On properties of (weakly) small groups

A group is small if it has countably many complete $n$-types over the empty set for each natural number n. More generally, a group $G$ is weakly small if it has countably many complete 1-types over every finite subset of G. We show here that in a weakly small group, subgroups which are definable with parameters lying in a finitely generated algebraic closure satisfy the descending chain conditions for their traces in any finitely generated algebraic closure. An infinite weakly small group has an infinite abelian subgroup, which may not be definable. A small nilpotent group is the central product of a definable divisible group with a definable one of bounded exponent. In a group with simple theory, any set of pairwise commuting elements is contained in a definable finite-by-abelian subgroup. First corollary : a weakly small group with simple theory has an infinite definable finite-by-abelian subgoup. Secondly, in a group with simple theory, a normal solvable group A of derived length n is contained in an A-definable almost solvable group of class n

Fields and rings with few types

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It is shown here that a field extension of finite degree of a weakly small field either is a finite field or has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. Every weakly small division ring of positive characteristic is locally finite dimensional over its centre. The Jacobson radical of a weakly small ring is locally nilpotent. Every weakly small division ring is locally, modulo its Jacobson radical, isomorphic to a product of finitely many matrix rings over division rings

Le silence sourd

Le silence est systématiquement associé à la situation du sourd (sourd de naissance, dit « muet ») pour de bonnes et de mauvaises raisons. Pour de mauvaises raisons car la réalité de la situation du sourd est loin de pouvoir être qualifiée de « silencieuse ». Mais aussi pour de bonnes raisons: le sourd fait en quelque sorte résonner chez l’entendant un certain silence suscitant particulièrement le rapport du corps au signifiant, faisant valoir le silence comme présence pulsionnelle du corps dans une énonciation langagière et donc comme présentification pulsionnelle de la voix. Paradoxalement, c’est aussi le rapport de la musique au silence qui s’en trouve éclairé.Silence is systematically associated with the situation of the deaf (those born deaf, the so-called deaf-mutes) for good and bad reasons. Bad, because the reality of the deaf is far from being “silent”. Good, because the deaf make a certain kind of silence resonate in the ear of the non-deaf, especially the relationship between the body and the signifiant, exploiting silence as a pulsional presence of the body in the enunciation of language and thus a pulsional presentification of the voice. Paradoxically, it is the relationship between music and silence that is thereby clarified

On the Generic Type of the Free Group

We answer a question raised by Pillay, that is whether the infinite weight of the generic type of the free group is witnessed in $F_{\omega}$. We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not $\aleph_1$-homogeneous.Comment: To appear in J. of Symbolic Logi

Creating single time-bin entangled photon pairs

When a single emitter is excited by two phase-coherent pulses with a time delay, each of the pulses can lead to the emission of a photon pair, thus creating a ``time-bin entangled'' state. Double pair emission can be avoided by initially preparing the emitter in a metastable state. We show how photons from separate emissions can be made indistinguishable, permitting their use for multi-photon interference. Possible realizations are discussed. The method might also allow the direct creation of n-photon entangled states (n>2).Comment: 4 pages, 1 figur

Life history observations on a few interstitial Opisthobranch gastropods from the Gulf of Marseilles, Bouches du Rhône, France

Foi estudada a vida reprodutiva das 5 espécies dominantes de opistobrânquios mediterrâneos intersticiais do Golfo de Marselha, Bouches-du-Rhône, França. Duas espécies hermafroditas Philine catena e Embletonia pulchra, provaram ser anuais, sendo a duração de vida da última ligeiramente maior que um ano no aquário. Essas duas espécies mostram, em biótopos de alta e média exposições, um único período de recrutamento no verão ou/e no outono, implicando em acasalmento no outono precedente, ovipostura no outono-inverno, eclosão das larvas e estabelecimento dos estádios meiobênticos jovens na areia, durante a estação quente, na primavera-verão. 0 Acochlidacea hermafrodito, Hedylopsis spiculifera, o qual pode sobreviver mais de um ano no aquário, é provavelmente também uma espécie anual, que passa por uma geração por ano. Contudo, uma fase flutuante de 4/5 meses, é registrada entre populações de biótopos de alta e média exposições: nos de média exposição há um recrutamento discreto na primavera enquanto que nos de alta exposição há um recrutamento mais importante no outono. Em biótopos de exposição intermediária há um prolongado período de recrutamento, do fim da primavera ao fim do outono e adultos podem ser observados no inverno e no verão. Os dois Acochlidiacea de sexos separados, Pontohedyle milaschewitschii e Unela glandulifera, mostraram ser espécies sub-anuais, cuja duração de vida é suposta ser não maior do que 6 a 7 meses; de fato, sua manutenção no aquário não ultrapassou algumas semanas. Essas duas espécies podem passar por 2 gerações por ano, desde que elas estejam no seu ambiente ótimo e se 2 estações de aquecimento (ou uma prolongada) forem registradas durante um ano, geralmente primavera e outono no Mediterrâneo. Uma primeira estação de ovipostura é presumida no inverno, eclosão e estabelecimento dos estádios jovens na areia, durante a primavera; esses jovens correspondem, onde e quando sobrevivem, à primeira geração descendente dos estádios adultos, alguns com espermatóforos, do outono precedente, morrendo no inverno após a ovipostura. Uma segunda estação de ovipostura, no verão ou/e outono, eclosão e estabelecimento no outono, corresponde à segunda geração; a última, bem sucedida na maioria dos cascalhos e areias, descende dos estádios adultos da primavera precedente, mortos no outono após a ovipostura. Uma certa fase flutuante é registrada entre populações de biótopos de exposição alta e média e em exposição intermediária parece haver reprodução quase o ano todo, exceto no inverno ou primavera. Os espermatóforos observados em P. milaschewitschii (até 3 por indivíduo) e U. glandulifera (1 ou 2 por indivíduo) são relevantes nos períodos de acasalmento na primavera e no outono

Quantum correlations of two optical fields close to electromagnetically induced transparency

We show that three-level atoms excited by two cavity modes in a $\Lambda$ configuration close to electromagnetically induced transparency can produce strongly squeezed bright beams or correlated beams which can be used for quantum non demolition measurements. The input intensity is the experimental "knob" for tuning the system into a squeezer or a quantum non demolition device. The quantum correlations become ideal at a critical point characterized by the appearance of a switching behavior in the mean fields intensities. Our predictions, based on a realistic fully quantum 3-level model including cavity losses and spontaneous emission, allow direct comparison with future experiments.Comment: 4 pages, 5 figure

Pure emitter dephasing : a resource for advanced solid-state single photon sources

We have computed the spectrum emitted spontaneously by a quantum dot coupled to an arbitrarily detuned single mode cavity, taking into account pure dephasing processes. We show that if the emitter is incoherent, the cavity can efficiently emit photons with its own spectral characteristics. This effect opens unique opportunities for the development of devices exploiting both cavity quantum electrodynamics effects and pure dephasing, such as wavelength stabilized single photon sources robust against spectral diffusion.Comment: 5 pages, 3 figure

Stability and stable groups in continuous logic

We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity