Mathematics

Cayley-Dickson construction

Fri 20 Apr - 2018

The Cayley–Dickson construction produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one. The algebras produced by this process are known as Cayley–Dickson algebras, for example complex numbers, quaternions, octonions, and n -ions in general. Gaea offers a new capability for generating such Cayley-Dickson algebras for general n . Closed-form expressions for the corresponding operations are derived algorithmically and translated into code. Applications of Cayley-Dickson algebras may include quantum theory and supersymmetry.

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Category: 
Mathematics

My Library

Sun 17 Sep - 2017

Here is a list of books that I have read, or I own:

Abelson, H., Sussman, G.J., Sussman, J. (1996). Structure and Interpretation of Computer Programs. The MIT Press. Argyris, J., Faust, G., Haase, M., Friedrich, R. (2010). Die Erforschung des Chaos. Springer-Verlag. Arnold, V.I. (2004). Catastrophe Theory. Springer-Verlag. Arnold, V.I. (1988). Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag. Arnold, V.I. (2004). Lectures on Partial Differential Equations. Springer-Verlag. Arnold, V.I. (1989). Mathemcatical Methods of Classical Mechanics. Springer...
Category: 
Mathematics

ICNAAM 2012, Kos, Greece

Thu 20 Sep - 2012

The 10th international conference of numerical analysis and applied mathematics, ICNAAM 2012 , started yesterday, honoring Gerhard Wanner on the occasion of his 70th birthday. Today, on his talk Gerhard Wanner talked about the work and influence on modern mathematics of Pappus , one of the last great greek mathematicians of antiquity. Pappus is known for his theorem on projective geometry.

The topics of the conference include numerical methods of fluid dynamics, numerical optimization, stochastic differential equations, methods of nanotechnology and nanomaterials,...

Category: 
Mathematics

Chaos economics

Wed 05 Oct - 2011

What is meant by chaos economics? In most economics schools the economics that are taught are standard and classic. The mathematics involved are kept to the minimum in order to be everything well understood, and all problems to be solvable. However, in real life is not like this; this, at least, has shown many economical crisis over the last two centuries. So, we need something different?

One important part of modern economics is time series forecasting. The aim of time series forecasting is to predict how a given variable will evolve in the future knowing its past behavior. Time...

Category: 
Mathematics