30,338 research outputs found
On the spectrum of genera of quotients of the Hermitian curve
We investigate the genera of quotient curves of the -maximal Hermitian curve , where is contained in the
maximal subgroup fixing a pole-polar
pair with respect to the unitary polarity associated with . To this aim, a geometric and group-theoretical description of is given. The genera of some other quotients with
are also computed. Thus we obtain new values in the
spectrum of genera of -maximal curves. A plane model for
is obtained when is cyclic of order , with a
divisor of
Economic inequality and mobility in kinetic models for social sciences
Statistical evaluations of the economic mobility of a society are more
difficult than measurements of the income distribution, because they require to
follow the evolution of the individuals' income for at least one or two
generations. In micro-to-macro theoretical models of economic exchanges based
on kinetic equations, the income distribution depends only on the asymptotic
equilibrium solutions, while mobility estimates also involve the detailed
structure of the transition probabilities of the model, and are thus an
important tool for assessing its validity. Empirical data show a remarkably
general negative correlation between economic inequality and mobility, whose
explanation is still unclear. It is therefore particularly interesting to study
this correlation in analytical models. In previous work we investigated the
behavior of the Gini inequality index in kinetic models in dependence on
several parameters which define the binary interactions and the taxation and
redistribution processes: saving propensity, taxation rates gap, tax evasion
rate, welfare means-testing etc. Here, we check the correlation of mobility
with inequality by analyzing the mobility dependence from the same parameters.
According to several numerical solutions, the correlation is confirmed to be
negative.Comment: 11 pages, 6 figures. Proceedings of the Sigma-Phi Conference on
Statistical Physics, Rhodes, 201
Extended Hamiltonians and shift, ladder functions and operators
In recent years, many natural Hamiltonian systems, classical and quantum,
with constants of motion of high degree, or symmetry operators of high order,
have been found and studied. Most of these Hamiltonians, in the classical case,
can be included in the family of extended Hamiltonians, geometrically
characterized by the structure of warped manifold of their configuration
manifold. For the extended manifolds, the characteristic constants of motion of
high degree are polynomial in the momenta of determined form. We consider here
a different form of the constants of motion, based on the factorization
procedure developed by S. Kuru, J. Negro and others. We show that an important
subclass of the extended Hamiltonians admits factorized constants of motion and
we determine their expression. The classical constants may be non-polynomial in
the momenta, but the factorization procedure allows, in a type of extended
Hamiltonians, their quantization via shift and ladder operators, for systems of
any finite dimension.Comment: 25 page
Indicator function and complex coding for mixed fractional factorial designs
In a general fractional factorial design, the -levels of a factor are
coded by the -th roots of the unity. This device allows a full
generalization to mixed-level designs of the theory of the polynomial indicator
function which has already been introduced for two level designs by Fontana and
the Authors (2000). the properties of orthogonal arrays and regular fractions
are discussed
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