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A pedestrian introduction to fast multipole methods
fast multipole method non-oscillatory kernels oscillatory kernels multiscale methods
2015/7/14
This paper provides a conceptual and non-rigorous description of the fast multipole methods for evaluating convolution kernel functions with source distributions. Both the non-oscillatory and the osci...
We consider the set C of pairs of real numbers (x, y), or equivalently of points on the plane R2. Two vectors z1 = (x1, x2) and z2 = (x2, y2) are equal if and only if x1 = x2 and y1 = y2. Two vectors ...
These notes are based on a series of lectures given by the first author at the school of `Poisson 2010', held at IMPA, Rio de Janeiro. They contain an exposition of the theory of super- and graded man...
A pedagogical introduction to the Slavnov formulation of quantum Yang-Mills theory
pedagogical introduction Slavnov formulation quantum Yang-Mills theory
2010/12/16
Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the gho...
Introduction of Frechet and Gateaux derivative
Banach space Fr´ echet differentiability Gˆ ateaux differentiability
2010/9/10
In this paper the Fr´echet and Gˆateaux differentiation of functions on Banach space has been introduced. We investigate the algebraic properties of Fr´echet and Gˆateaux differe...
An introduction of a combined space-time manifold
4-manifolds dark matter dual universe invisible energy
2010/9/15
This paper introduces the term, ”combined manifold,” which essentially is the graph of a diffeomorphism from one manifold to another.Following a previously published article about “invisible energies”...