We revisit some topics of classical thermostatistics from the perspective of the nonextensive optimal Lagrange multipliers (OLM), a recently introduced technique for dealing with the maximization of Tsallis' information measure. It is shown that Equipartition and Virial theorems can be reproduced by Tsal-lis' nonextensive formalism independently of the value of the nonextensivity index.

We continue the study of multidimensional operator multipliers initiated in [12]. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and...

We give a new combinatorial interpretation of the noncommutative Lagrange inversion formula, more precisely, of the formula of Brouder-FrabettiKrattenthaler for the antipode of the noncommutative Faà di Bruno algebra.

A Bessel generator multiplier for a unitary system is a bounded linear operator that sends Bessel generator vectors to Bessel generator vectors. We characterize some special (but useful) Bessel generator multipliers for the unitary systems that are ordered products of two unitary groups. These include the wavelet and the Gabor unitary systems. We also provide a detailed exposition of some of th...

In this talk we present some results concerning the interpolation of discontinuous functions. First we consider an index of convergence associated to converging subsequences of a general sequence of real numbers (x n) n≥1. Namely, if L ∈ R, the index of convergence of (x n) n≥1 to L is defined by The definition can be extended to the cases L = ±∞ and also to the case where A ⊂ R. In the case wh...

We show that standard expenditure multipliers capture economy-wide effects of new government projects only when financing constraints are not binding. In actual policy making, however, new projects usually need financing. Under liquidity constraints, new projects are subject to two opposite effects: an income effect and a set of spending substitution effects. The former is the traditional, unre...

Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. W...

Reading a book is also kind of better solution when you have no enough money or time to get your own adventure. This is one of the reasons we show the lagrange multiplier approach to variational problems and applications advances in design and control as your friend in spending the time. For more representative collections, this book not only offers it's strategically book resource. It can be a...

It is proved that stability multipliers such as Zames–Falb multipliers, Popov multipliers, and RL/RC multipliers, known to preserve positivity of monotone memoryless nonlinearities, do not, in general, preserve their incremental positivity. Our result implies that stability results based on these multipliers should be interpreted with caution since without incremental positivity the continuity ...

For n 1, let fxjngnj=1 be n distinct points and let Ln[ ] denote the corresponding Lagrange Interpolation operator. Let W : R ! [0;1). What conditions on the array fxjng1 j n; n 1 ensure the existence of p > 0 such that lim n!1 k (f Ln[f ])W b kLp(R)= 0 for every continuous f : R ! Rwith suitably restricted growth, and some “weighting factor” ? We obtain a necessary and su¢ cient condition for ...