Enumeration of the Monomials of a Polynomial and Related Complexity Classes

We study the problem of generating monomials of a polynomial in the context of enumeration complexity. In this setting, the complexity measure is the delay between two solutions and the total time. We present two new algorithms for restricted classes of polynomials, which have a good delay and the same global running time as the classical ones. Moreover they are simple to describe, use little evaluation points and one of them is parallelizable. We introduce three new complexity classes, TotalPP, IncPP and DelayPP, which are probabilistic counterparts of the most common classes for enumeration problems, hoping that randomization will be a tool as strong for enumeration as it is for decision. Our interpolation algorithms proves that a lot of interesting problems are in these classes like the enumeration of the spanning hypertrees of a 3-uniform hypergraph. Finally we give a method to interpolate a degree 2 polynomials with an acceptable (incremental) delay. We also prove that finding a specified monomial in a degree 2 polynomial is hard unless RP = NP. It suggests that there is no algorithm with a delay as good (polynomial) as the one we achieve for multilinear polynomials

Denis Diderot 'Rameau's Nephew' - 'Le Neveu de Rameau'

"In a famous Parisian chess café, a down-and-out, HIM, accosts a former acquaintance, ME, who has made good, more or less. They talk about chess, about genius, about good and evil, about music, they gossip about the society in which they move, one of extreme inequality, of corruption, of envy, and about the circle of hangers-on in which the down-and-out abides. The down-and-out from time to time is possessed with movements almost like spasms, in which he imitates, he gestures, he rants. And towards half past five, when the warning bell of the Opera sounds, they part, going their separate ways. Probably completed in 1772-73, Denis Diderot’s Rameau’s Nephew fascinated Goethe, Hegel, Engels and Freud in turn, achieving a literary-philosophical status that no other work by Diderot shares. This interactive, multi-media and bilingual edition offers a brand new translation of Diderot’s famous dialogue, and it also gives the reader much more. Portraits and biographies of the numerous individuals mentioned in the text, from minor actresses to senior government officials, enable the reader to see the people Diderot describes, and provide a window onto the complex social and political context that forms the backdrop to the dialogue. Links to musical pieces specially selected by Pascal Duc and performed by students of the Conservatoire national supérieur de musique et de danse de Paris, illuminate the wider musical context of the work, enlarging it far beyond its now widely understood relation to opéra comique. This new edition includes: - Introduction - Original text - English translation - Embedded audio-files - Explanatory Notes - Interactive Material

Rank differences for overpartitions

In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulas for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulas for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.Comment: 17 pages, final version, accepted for publication in the Quarterly Journal of Mathematic

Scattering rates and lifetime of exact and boson excitons

Although excitons are not exact bosons, they are commonly treated as such provided that their composite nature is included in effective scatterings dressed by exchange. We here \emph{prove} that, \emph{whatever these scatterings are}, they cannot give both the scattering rates $T_{ij}^{-1}$ and the exciton lifetime $\tau_0$, correctly: A striking factor 1/2 exists between $\tau_0^{-1}$ and the sum of $T_{ij}^{-1}$'s, which originates from the composite nature of excitons, irretrievably lost when they are bosonized. This result, which appears as very disturbing at first, casts major doubts on bosonization for problems dealing with \emph{interacting} excitons

Theory of spin precession monitored by laser pulse

We first predict the splitting of a spin degenerate impurity level when this impurity is irradiated by a circularly polarized laser beam tuned in the transparency region of a semiconductor. This splitting, which comes from different exchange processes between the impurity electron and the virtual pairs coupled to the pump beam, induces a spin precession around the laser beam axis, which lasts as long as the pump pulse. It can thus be used for ultrafast spin manipulation. This effect, which has similarities with the exciton optical Stark effect we studied long ago, is here derived using the concepts we developed very recently to treat many-body interactions between composite excitons and which make the physics of this type of effects quite transparent. They, in particular, allow to easily extend this work to other experimental situations in which a spin rotates under laser irradiation.Comment: 12 pages + 1 figur

Recueil de planches, sur les sciences, les arts libéraux et les arts mechaniques avec leur explication : tome III

Contiene : Letras C-DTexto a dos col.Antep.Port. con grab. xil.Grab. calc. en todo el vol.Enc. Past

Recueil de planches, sur les sciences, les arts libéraux et les arts mechaniques avec leur explication : tome VIII

Texto a dos col.Antep.Port. con grab. xil.Grab. calc. en todo el vol.Enc. Past