We have first demonstrated that Debreu’s view regarding the publication of The Theory of Games and Economic Behavior by von Neumann and Morgenstern in 1944 as the birth of modern mathematical economics is not convincing. In this paper, we have proposed the hypothesis that the coordinated research programs in the 1930’s, initiated by the Econometric Society and the Cowles Commission for Research...

We draw an analogy between Godel's Incompleteness Theorem in mathematics, and the impossibility of achieving a Universal Computer in computer science. Speci cally, Godel proved that there exist formal systems of mathematics that are consistent but not complete. In the same way, we show that there does not exist a general-purpose computer that is universal in the sense of being able to simulat...

This article reconsiders the Austrian school’s historical position regarding role of mathematics in economics light complexity economics’ approach to this issue. It first shows three typical objections traditional use raised by economics. Secondly, it presents critique algebraic mathematics, which is employed mainstream economics, and its proposal for using algorithmic computation. Then, analyz...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

Numerical homotopy continuation of solutions to polynomial equations is the foundation for numerical algebraic geometry, whose development has been driven by applications of mathematics. We use numerical homotopy continuation to investigate the problem in pure mathematics of determining Galois groups in the Schubert calculus. For example, we show by direct computation that the Galois group of t...

We investigate the three strand positive braid monoid. We propose a syntactical linear time algorithm for the word problem, a nearly canonical rewriting system and the computation of the growth function. Mathematics Subjects Classi cation : 20F36, 20F10, 68R15.

the volterra model is widely used for nonlinearity identification in practical applications. in this paper, we employed volterra model to find the nonlinearity relation between electroencephalogram (eeg) signal and the noise that is a novel approach to estimate noise in eeg signal. we show that by employing this method. we can considerably improve the signal to noise ratio by the ratio of at le...