Tax evasion, information reporting, and the regressive bias hypothesis

A robust prediction from the tax evasion literature is that optimal auditing induces a regressive bias in e¤ective tax rates compared to statutory rates. If correct, this will have important distributional consequences. Nevertheless, the regressive bias hypothesis has never been tested empirically. Using a unique data set, we provide evidence in favor of the regressive bias prediction but only when controlling for the tax agency�s use of third-party information in predicting true incomes. In aggregate data, the regressive bias vanishes because of the systematic use of third-party information. These results are obtained both in simple reduced-form regressions and in a data-calibrated state-of-the-art model

A time-extended Hamiltonian formalism

A Poisson structure on the time-extended space R x M is shown to be appropriate for a Hamiltonian formalism in which time is no more a privileged variable and no a priori geometry is assumed on the space M of motions. Possible geometries induced on the spatial domain M are investigated. An abstract representation space for sl(2,R) algebra with a concrete physical realization by the Darboux-Halphen system is considered for demonstration. The Poisson bi-vector on R x M is shown to possess two intrinsic infinitesimal automorphisms one of which is known as the modular or curl vector field. Anchored to these two, an infinite hierarchy of automorphisms can be generated. Implications on the symmetry structure of Hamiltonian dynamical systems are discussed. As a generalization of the isomorphism between contact flows and their symplectifications, the relation between Hamiltonian flows on R x M and infinitesimal motions on M preserving a geometric structure therein is demonstrated for volume preserving diffeomorphisms in connection with three-dimensional motion of an incompressible fluid.Comment: 14 pages, late

The Bianchi Ix (MIXMASTER) Cosmological Model is Not Integrable

The perturbation of an exact solution exhibits a movable transcendental essential singularity, thus proving the nonintegrability. Then, all possible exact particular solutions which may be written in closed form are isolated with the perturbative Painlev\'e test; this proves the inexistence of any vacuum solution other than the three known ones.Comment: 14 pages, no figure

G3-homogeneous gravitational instantons

We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group. The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3). New and general solutions are found for Bianchi III.Comment: 24 pages, few correction

On the 7th order ODE with submaximal symmetry

We find a general solution to the unique 7th order ODE admitting ten dimensional group of contact symmetries. The integral curves of this ODE are rational contact curves in \PP^3 which give rise to rational plane curves of degree six. The moduli space of these curves is a real form of the homogeneous space $Sp(4)/SL(2)$.Comment: 6 pages, 2 figures. Final version - to appear in JG

Ricci flows and expansion in axion-dilaton cosmology

We study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified with renormalization-group flow and time coordinate can appear as Liouville field. The resulting space-time interpretation is that of a homogeneous isotropic Friedmann-Robertson-Walker universe in axion-dilaton cosmology. We find as general behaviour the superposition of a big-bang (polynomial) expansion with a finite number of oscillations at early times. Any initial anisotropy disappears during the evolution.Comment: 22 page

Analytic doubly periodic wave patterns for the integrable discrete nonlinear Schroedinger (Ablowitz-Ladik) model

We derive two new solutions in terms of elliptic functions, one for the dark and one for the bright soliton regime, for the semi-discrete cubic nonlinear Schroedinger equation of Ablowitz and Ladik. When considered in the complex plane, these two solutions are identical. In the continuum limit, they reduce to known elliptic function solutions. In the long wave limit, the dark one reduces to the collision of two discrete dark solitons, and the bright one to a discrete breather.Comment: 12 pages, 2 figures. To appear, Physics Letters

Detection and construction of an elliptic solution to the complex cubic-quintic Ginzburg-Landau equation

In evolution equations for a complex amplitude, the phase obeys a much more intricate equation than the amplitude. Nevertheless, general methods should be applicable to both variables. On the example of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation (CGL5), we explain how to overcome the difficulties arising in two such methods: (i) the criterium that the sum of residues of an elliptic solution should be zero, (ii) the construction of a first order differential equation admitting the given equation as a differential consequence (subequation method).Comment: 12 pages, no figure, to appear, Theoretical and Mathematical Physic

A new family of surfaces with pg=q=2p_g=q=2 and K2=6K^2=6 whose Albanese map has degree 44

We construct a new family of minimal surfaces of general type with $p_g=q=2$ and $K^2=6$, whose Albanese map is a quadruple cover of an abelian surface with polarization of type $(1,3)$. We also show that this family provides an irreducible component of the moduli space of surfaces with $p_g=q=2$ and $K^2=6$. Finally, we prove that such a component is generically smooth of dimension 4 and that it contains the 2-dimensional family of product-quotient examples previously constructed by the first author. The main tools we use are the Fourier-Mukai transform and the Schr\"odinger representation of the finite Heisenberg group $\mathscr{H}_3$.Comment: 23 pages. To appear in the Journal of the London Mathematical Society. This is a preprint version, slightly different from the published versio

Воздействие альтернативных источников энергии на жизнь человека, перспективы развития в России

Альтернативной энергетике вполне по силам обеспечить энергетическую, экологическую и продовольственную безопасность населения страны на длительную перспективу. Ведь количество энергии, которую человек может уловить, аккумулировать и использовать, всегда оптимально. Данный вид энергетики в основном использует прямую энергию солнца и опосредованно применяется энергия ветра, приливов, отливов, биомассы, геотермальная энергия. В данной статье исследованы перспективы развития альтернативной энергетики в пределах территории России, влияние альтернативной энергетики на жизнь людей, а так же те глобальные проблемы, которые могут быть решены при помощи планового введения альтернативной энергетики. Целью данной работы является выявление явных преимущество альтернативных видов энергетики перед традиционными