The paradox of trees in type theory

We show how to represent a paradox similar to Russell's paradox in Type Theory withW-types and a type of all types, and how to use this in order to represent a fixed-point operator in such a theory. It is still open whether such a construction is possible without theW-type.This research was partly supported by ESPIRIT Basic Research Action Logical Frameworks.     

Inégalités de Gagliardo-Nirenberg pour les semi-groupes d'opérateurs et applications

One shows the equivalence between an abstract form of a Gagliardo-Nirenberg inequality and an estimate of the decay of the L ¹–L norm of a semigroup of operators. This equivalence, contrary to the one with the classical Sobolev inequalities, allows the treatment of situations where the decay is exponential. Related results and applications are given.

Cet article a pu être terminé pendant un séjour de l'auteur à l'université d'Edimbourg.     

Rapidly decaying solutions of the nonlinear Schrödinger equation

We consider global solutions of the nonlinear Schrödinger equation

A Theoretical Study of Complex Formation between Formaldehyde and Lithium

Ab initio SCF and CI calculations on the cationic and neutral complexes of formaldehyde and lithium are reported. For the cationic complex CH₂O/Li⁺, the stabilization energy of 41.7 kcal/mol obtained from the SCF calculation increases to 51.6 kcal/mol if a configuration interaction is introduced. For the neutral complex CH₂O^?/Li⁺, the C_2v-conformer of the ²A₁-state with the equilibrium bond distances of d(C? O) = 1.23 Å and d (O? Li) = 1.90 Å is calculated to be more stable than the ₂B₁-state with d (C? O) = 1.34 Å, and d (O? Li) = 1.65 Å. Charge transfer and polarization effects upon complex formation are discussed.     

Molecular tectonics. Selective exchange of cations in porous anionic hydrogen-bonded networks built from derivatives of tetraphenylborate

Tetraphenylmethanes with multiple hydrogen-bonding sites are known to associate to form robust porous supramolecular networks. Analogous anionic networks can be built from the corresponding tetraphenylborates. Crystallization of the tetraphenylphosphonium salt of tetraphenylborate 2 produces an anionic network in which 74% of the volume is available for including cations and neutral guests. Other salts of anion 2 with diverse cations crystallize consistently to form the same network, whereas a neutral analogue of anion 2, tetraphenylmethane 1, produces an uncharged network that is far less open. Cations can be exchanged in single crystals of salts of tetraphenylborate 2 with retention of crystallinity and with selectivities similar to those observed in typical zeolites. Together, these observations provide new strategies for making ordered molecular materials by design, and they reveal that constructing such materials from charged subunits offers special advantages.     

Ring-opening polymerization of lactide with group 3 metal complexes supported by dianionic alkoxy-amino-bisphenolate ligands: combining high activity, productivity, and selectivity

A series of new alkoxy-amino-bis(phenols) (H2L 1-6) has been synthesized by Mannich condensations of substituted phenols, formaldehyde, and amino ethers or diamines. The coordination properties of these dianionic ligands towards yttrium, lanthanum, and neodymium have been studied. The resulting Group 3 metal complexes have been used as initiators for the ring-opening polymerization of rac-lactide to provide poly(lactic acid)s (PLAs). The polymerizations are living, as evidenced by the narrow polydispersities of the isolated polymers, together with the linear natures of number average molecular weight versus conversion plots and monomer-to-catalyst ratios. Complex [Y(L6){N(SiHMe2)2}(THF)] (17) polymerized rac-lactide to heterotactic PLA (Pr = 0.90 at 20 degrees C) and meso-lactide to syndiotactic PLA (Pr = 0.75 at 20 degrees C). The in situ formation of [Y(L6)(OiPr)(THF)] (18) from 17 and 2-propanol resulted in narrower molecular weight distributions (PDI = 1.06). With complex 18, highly heterotactic PLAs with narrow molecular weight distributions were obtained with high activities and productivities at room temperature. The natures of the ligand substituents were shown to have a significant influence on the degree of control of the polymerizations, and in particular on the tacticity of the polymer.     

Recognition-induced transformation of microspheres into vesicles: morphology and size control

Polystyrene functionalized with diamidopyridine (DAP) recognition units self-assembles in nonpolar media to form thermally reversible micrometer-scale spherical aggregates. The size and the thermal stability of these microspheres can be controlled by the molecular weight of the polymer. The addition of thymine-functionalized polymer to these self-assembled microspheres converted them into vesicular aggregates with a controlled size. The morphology change was reversible: the addition of DAP-functionalized polymer converted the vesicles back to microspheres.     

Total synthesis of phytoprostane F1 and its 16 epimer

The first synthesis of the two enantiomers of phytoprostane F₁ methyl ester 1 and 2 is described using the syn-anti-syn alcoxy ester 3 as starting material.     

Synthesis of original benzo[g]quinoxaline‐5,10‐diones by bis‐SRN1 methodology

A new heterocyclic bioreductive bis‐alkylating agent, 2,3‐bis(chloromethyl)benzo[g]quinoxaline‐5,10‐dione, was prepared in a four‐steps synthesis. It was shown to react under electron transfer conditions with 2‐nitropropane anion by an bis‐S_RN1 mechanism to give three C‐alkylation products in excellent yields. Extension of this bis‐S_RN1 reaction to various nitronate or malonate anions and S‐centered anions led to a new class of potentially active benzo[g]quinoxaline‐5,10‐dione derivatives.     

Random Evolutionary Dynamics Driven by Fitness and House-of-Cards Mutations: Sampling Formulae

We first revisit the multi-allelic mutation-fitness balance problem, especially when mutations obey a house of cards condition, where the discrete-time deterministic evolutionary dynamics of the allelic frequencies derives from a Shahshahani potential. We then consider multi-allelic Wright–Fisher stochastic models whose deviation to neutrality is from the Shahshahani mutation/selection potential. We next focus on the weak selection, weak mutation cases and, making use of a Gamma calculus, we compute the normalizing partition functions of the invariant probability densities appearing in their Wright–Fisher diffusive approximations. Using these results, generalized Ewens sampling formulae (ESF) from the equilibrium distributions are derived. We start treating the ESF in the mixed mutation/selection potential case and then we restrict ourselves to the ESF in the simpler house-of-cards mutations only situation. We also address some issues concerning sampling problems from infinitely-many alleles weak limits.