Special non uniform lattice (snulsnul) orthogonal polynomials on discrete dense sets of points.

Difference calculus compatible with polynomials (i.e., such that the divided difference operator of first order applied to any polynomial must yield a polynomial of lower degree) can only be made on special lattices well known in contemporary $q-$calculus. Orthogonal polynomials satisfying difference relations on such lattices are presented. In particular, lattices which are dense on intervals ($|q|=1$) are considered

Dynamic core-theoretic cooperation in a two-dimensional international environmental model

stock pollutant, capital accumulation, international environmental agreements, dynamic core solution

Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials

AbstractRecurrence coefficients of semi-classical orthogonal polynomials (orthogonal polynomials related to a weight function w such that w′w is a rational function) are shown to be solutions of nonlinear differential equations with respect to a well-chosen parameter, according to principles established by D. Chudnovsky and G. Chudnovsky. Examples are given. For instance, the recurrence coefficients in an + 1Pn + 1 (x) = xpn(x) − anpn − 1 (x) of the orthogonal polynomials related to the weight exp (− x44 − tx2) on R satisfy 4an3än = (3an4 + 2tan2 − n)(an4 + 2tan2 + n), and an2 satisfies a Painlevé PIV equation

Toeplitz matrix techniques and convergence of complex weight Padé approximants

AbstractOne considers diagonal Padé approximants about ∞ of functions of the form f(z)=∫−11(z−x)−1w(x)dx,z∉[−1,1], where w is an integrable, possibly complex-valued, function defined on [-1, 1].Convergence of the sequence of diagonal Padé approximants towards f is established under the condition that there exists a weight ω, positive almost everywhere on [-1, 1], such that g(x)=w(x)/ω(x) is continuous and not vanishing on [-1, 1].The rate of decrease of the error is also described.The proof proceeds by establishing the link between the Padé denominators and the orthogonal polynomials related to ω, in terms of the Toeplitz matrix of symbol g(cos Φ)

Should developing countries participate in the Clean Development Mechanism under the Kyoto Protocol ? The low-hanging fruits and baseline issues

Under the Kyoto Protocol, industrialized countries committed to emission reductions may fullfil part of their obligations by implementing emission reduction projects in developing countries. In doing so, they make use of the so-called Clean Development Mechansim (CDM). Two important issues surround the implementation of the CDM. First, if the cheapest abatment measures are implemented for CDM projects, developing countries may be left with only more expensive measures when they have to meet their own commitments in the future (the so-called low-hanging fruits issue). Second, a choice must be made on the type of baseline against which emission reductions are measured : an absolute baseline or a relative (to output) one (the baseline issue). The purpose of this paper is to study the interactions between these two issues from the point of view of the developing country. Two major results are obtained. First, when possible future commitments for developing countries and irreversibility of abatement measures are taken into account, we show that the industry where CDM projects are implemented enjoys large profits under an absolute baseline than under a relative one. Second, concerning the low-hanging fruits problem, the financial compensation required by the developing country for implementing ‘too many’ CDM projects is larger under the relative baseline.

Rational interpolation to solutions of Riccati difference equations on elliptic lattices

AbstractIt is shown how to define difference equations on particular lattices {xn}, n∈Z, where the xns are values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations (elliptic Riccati equations) have remarkable simple (!) interpolatory continued fraction expansions