Taxation in Walrasian Economy

We consider two models of lump sum taxation in pure exchange economy in which the state imposes taxes on (or offers financial aid to) economic agents characterized by their demand functions and initial resources. In the first model the state has its own preferences and uses the collected money to enter the market and maximize its utility while in the second model it uses the taxes to acquire fixed resources necessary for its functioning. We study the existence and structure of equilibria in general economies, the possibility of using taxation to realize Pareto optimal allocations, and the role of taxation as a possible cause of inflation. Special attention is paid to economies with gross substitutability. Bibliography 18 items.Lump sum taxation, equilibrium, pure exchange economy, regular economy, price adjustment

Entropy on the von Neumann lattice and its evaluation

Based on the recently introduced averaging procedure in phase space, a new type of entropy is defined on the von Neumann lattice. This quantity can be interpreted as a measure of uncertainty associated with simultaneous measurement of the position and momentum observables in the discrete subset of the phase space. Evaluating for a class of the coherent states, it is shown that this entropy takes a stationary value for the ground state, modulo a unit cell of the lattice in such a class. This value for the ground state depends on the ratio of the position lattice spacing and the momentum lattice spacing. It is found that its minimum is realized for the perfect square lattice, i.e., absence of squeezing. Numerical evaluation of this minimum gives 1.386....Comment: 14 pages, no figures; J. Phys. A, in pres

A room temperature CO2_2 line list with ab initio computed intensities

Atmospheric carbon dioxide concentrations are being closely monitored by remote sensing experiments which rely on knowing line intensities with an uncertainty of 0.5% or better. We report a theoretical study providing rotation-vibration line intensities substantially within the required accuracy based on the use of a highly accurate {\it ab initio} dipole moment surface (DMS). The theoretical model developed is used to compute CO$_2$ intensities with uncertainty estimates informed by cross comparing line lists calculated using pairs of potential energy surfaces (PES) and DMS's of similar high quality. This yields lines sensitivities which are utilized in reliability analysis of our results. The final outcome is compared to recent accurate measurements as well as the HITRAN2012 database. Transition frequencies are obtained from effective Hamiltonian calculations to produce a comprehensive line list covering all $^{12}$C$^{16}$O$_2$ transitions below 8000 cm$^{-1}$ and stronger than 10$^{-30}$ cm / molecule at $T=296$~

Multi-Resolution Analysis and Fractional Quantum Hall Effect: an Equivalence Result

In this paper we prove that any multi-resolution analysis of \Lc^2(\R) produces, for some values of the filling factor, a single-electron wave function of the lowest Landau level (LLL) which, together with its (magnetic) translated, gives rise to an orthonormal set in the LLL. We also give the inverse construction. Moreover, we extend this procedure to the higher Landau levels and we discuss the analogies and the differences between this procedure and the one previously proposed by J.-P. Antoine and the author.Comment: Submitted to Journal Mathematical Physisc

Liquid mixing time and gas distribution in aerated multiple-impeller stirred tanks

Gas-liquid fluid dynamics and mass transfer are crucial aspects of aerobic fermentation and robust methodologies for their determination in industrial bioreactors are expected to provide significant improvements in many production processes. In this work, a gas-liquid stirred tank of high aspect ratio, that replicates the geometry of typical industrial aerated fermenters, is investigated. In particular, the liquid phase homogenization dynamics and the gas phase spatial distribution are determined. The selected methodology is based on the analysis of the conductivity measurements obtained by Electrical Resistance Tomography. The gas-liquid flow regimes and the mixing time are identified at various gas flow rates and impeller speeds, thus covering different gas-liquid regimes. Data col lected with vertical and horizontal arrangements of the electrodes allow to obtain a tailed picture of the equipment working mode and to gain insight into the gas-liquid flow dynamics under optically inaccessible conditions. Quantitative evaluation of the bility of the collected data is attempted by comparing the results obtained with the tical and horizontal arrangements in the same locations

von Neumann Lattices in Finite Dimensions Hilbert Spaces

The prime number decomposition of a finite dimensional Hilbert space reflects itself in the representations that the space accommodates. The representations appear in conjugate pairs for factorization to two relative prime factors which can be viewed as two distinct degrees freedom. These, Schwinger's quantum degrees of freedom, are uniquely related to a von Neumann lattices in the phase space that characterizes the Hilbert space and specifies the simultaneous definitions of both (modular) positions and (modular) momenta. The area in phase space for each quantum state in each of these quantum degrees of freedom, is shown to be exactly $h$, Planck's constant.Comment: 16 page

An invariant analytic orthonormalization procedure with applications

We apply the orthonormalization procedure previously introduced by two of us and adopted in connection with coherent states to Gabor frames and other examples. For instance, for Gabor frames we show how to construct $g(x)\in L^2(\Bbb{R})$ in such a way the functions $g_{\underline n}(x)=e^{ian_1x}g(x+an_2)$, $\underline n\in\Bbb{Z}^2$ and $a$ some positive real number, are mutually orthogonal. We discuss in some details the role of the lattice naturally associated to the procedure in this analysis

Emergent Classicality via Commuting Position and Momentum Operators

Any account of the emergence of classicality from quantum theory must address the fact that the quantum operators representing positions and momenta do not commute, whereas their classical counterparts suffer no such restrictions. To address this, we revive an old idea of von Neumann, and seek a pair of commuting operators $X,P$ which are, in a specific sense, "close" to the canonical non-commuting position and momentum operators, $x,p$. The construction of such operators is related to the problem of finding complete sets of orthonormal phase space localized states, a problem severely limited by the Balian-Low theorem. Here these limitations are avoided by restricting attention to situations in which the density matrix is reasonably decohered (i.e., spread out in phase space).Comment: To appear in Proceedings of the 2008 DICE Conferenc

Biochemical correlates of cardiac hypertrophy. I. Experimental model; changes in heart weight, RNA content, and nuclear RNA polymerase activity

Cardiac hypertrophy occurred in mature rats after producing supravalvular aortic stenosis with a specially designed silver clip. For 2 weeks following this procedure, heart weight, body weight, and RNA content of the myocardium were serially determined. Heart weight and RNA content increased within 24 hours of aortic banding, reaching a maximal level in 2 days and remaining elevated during the 2 weeks of observation. Nuclei were isolated and purified from heart muscle homogenates, and changes in RNA polymerase activity following aortic banding were determined. The nearest neighbor frequency of the bases of the RNA synthesized by the polymerase from nuclear preparations was identical in both the banded animals and the sham-operated controls. Both groups could thus be compared on the basis of the enzyme assay. RNA polymerase activity in nuclei from the hearts of banded rats rose rapidly when compared with the activity in sham-operated rats; peak values were reached on the second day, the earliest detectable change being around 12 hours. The increase in RNA polymerase activity represents one of the earliest biochemical events that take place in the myocardium following aortic banding