4,476 research outputs found
Some Applications of Fractional Equations
We present two observations related to theapplication of linear (LFE) and
nonlinear fractional equations (NFE). First, we give the comparison and
estimates of the role of the fractional derivative term to the normal diffusion
term in a LFE. The transition of the solution from normal to anomalous
transport is demonstrated and the dominant role of the power tails in the long
time asymptotics is shown. Second, wave propagation or kinetics in a nonlinear
media with fractal properties is considered. A corresponding fractional
generalization of the Ginzburg-Landau and nonlinear Schrodinger equations is
proposed.Comment: 11 page
Fokker-Planck Equation with Fractional Coordinate Derivatives
Using the generalized Kolmogorov-Feller equation with long-range interaction,
we obtain kinetic equations with fractional derivatives with respect to
coordinates. The method of successive approximations with the averaging with
respect to fast variable is used. The main assumption is that the correlator of
probability densities of particles to make a step has a power-law dependence.
As a result, we obtain Fokker-Planck equation with fractional coordinate
derivative of order .Comment: LaTeX, 16 page
Six signed Petersen graphs, and their automorphisms
Up to switching isomorphism there are six ways to put signs on the edges of
the Petersen graph. We prove this by computing switching invariants, especially
frustration indices and frustration numbers, switching automorphism groups,
chromatic numbers, and numbers of proper 1-colorations, thereby illustrating
some of the ideas and methods of signed graph theory. We also calculate
automorphism groups and clusterability indices, which are not invariant under
switching. In the process we develop new properties of signed graphs,
especially of their switching automorphism groups.Comment: 39 pp., 7 fi
Totally frustrated states in the chromatic theory of gain graphs
We generalize proper coloring of gain graphs to totally frustrated states,
where each vertex takes a value in a set of `qualities' or `spins' that is
permuted by the gain group. (An example is the Potts model.) The number of
totally frustrated states satisfies the usual deletion-contraction law but is
matroidal only for standard coloring, where the group action is trivial or
nearly regular. One can generalize chromatic polynomials by constructing spin
sets with repeated transitive components.Comment: 14 pages, 2 figure
Sampling from a Bayesian Menu
Discussion of "Bayesian Models and Methods in Public Policy and Government
Settings" by S. E. Fienberg [arXiv:1108.2177]Comment: Published in at http://dx.doi.org/10.1214/11-STS331C the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
The prevention of wind erosion in agriculture
The wind erosion is a problem over more than 80 000 hectares in the Netherlands. The damage in wind erodible areas is on the average at least 150 Dfl. per hectare per year. A lot of damages very probably pass unobserved or unreported
- …