Reachability analysis of linear systems using support functions

This work is concerned with the algorithmic reachability analysis of continuous-time linear systems with constrained initial states and inputs. We propose an approach for computing an over-approximation of the set of states reachable on a bounded time interval. The main contribution over previous works is that it allows us to consider systems whose sets of initial states and inputs are given by arbitrary compact convex sets represented by their support functions. We actually compute two over-approximations of the reachable set. The first one is given by the union of convex sets with computable support functions. As the representation of convex sets by their support function is not suitable for some tasks, we derive from this first over-approximation a second one given by the union of polyhedrons. The overall computational complexity of our approach is comparable to the complexity of the most competitive available specialized algorithms for reachability analysis of linear systems using zonotopes or ellipsoids. The effectiveness of our approach is demonstrated on several examples.     

Far-field imaging of the electromagnetic local density of optical states

We introduce a new experimental method to measure the local electromagnetic density of states (LDOS) by integrating the differential scattering cross section. The signal detected essentially reflects the intrinsic scattering response of the photonic structures and renders the partial LDOS dominated by evanescent modes. We give a theoretical understanding of the LDOS image formation and show a qualitative agreement between experimental images and theoretical maps. This approach can be practically applied to the direct measurement of an optical antenna's scattering efficiency and can provide valuable information for designing optimum structures utilized in radiative decay engineering.     

Scalable Synthesis of Piperazines Enabled by Visible‐Light Irradiation and Aluminum Organometallics

The development of more active C? H oxidation catalysts has inspired a rapid, scalable, and stereoselective assembly of multifunctional piperazines through a [3+3] coupling of azomethine ylides. A combination of visible‐light irradiation and aluminum organometallics is essential to promote this transformation, which introduces visible‐light photochemistry of main‐group organometallics and sets the basis for new and promising catalysts.     

Sémi-microdosage de quelques constituants du lait par séparation chromatographique

Résumé La complexité de l'état physique dans lequel se trouvent les constituants du lait à l'état naturel fait de leur séparation un problème difficilement soluble, surtout quand il s'agit d'analyser de petites quantités.Une séparation des constituants du lait est possible sur une colonne d'alumine hydratée.Le mécanisme de cette séparation réside dans un échange d'ions, résultant des propriétés conférées par la couche de graisse déposée sur le grain d'alumine hydraté.Le lactose, le premier constituant recueilli, passe par simple filtration indifféremment duh de l'alumine.Les protéides sont élués par une solution alcaline. Leh de l'alumine a une grande influence à la fois sur leur adsorption et sur leur élution. Une alumine acide retient la presque totalité des protéines, tandis qu'une alumine neutre ou légèrement alcaline en permet une élution facile.Dans les conditions de nos expériences l'alumine employée ne peut adsorber qu'une quantité déterminée de protéines. L'excès passe immédiatement dans le filtrat. Ainsi, l'on peut différencier deux fractions protéiques qui sont récoltées après le passage du lait dans la colonne: l'une dans le filtrat, quand la colonne est déjà saturée, l'autre dans l'éluat alcalin.Les phosphates minéraux sont élués par une solution acide; leur rétention n'est pas influencée par leh de la colonne.

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Summary The complexity of the physical state, in which the constituents of milk occur naturally, makes their separation a difficult problem, particularly when small quantities are to be analyzed. The constituents of milk can be separated on a column of hydrated alumina.The mechanism of this separation resides in an exchange of ions resulting from properties conferred by the layer of fat deposited on the grains of hydrated alumina.Lactose, the first constituent collected, passes through by simple filtration, indifferent to theh of the alumina.The proteins are eluted by means of an alkaline solution. Theh of the alumina has a large influence both on their adsorption and elution. An acidic alumina retains practically all of the proteins, whereas a neutral or slightly alkaline alumina makes their elution easy.Under the conditions of the author's experiments, the alumina employed could adsorb only a determinate quantity of proteins. The excess immediately passed into the filtrate. It is thus possible to differentiate two protein fractions, which are collected after the passage of the milk through the column: one in the filtrate, when the column is already saturated, the other in the alkaline eluate.The mineral phosphates are eluted by an acid solution; their retention is not influenced by theh of the column.

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Zusammenfassung Die verwickelten physikalischen Verhältnisse unter den Bestandteilen der Milch im natürlichen Zustand macht deren Trennung zu einem schwierigen Problem, besonders wenn es sich um die Analyse kleiner Mengen handelt. Diese Trennung wird durch Verwendung einer Säule von Aluminiumoxydhydrat ermöglicht. Der Trennungsmechanismus beruht auf einem Ionenaustausch zufolge jener Umstände, die sich aus der Bindung des Fettes an das gekörnte Adsorptionsmittel ergeben. Die Lactose, der zuerst erhältliche Bestandteil, passiert das Aluminiumoxyd unabhängig vomh. Die Proteide werden alkalisch eluiert. Dash des Aluminiumoxyds ist von großem Einfluß auf deren Adsorption und Elution. Saures Aluminiumoxyd hält das Eiweiß fast zur Gänze zurück, während neutrales oder schwach basisches Aluminiumoxyd die Elution erleichtert. Unter den von uns gewählten Versuchsbedingungen kann das verwendete Aluminiumoxyd nur eine bestimmte Menge der Eiweißkörper adsorbieren. Der Überschuß geht unmittelbar ins Filtrat. So lassen sich zwei Eiweißfraktionen unterscheiden, von denen sich die eine nach der Sättigung der Trennsäule im Filtrat, die andere im Eluat findet. Das anorganische Phosphat wird sauer eluiert; dessen Adsorption wird durch dash der Kolonne nicht beeinflußt.

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Avec 10 figures.     

Assignment of Relative Configuration of Desoxypropionates by 1H NMR Spectroscopy: Method Development,Proof of Principle by Asymmetric Total Synthesis of Xylarinic Acid A and Applications

The determination of the relative configuration of 1,3‐dimethyl‐substituted alkyl chains is possible by interpretation of ¹H NMR shift differences. Additionally, assignments are feasible in a variety of deuterated solvents, because the corresponding shift differences are not significantly influenced by the solvent. The trends for Δδ values depending on functional groups adjacent to the stereogenic centers are shown. Based on a thorough comparison with literature data, the relative configuration of natural products can be predicted. For this purpose, we derived an empirical rule for the ranges in which Δδ values usually occur. Furthermore, we were able to proof the validity of our method by the successful prediction of the relative configuration for the polyketide natural product xylarinic acid A, which was confirmed by the asymmetric total synthesis of its enantiomer. Based on the proposed simple analysis of published ¹H NMR data and the determination of the relevant chemical‐shift differences, we predicted the relative configurations of several previously unassigned natural products.     

Tunnel injection into GaAs/AlGaAs long period superlattices

Electron injection through a tunnel barrier into a long period GaAs/AlGaAs superlattice is investigated. Seven negative differential resistance (NDR) regions are observed, resulting from resonant tunneling into the first well of the superlattice. Their positions can be quantitatively accounted for by considering the distribution of the electric field in the depletion region and the tunnel barrier. Upon application of a magnetic field parallel to the layers, the NDR's are shifted and weakened, which can be explained in terms of conservation of energy and canonical momentum. Furthermore, optical phonon generated conductance oscillations are observed although the depletion region is punctuated by the superlattice structure.     

Resolving Inflammation: Synthesis,Configurational Assignment,and Biological Evaluations of RvD1n−3 DPA

New drugs that can resolve inflammation without immunosuppressive effects are at the medicinal chemistry frontier. Pro-resolving endogenously formed small molecules, that is, the resolvins, are excellent candidates displaying such bioactions. The first total synthesis of the specialized pro-resolving mediator RvD1_{n−3 DPA} has been achieved using the underutilized sp³–sp³ Negishi cross coupling reaction and an alkyne hydrosilylation–protodesilylation protocol. Biological evaluations revealed that this novel mediator displays low nanomolar pro-resolving properties and potently activates the human DRV1/GPR32 receptor. As such, this endogenous natural product is a lead compound for the development of novel immunoresolvents.     

Parametric study of 2D potential structures induced by RF sheaths coupled with transverse currents in front of ICRH antenna

Hot-spot formation on the corners of the ICRH antenna can be explained by high DC potential structures, which accelerate ion fluxes and generate strong convective fluxes to the antenna surface. This comes from RF sheaths at the end of open magnetic lines, which rectify RF potential resulting from parallel electric fields. As these electric fields are not homogeneous in front of the antenna, transverse potential gradients generate transverse polarization currents which modify the potential structure. These potentials are studied with a simple flux-tube model and then a 2D-fluid model was elaborated to obtain analytical expressions for rectified potential with respect to these transverse currents. We compare them to numerical results coming from a 2D-fluid code executed in a poloidal plane in front of the antenna. Then we build a potential peak criterion to determine the peaking of DC-potential structures for typical parameters in Tore Supra. Finally, current interaction between different magnetic line lengths is approached.Presented at the Workshop Electric Fields Structures and Relaxation in Edge Plasmas, Nice, France, October 26–27, 2004.     

Mode solvers for very thin long–range plasmonic waveguides

We present two mode solvers applied to a very thin long–range plasmonic waveguide. We compare the guided mode complex effective index obtained either applying a Fourier modal method or calculating density of guided modes using the Green’s dyad technique. We achieve good agreement for both effective indices and mode profiles. We also observe a different behaviour compared to long–range surface plasmon supported by thicker films.