Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Carrier Concentration Control of GaSb/GaInAsSb System

International audienc

Structural, Optical and Electrical Characterizations of Midwave Infrared Ga-Free Type-II InAs/InAsSb Superlattice Barrier Photodetector

In this paper, a full set of structural, optical and electrical characterizations performed on midwave infrared barrier detectors based on a Ga-free InAs/InAsSb type-II superlattice, grown by molecular beam epitaxy (MBE) on a GaSb substrate, are reported and analyzed. a Minority carrier lifetime value equal to 1 µs at 80 K, carried out on dedicated structure showing photoluminescence peak position at 4.9 µm, is extracted from a time resolved photoluminescence measurement. Dark current density as low as 3.2 × 10−5 A/cm2 at 150 K is reported on the corresponding device exhibiting a 50% cut-off wavelength around 5 µm. A performance analysis through normalized spectral response and dark current density-voltage characteristics was performed to determine both the operating bias and the different dark current regimes

Una nuova dedica a Ercole da un manoscritto di Bonifacius Amerbach

The manuscript C VI a 77, once belonged to the XVIth century humanist Bonifacius Amerbach and now preserved in the Universitätsbibliothek Basel, is not a high quality epigraphic manuscript, but includes at least a couple of Roman inscriptions elsewhere unknown. One of them, already published in the previous years, is a dedication to Iuppiter Optimus Maximus set by an eques singularis; the other one is a dedication to Hercules Invictus – here published for the first time - set, when he was an urban praetor, by L. Turranius Venustus Gratianus, member of a well known senatorial family of the III/IV century AD

The ubiquitous Prouhet-Thue-Morse sequence

We discuss a well-known binary sequence called the ThueMorse sequence, or the Prouhet-Thue-Morse sequence. This sequence was introduced by Thue in 1906 and rediscovered by Morse in 1921. However, it was already implicit in an 1851 paper of Prouhet. The Prouhet-Thue-Morse sequence appears to be somewhat ubiquitous, and we describe many of its apparently unrelated occurrences

Number Theory And Formal Languages

. I survey some of the connections between formal languages and number theory. Topics discussed include applications of representation in base k, representation by sums of Fibonacci numbers, automatic sequences, transcendence in finite characteristic, automatic real numbers, fixed points of homomorphisms, automaticity, and k-regular sequences. Key words. finite automata, automatic sequences, transcendence, automaticity AMS(MOS) subject classifications. Primary 11B85, Secondary 11A63 11A55 11J81 1. Introduction. In this paper, I survey some interesting connections between number theory and the theory of formal languages. This is a very large and rapidly growing area, and I focus on a few areas that interest me, rather than attempting to be comprehensive. (An earlier survey of this area, written in French, is [1].) I also give a number of open questions. Number theory deals with the properties of integers, and formal language theory deals with the properties of strings. At the interse..