Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an $L^2$-function on an appropriately chosen group, while the Wigner function is defined on a coadjoint orbit of the group and serves as an alternative characterization of the signal, which is often used in practical applications. The Plancherel transform maps $L^2$-functions on a group unitarily to fields of Hilbert-Schmidt operators, indexed by unitary irreducible representations of the group. The wavelet transform can essentiallly be looked upon as restricted inverse Plancherel transform, while Wigner functions are modified Fourier transforms of inverse Plancherel transforms, usually restricted to a subset of the unitary dual of the group. Some known results both on Wigner functions and wavelet transforms, appearing in the literature from very different perspectives, are naturally unified within our approach. Explicit computations on a number of groups illustrate the theory.Comment: 41 page

Wage determination and wage inequality inside a Russian firm in late transition: Evidence from personnel data – 1997 to 2002.

personnel economics, Russia, transition;wage determination;

Wage Policies of a Russian Firm and the Financial Crisis of 1998: Evidence from Personnel Data - 1997 to 2002

We use a rich personnel data set from a Russian firm for the years 1997 to 2002 to analyze how the financial crisis in 1998 and the resulting change in external labor market conditions affect the wages and the welfare of workers inside a firm. We provide evidence that large shocks to external conditions affect the firm's personnel policies, and show that the burden of the shock is not evenly spread across the workforce. The firm takes advantage of a high-inflationary environment and of a fall in workers' outside options after the financial crisis and cuts real wages. Earnings are curbed most for those who earned the highest rents, resulting in a strong compression of real wages. The fact that real wages and real compensation levels never recovered to pre-crisis levels even though the firm's financial situation was better in 2002 than before the crisis and the differential treatment of employee groups within the firm can be taken as evidence that market forces strongly influence the wage policies of our firm.Internal labor markets, wage policies of a firm, personnel data, Russia

Reentrant transitions in colloidal or dusty plasma bilayers

The phase diagram of crystalline bilayers of particles interacting via a Yukawa potential is calculated for arbitrary screening lengths and particle densities. Staggered rectangular, square, rhombic and triangular structures are found to be stable including a first-order transition between two different rhombic structures. For varied screening length at fixed density, one of these rhombic phases exhibits both a single and even a double reentrant transition. Our predictions can be verified experimentally in strongly confined charged colloidal suspensions or dusty plasma bilayers.Comment: 4 pages, 3 eps figs - revtex4. PRL - in pres

Wage Determination and Wage Inequality Inside a Russian Firm in Late Transition: Evidence from Personnel Data - 1997 to 2002

We use personnel data from a Russian firm for the years 1997 to 2002 to study thedeterminants of wages during transition. Our findings indicate that remuneration isnot predetermined by formal rules and a stable institutionalized structure of wages,but rather that local labor market conditions have a strong impact on wage setting atthe firm level. In particular, we document that real wages fall substantially during aperiod of high inflation and worsening local labor market conditions. Relative wagedecreases are most pronounced for employees who initially earned the highest rents.The process of rent extraction leads to a strong compression of real wages and realcompensation at the firm.

Wage Policies of a Russian Firm and the Financial Crisis of 1998: Evidence from Personnel Data - 1997 to 2002

We use a rich personnel data set from a Russian firm for the years 1997 to 2002 to analyze how the financial crisis in 1998 and the resulting change in external labor market conditions affect the wages and the welfare of workers inside a firm. We provide evidence that large shocks to external conditions affect the firm's personnel policies, and show that the burden of the shock is not evenly spread across the workforce. The firm takes advantage of a high-inflationary environment and of a fall in workers' outside options after the financial crisis and cuts real wages. Earnings are curbed most for those who earned the highest rents, resulting in a strong compression of real wages. The fact that real wages and real compensation levels never recovered to pre-crisis levels even though the firm's financial situation was better in 2002 than before the crisis and the differential treatment of employee groups within the firm can be taken as evidence that market forces strongly influence the wage policies of our firm.Internal labor markets, wage policies of a firm, personnel data, Russia

Statistics of polymer adsorption under shear flow

Using non-equilibrium Brownian dynamics computer simulations, we have investigated the steady state statistics of a polymer chain under three different shear environments: i) linear shear flow in the bulk (no walls), ii) shear vorticity normal to the adsorbing wall, iii) shear gradient normal to the adsorbing wall. The statistical distribution of the chain end-to-end distance and its orientational angles are calculated within our monomer-resolved computer simulations. Over a wide range of shear rates, this distribution can be mapped onto a simple theoretical finite-extensible-nonlinear-elastic dumbbell model with fitted anisotropic effective spring constants. The tails of the angular distribution functions are consistent with scaling predictions borrowed from the bulk dumbbell model. Finally, the frequency of the characteristic periodic tumbling motion has been investigated by simulation as well and was found to be sublinear with the shear rate for the three set-ups, which extends earlier results done in experiments and simulations for free and tethered polymer molecules without adsorption.Comment: 10 figure

Binary crystals in two-dimensional two-component Yukawa mixtures

The zero-temperature phase diagram of binary mixtures of particles interacting via a screened Coulomb pair potential is calculated as a function of composition and charge ratio. The potential energy obtained by a Lekner summation is minimized among a variety of candidate two-dimensional crystals. A wealth of different stable crystal structures is identified including $A,B,AB_2, A_2B, AB_4$ structures [$A$ $(B)$ particles correspond to large (small) charge.] Their elementary cells consist of triangular, square or rhombic lattices of the $A$ particles with a basis comprising various structures of $A$ and $B$ particles. For small charge asymmetry there are no intermediate crystals besides the pure $A$ and $B$ triangular crystals.Comment: RevTeX 4 - 17 pages - 6 main figure