boundary layers should be specified. This paper, investigates this issue for a singular perturbation problem including a first order differential equation with gen...

Despite centuries of using mathematical notation, surprisingly little is known about how mathematicians perceive equations. The present experiment provides an initial step in understanding what sort of internal representation is used by experienced mathematicians. In particular, we examined if mathematical syntax plays a role in how mathematicians encode algebraic equations, or if just a simple...

1. INTRODUCTION AND EARLY DEVELOPMENTS. Logic and foundations are a domain of mathematics concerned with basic mathematical structures (in terms of which one can define all other mathematical structures), with the correctness and significance of mathematical reasoning, and with the effectiveness of mathematical computations. In the twentieth century, these areas have crystallized into three lar...