Singular ARMA signals

Singular random signals are characterized by the fact that their values at each time are singular random variables, which means that their distribution functions are continuous but with a derivative almost everywhere equal to zero. Such random variables are usually considered as without interest in engineering or signal processing problems. The purpose of this paper is to show that very simple signals can be singular. This is especially the case for autoregressive moving average (ARMA) signals defined by white noise taking only discrete values and filters with poles located in a circle of singularity introduced in this paper. After giving the origin of singularity and analyzing its relationships with fractal properties, various simulations highlighting this structure will be presented

Canonical bases of q-deformed Fock spaces

We define a canonical basis of the $q$-deformed Fock space representation of the affine Lie algebra \glchap_n. We conjecture that the entries of the transition matrix between this basis and the natural basis of the Fock space are $q$-analogues of decomposition numbers of the $v$-Schur algebras for $v$ specialized to a $n$th root of unity.Comment: 7 pages, LaTe

Littlewood-Richardson coefficients and Kazhdan-Lusztig polynomials

We show that the Littlewood-Richardson coefficients are values at 1 of certain parabolic Kazhdan-Lusztig polynomials for affine symmetric groups. These q-analogues of Littlewood-Richardson multiplicities coincide with those previously introduced in terms of ribbon tableaux.Comment: 51 pages, 10 Figures, Minor corrections and typos, and some new comments concerning Soergel's character formula for tilting module

Fine structure of high-energy absorption cross sections for black holes

The high-energy absorption cross section of the Schwarzschild black hole is well approximated, in the eikonal regime, by the sum of two terms: the geometrical cross section of the black hole photon sphere and the contribution of a sinc function involving the geometrical characteristics (orbital period and Lyapunov exponent) of the null unstable geodesics lying on this photon sphere. From a numerical analysis, we show that, beyond the eikonal description, this absorption cross section presents a simple fine structure. We then describe it analytically by using Regge pole techniques and interpret it in geometrical terms. We naturally extend our analysis to arbitrary static spherically symmetric black holes endowed with a photon sphere and we then apply our formalism to Schwarzschild-Tangherlini and Reissner-Nordstr\"om black holes. Finally, on the example of the Schwarzschild black hole, we show numerically that a complicated hyperfine structure lying beyond the fine structure can also be observed.Comment: v2: Minor corrections; v3: Minor changes to match the published versio

Flag varieties and the Yang-Baxter equation

We investigate certain bases of Hecke algebras defined by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coefficients in the expansion of the Yang-Baxter basis on the usual basis of the algebra with specializations of double Schubert polynomials. We also describe the expansions associated to other specializations of the generic Hecke algebra.Comment: 14 pages, latex. To appear in Lett. Math. Phy

Quebec's Green Future: The Lowest-Cost Route to Green Gas Reductions

The authors say Quebec’s efforts to reduce greenhouse gas (GHG) emissions must face some key facts. First, the possibilities of an effective reduction of GHG emissions through the substitution of one energy source for another are limited in Quebec. Second, Quebec’s era of low-cost hydroelectric production is finished. And third, low domestic electricity prices favour heavy usage and limit Quebec’s capacity to export clean hydroelectricity. This Backgrounder is also available in French.economic growth and innovation, greenhouse gas emissions (GHG), Quebec, carbon tax