Linearity of the exceptional set for maps of P<Subscript><Emphasis Type="Italic">k</Emphasis></Subscript>(C)

Let f be a holomorphic self-map of P_k(C), with degree larger than 2. We show that its exceptional set is a finite union of linear subspaces.Revised version: 16 December 2004     

A NMR and theoretical study of the aggregates between alkyllithium and chiral lithium amides: control of the topology through a single asymmetric center

The complexes between methyllithium and chiral 3-aminopyrrolidine (3-AP) lithium amides bearing a second asymmetric center on their lateral amino group were studied using multinuclear ((1)H, (6)Li, (13)C, (15)N) low-temperature NMR spectroscopies in tetrahydrofuran-d(8). The results indicate that lithium chelation forces the pyrrolidine ring of the 3-AP to adopt a norbornyl-like conformation and that robust 1:1 noncovalent complexes between methyllithium and 3-AP lithium amides form in the medium. A set of (1)H-(1)H and (1)H-(6)Li NMR cross-coupling correlations shows that the binding of methyllithium can take place along the "exo" or the "endo" face of this puckered structure, depending on the relative configuration of the lateral chiral group. This aggregation step renders the nitrogen of the 3-amino group chiral, the "exo" and "endo" topologies corresponding to the (S) and (R) configurations, respectively, of this atom. Density functional theory calculations show that the "exo" and "endo" arrangements are, for both diastereomers, almost isoenergetic even when solvent is taken into account. This result suggests that the formation of the mixed aggregates is under strict kinetic control. A relationship between the topology of these complexes and the sense of induction in the enantioselective alkylation of aromatic aldehydes by alkyllithiums is proposed.     

Deux caractérisations de la mesure d'équilibre d'un endomorphisme de P k (C)

Résumé. — Soit μ la mesure d'équilibre d'un endomorphisme de P ^k (C). Nous montrons ici qu'elle est son unique mesure d'entropie maximale. Nous construisons directement μ comme distribution asymptotique des préimages de tout point hors d'un ensemble exceptionnel algébraique.

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— Let μ be the equilibrium measure of an endomorphism of P ^k (C). We show that it is its unique measure of maximal entropy. We build μ directly as the distribution of premiages of any point outside an algebraic exceptional set.

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Manucsrit re?u le 30 novembre 2000.     

On evolution of thermo-plastic shear band

The present paper briefly reviews analytical studies of the evolution of thermoplastic shear band, i.e. emergence from uniform deformation, post-instability growth and late stage behaviour. The case studied is the simple shear of temperature and rate-dependent materials with heat transfer. Uniform mode exists before a critical state, if no heat flows out of testpiece. Upon reaching the critical state, bifurcation appears as a result of disturbances, which leads to instability and the formation of narrow shear band. Initially, the band, due to temperature disturbance, can shrink with increasing temperature and strain rate owing to unsteady flow. Then heat conduction dominates and causes the shear band to expand. The postmortem appearance of thermo-plastic shear band manifests itself as balance of plastic work rate and heat diffusion. Melting may also take place within the band.     

A risk forecasting process for nanostructured materials, and nanomanufacturing

Nanomaterials exhibit novel properties that enable new applications ranging from molecular electronics to energy production. Proactive consideration of the potential impacts on human health and the environment resulting from nanomaterial production and use requires methods for forecasting risk associated with of these novel materials. However, the potential variety of nanomaterials is virtually infinite and a case-by-case analysis of the risks these materials may pose is not possible. The challenge of forecasting risk for a broad number of materials is further complicated by large degrees of uncertainty concerning production amounts, the characteristics and uses of these materials, exposure pathways, and a scarcity of data concerning the relationship between nanomaterial characteristics and their effects on organisms and ecosystems. A traditional risk assessment on nanomaterials is therefore not possible at this time. In its place, an evolving process is needed for analyzing the risks associated with emerging nanomaterials-related industries.In this communication, we propose that such a process should include the following six key features: (1) the ability to generate forecasts and associated levels of uncertainty for questions of immediate concern; (2) a consideration of all pertinent sources of nanomaterials; (3) an inclusive consideration of the impacts of activities stemming from nanomaterial use and production that extends beyond the boundaries of toxicology and include full life cycle impacts; (4) the ability to adapt and update risk forecasts as new information becomes available; (5) feedback to improve information gathering; and (6) feedback to improve nanomaterial design. Feature #6 implies that the potential risks of nanomaterials must ultimately be determined as a function of fundamental, quantifiable properties of nanomaterials, so that when these properties are observed in a new material, they can be recognized as indicators of risk. Thus, the required risk assessment process for nanomaterials addresses needs that span from urgent, short-term questions dealing with nanomaterials currently in commerce, to longer-term issues that will require basic research and advances in theory. In the following sections we outline issues surrounding each of these six features and discuss.     

Structural vibration control by synchronized switch damping energy transfer

The synchronized switch damping (SSD) technique has been demonstrated as an efficient means of suppressing structure vibrations. This paper presents a novel SSD technique based on an energy transfer (SSDET) scheme that transmits energy from an energy-source structure to a target structure in order to damp the latter. As a matter of fact, the transferred energy enhanced the synchronized switch damping on inductor (SSDI) with an initial current, thus leading to a better vibration control capability. The experiment, performed on a beam/plate system, succeeded in delivering an enhanced damping effect as compared to the SSDI technique by adopting the proposed control law. Comparisons between simulation and experiment also confirmed the effectiveness of the proposed mathematical model. The stability was discussed in order to determine the stability limit.     

Tuning the Raman resonance behavior of single-walled carbon nanotubes via covalent functionalization

We present a systematic Raman study over a range of excitation energies of arc discharge single-walled carbon nanotubes (SWCNTs) covalently functionalized according to two processes, esterification and reductive alkylation. The SWCNTs are characterized by resonance Raman spectroscopy at each step of the functionalization process, showing changes in radial breathing mode frequencies and transition energies for both semiconducting and metallic tubes. Particular attention is given to a family of tubes clearly identified in the Kataura plot for which we continuously tune the excitation energy from 704 to 752 nm. This allows us to quantify the energy shift occurring in the spacing of the van Hove singularities. We demonstrate that, independently of the functionalization technique, the type of chain covalently bound to the tubes plays an important role, notably when oxygen atoms lie close to the tubes, inducing a larger shift in transition energy as compared to that of other carbonaceous chains. The study shows the complexity of interpreting Raman data and suggests many interpretations in the literature may need to be revisited.