Dual-frequency single-axis laser using a lead lanthanum zirconate tantalate (PLZT) birefringent etalon for millimeter wave generation: beyond the standard limit of tunability

We demonstrate the generation of optically carried, broadly tunable, millimeter-wave signals with a dual-frequency single-axis Nd:YAG laser. A frequency difference as high as 127 GHz is reached thanks to an intracavity electro-optically tunable etalon made of lead zirconate tantalate (PLZT) ceramic. We show that the available frequency range is actually limited by the bandwidth of the amplification medium, namely, far beyond the usually accepted free spectral range value in the case of a single-axis laser. Both coarse discrete and fine continuous tunabilities are obtained with the same voltage-controlled device, opening the way to widely tunable low-phase-noise optically carried submillimeter or even terahertz sources.     

A general extension theorem for cohomology classes on non reduced analytic subspaces

The main purpose of this paper is to generalize the celebrated L~2 extension theorem of Ohsawa and Takegoshi in several directions: The holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety from which the extension is performed may be non reduced, the ambient manifold is K¨ahler and holomorphically convex, but not necessarily compact.     

A Logical Analysis of the Anselm’s Unum Argumentum (from <Emphasis Type="BoldItalic">Proslogion</Emphasis>)

Anselm of Cantorbery wrote Proslogion (1077–1078), where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, that “quod non posit cogitare non esse” by using the hypothesis: “to think in re” is taller than “to think in solo intelectu”. We discuss this relation and the difference between the meanings of the elementary predicates ‘to be in re’, ‘to be in intellectu’ and ‘to be in solo intellectu’. We propose a new logical approach of this ‘Unum argumentum’ of Anselm by using Curry’s Combinatory Logic (1958, 1973). Indeed, Combinatory Logic is an abstract applicative formalism of operators applied to operands; in this formalism, the predicates, viewed as specific operators, can be composed and can be transformed, by an intrinsic way, into more complex predicates, by means of abstract operators, called “combinators”, studied by Combinatory Logic. We show that this formalism is a logical frame where it becomes possible to discuss and to formulate cognitive representations of the meanings of predicates used inside of the ‘Unum argumentum’ and to explain how the argument runs.     

Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

CLT for Random Walks of Commuting Endomorphisms on Compact Abelian Groups

Let \(\mathcal S\) be an abelian group of automorphisms of a probability space \((X, {\mathcal A}, \mu )\) with a finite system of generators \((A_1, \ldots , A_d).\) Let \(A^{{\underline{\ell }}}\) denote \(A_1^{\ell _1} \ldots A_d^{\ell _d}\), for \({{\underline{\ell }}}= (\ell _1, \ldots , \ell _d).\) If \((Z_k)\) is a random walk on \({\mathbb {Z}}^d\), one can study the asymptotic distribution of the sums \(\sum _{k=0}^{n-1} \, f \circ A^{\,{Z_k(\omega )}}\) and \(\sum _{{\underline{\ell }}\in {\mathbb {Z}}^d} {\mathbb {P}}(Z_n= {\underline{\ell }}) \, A^{\underline{\ell }}f\), for a function f on X. In particular, given a random walk on commuting matrices in \(SL(\rho , {\mathbb {Z}})\) or in \({\mathcal M}^*(\rho , {\mathbb {Z}})\) acting on the torus \({\mathbb {T}}^\rho \), \(\rho \ge 1\), what is the asymptotic distribution of the associated ergodic sums along the random walk for a smooth function on \({\mathbb {T}}^\rho \) after normalization? In this paper, we prove a central limit theorem when X is a compact abelian connected group G endowed with its Haar measure (e.g., a torus or a connected extension of a torus), \(\mathcal S\) a totally ergodic d-dimensional group of commuting algebraic automorphisms of G and f a regular function on G. The proof is based on the cumulant method and on preliminary results on random walks.     

Spontaneous symmetry-breaking in the 3-D wake of a long cylinder simulated by the lattice gas method and drag coefficient measurements

We present a direct numerical simulation by the lattice gas method of the three-dimensional non-stationary incompressible flow at a Reynolds number of 74, past a circular cylinder, with a uniform incident flow. We describe the three-dimensional structure and the time-evolution of the wake, which leads to an oblique vortex shedding situation.We also present early results on measurements of drag coefficients for spheres and cylinders at a Reynolds number of 20.     

Selectivity among two lectins: probing the effect of topology, multivalency and flexibility of "clicked" multivalent glycoclusters

The design of multivalent glycoconjugates has been developed over the past decades to obtain high-affinity ligands for lectin receptors. While multivalency frequently increases the affinity of a ligand for its lectin through the so-called "glycoside cluster effect", the binding profiles towards different lectins have been much less investigated. We have designed a series of multivalent galactosylated glycoconjugates and studied their binding properties towards two lectins, from plant and bacterial origins, to determine their potential selectivity. The synthesis was achieved through copper(I)-catalysed azide-alkyne cycloaddition (CuAAC) under microwave activation between propargylated multivalent scaffolds and an azido-functionalised carbohydrate derivative. The interactions of two galactose-binding lectins from Pseudomonas aeruginosa (PA-IL) and Erythrina cristagalli (ECA) with the synthesized glycoclusters were studied by hemagglutination inhibition assays (HIA), surface plasmon resonance (SPR) and isothermal titration microcalorimetry (ITC). The results obtained illustrate the influence of the scaffold's geometry on the affinity towards the lectin and also on the relative potency in comparison with a monovalent galactoside reference probe.     

Transition-metal-complexed cyclic [3]- and [4]pseudorotaxanes containing rigid ring-and-filament conjugates: synthesis and solution studies

By using the "gathering-and-threading" effect of copper(I) with rigid ring-and-string conjugates, daisy-chain-type [3]- and [4]pseudorotaxanes could be prepared in high yields. The organic fragment used consisted of a 2,9-diphenyl-1,10-phenanthroline (dpp)-containing ring attached to a coordinating filament capable of threading through the ring of another molecule by coordination to copper(I). The bidentate chelate introduced in the axis was also a 1,10-phenanthroline (phen) derivative with two methyl groups ortho to the nitrogen atoms of the phen unit. The organic component was prepared following a multistep strategy, one of the key steps being the attachment of the ring to the lateral axis. This connection was done by a condensation reaction between an ortho dione located at the back of a ring-incorporated phen and an aromatic aldehyde, which was the end-function of the thread. An oxazole nucleus was obtained after the condensation, which provided a rigid connection between the ring and the axis. In this way, the coordination axes of the ring-incorporated bidentate chelate and of the ligand belonging to the lateral filament were approximately orthogonal to one another. The design was such that the tetrameric complex, a [4]pseudorotaxane, seemed to be the most stable species, owing to the mutual geometrical arrangement of the filament and the ring. Various spectroscopic techniques, such as (1)H NMR spectroscopy, including DOSY, and electrospray ionization mass spectroscopy (ESI-MS), clearly demonstrated that a mixture of cyclic [3]- and [4]pseudorotaxane was obtained; the proportions of both components depended on concentration and temperature. Copper(I) was not the only metal center leading to the formation of cyclic pseudorotaxanes. A similar effect was observed with silver(I) as the templating metal: quantitative formation of threaded species was observed, with a higher proportion of trimer over tetramer than in the copper(I) case. Concentration and temperature effects were investigated for both series of Cu(I) - and Ag(I) -complexed threaded species showing that formation of the trimer was favored upon dilution or heating of the solution.