Symbolic calculus on the time-frequency half-plane

The study concerns a special symbolic calculus of interest for signal analysis. This calculus associates functions on the time-frequency half-plane f>0 with linear operators defined on the positive-frequency signals. Full attention is given to its construction which is entirely based on the study of the affine group in a simple and direct way. The correspondence rule is detailed and the associated Wigner function is given. Formulas expressing the basic operation (star-bracket) of the Lie algebra of symbols, which is isomorphic to that of the operators, are obtained. In addition, it is shown that the resulting calculus is covariant under a three-parameter group which contains the affine group as subgroup. This observation is the starting point of an investigation leading to a whole class of symbolic calculi which can be considered as modifications of the original one.Comment: 25 pages, Latex, minor changes and more references; to be published in the "Journal of Mathematical Physics" (special issue on "Wavelet and Time-Frequency Analysis"

Free cooling and high-energy tails of granular gases with variable restitution coefficient

We prove the so-called generalized Haff's law yielding the optimal algebraic cooling rate of the temperature of a granular gas described by the homogeneous Boltzmann equation for inelastic interactions with non constant restitution coefficient. Our analysis is carried through a careful study of the infinite system of moments of the solution to the Boltzmann equation for granular gases and precise Lp estimates in the selfsimilar variables. In the process, we generalize several results on the Boltzmann collision operator obtained recently for homogeneous granular gases with constant restitution coefficient to a broader class of physical restitution coefficients that depend on the collision impact velocity. This generalization leads to the so-called L1-exponential tails theorem. for this model

Topologically Massive Gauge Theories and their Dual Factorised Gauge Invariant Formulation

There exists a well-known duality between the Maxwell-Chern-Simons theory and the self-dual massive model in 2+1 dimensions. This dual description has been extended to topologically massive gauge theories (TMGT) in any dimension. This Letter introduces an unconventional approach to the construction of this type of duality through a reparametrisation of the master theory action. The dual action thereby obtained preserves the same gauge symmetry structure as the original theory. Furthermore, the dual action is factorised into a propagating sector of massive gauge invariant variables and a sector with gauge variant variables defining a pure topological field theory. Combining results obtained within the Lagrangian and Hamiltonian formulations, a new completed structure for a gauge invariant dual factorisation of TMGT is thus achieved.Comment: 1+7 pages, no figure

Aligning a Service Provisioning Model of a Service-Oriented System with the ITIL v.3 Life Cycle

Bringing together the ICT and the business layer of a service-oriented system (SoS) remains a great challenge. Few papers tackle the management of SoS from the business and organizational point of view. One solution is to use the well-known ITIL v.3 framework. The latter enables to transform the organization into a service-oriented organizational which focuses on the value provided to the service customers. In this paper, we align the steps of the service provisioning model with the ITIL v.3 processes. The alignment proposed should help organizations and IT teams to integrate their ICT layer, represented by the SoS, and their business layer, represented by ITIL v.3. One main advantage of this combined use of ITIL and a SoS is the full service orientation of the company.Comment: This document is the technical work of a conference paper submitted to the International Conference on Exploring Service Science 1.5 (IESS 2015

Contractual savings for housing : How suitable are they for transitional economies?

Problems of developing financial services for housing are acute in transitional socialist economies. The authors examine contractual savings for housing (CSH), which are often advocated as a primary solution, especially in Central and Eastern European countries. A CSH instrument links a phase of contractual savings remunerated at below-market rate to the promise of a housing loan at a rate also fixed below market at the time the contract is signed. This contract can contain a variety of options. CSH were used very successfully in Europe after World War II. The issue today is not whether such specialized instruments can work. They clearly can under low inflation. The issue is whether CSH systems are advisable today in latecomer countries with vastly different financial technology and financial policy environments. The authors focus on two influential CSH systems: the"closed"German Bausparsystem and the"open"French epargne-logement. In a"closed"CSH system, access to a housing loan is based on queuing: a loan can be made only if funds are available in the specialist institution. In an"open"system, the saver can legally call his or her loan at contract maturity, regardless of the liquidity conditions in the CSH system. From the perspective of households, CSH contracts facilitate the accumulation of equity and offer the prospect of a low-interest loan. They promote savings discipline and provide a concrete goal that many households find important. But CSH instruments leave the objective of providing a primary loan unmet. In additon, even moderate inflation quickly leads to very low loan-to-value ratios for CSH loans and a large financing gap for housing purchases. From the perspective of financial institutions, CSH can help overcome the severe information asymmetries they face in transitional socialist economies, where there are no retail financial markets, no credit bureaus, problematic income reporting. CSH are very effective in screening, monitoring, and establishing the reputation of steady savers as future borrowers, and they are good at lowering credit risks. With their saving periods of four to five years, CSH also help bridge the gap between long-term loans and short-term deposits. Finally, CSH can be an important commercial tool for developing cross-lending activities. But CSH can be risky. When the interest rate on outstanding contracts is low compared with current market rates, holders of mature contracts will want to call their loans. And new savers will be reluctant to sign on at very low contract rates. Eliminating this liquidity risk with a"closed"CSH system erodes the attractiveness of CSH. From the perspective of government, a CSH instrument can work in a noninflationary environment, yet a CSH system would have no justification in fully developed and competitive financial markets today. CSH instruments can play a useful but not a dominant role in housingfinance. After stabilization, they can overcome information constraints on financial contracts, and contribute to higher financial savings rates. CSH instruments are best used to finance home improvements. They can also be used as part of a social policy to reach targeted social groups.Financial Intermediation,Banks&Banking Reform,Payment Systems&Infrastructure,Public Sector Economics&Finance,Housing Finance,Public Sector Economics&Finance,Banks&Banking Reform,Housing Finance,Financial Intermediation,Non Bank Financial Institutions