Constrained regulation of continuous Petri nets

This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given.     

Biosynthetic studies on the botcinolide skeleton: new hydroxylated lactones from Botrytis cinerea

[reaction: see text] The biosynthetic origin of the botcinolide skeleton was investigated by means of feeding 13C- and 2H-labeled precursors to Botrytis cinerea. Three new compounds, two homobotcinolide derivatives, 3-O-acetylhomobotcinolide (5) and 8-methylhomobotcinolide (6), and a new 11-membered lactone (7), were isolated. Their structures were elucidated on the basis of spectroscopic data, including one-bond and long-range 1H-13C correlations. The relative stereochemistries were determined by combined analyses of NOE data and 1H-1H coupling constants. According to the results of feeding experiments with 13C- and 2H-labeled acetate and l-S-methylmethionine, 5 is an acetate-derived polyketide whose methyl groups originate from l-S-methylmethionine. This is a rare example of the incorporation of a methyl from methionine into a supposed C3 starter unit of the polyketide synthesis.     

Reaction of (1,3-dioxo-2,3-dihydro-1H-inden-2-ylidene)propanedinitrile with N-arylisoindolines

In a multistep reaction, 3,3′-(2-aryl-2H-isoindol-1,3-ylene)-di-(1,4-naphthoquinone-2-carbonitriles) 13a-f have been formed in 25-61% yield from a series of N-arylisoindolines 8a-f with (1,3-dioxo-2,3-dihydro-1H-inden-2-ylidene)propanedinitrile (1) in aerated pyridine. The structure of one of these products (13f) has been unambiguously confirmed by a single crystal X-ray structure analysis. Under otherwise the same conditions, 2-(3-methoxyphenyl)-isoindoline (8g) and 1 gave 38% of [4-(2,3-dihydro-1H-isoindol-2-yl)-2-methoxyphenyl]-1,3-dioxoindan-2-ylidene)acetonitrile (15). Rationales for these conversions involving the known rearrangement of the radical anion of 1 into the radical anion of 1,4-naphthoquinone-2,3-dicarbonitrile (3) are presented.     

Automatic alignment of a Kirkpatrick-Baez active optic by use of a soft-x-ray Hartmann wavefront sensor

We present what we believe to be the first automatic alignment of a synchrotron beamline by the Hartmann technique. Experiments were performed, in the soft-x-ray range (E=3 keV, lambda=0.414 nm), by using a four-actuator Kirkpatrick-Baez (KB) active optic. A system imaging the KB focal spot and a soft-x-ray Hartmann wavefront sensor were used alternatively to control the KB optic. The beam corrected with the help of the imaging system was used to calibrate the wavefront sensor. With both closed loops, we focused the beam into a 6.8 microm x 9 microm FWHM focal spot.     

Motion of charged particles in a NUTty Einstein–Maxwell spacetime and causality violation

We investigate the motion of electrically charged test particles in spacetimes with closed timelike curves, a subset of the black hole or wormhole Reissner–Nordström-NUT spacetimes without periodic identification of time. We show that, while in the wormhole case there are closed worldlines inside a potential well, the wordlines of initially distant charged observers moving under the action of the Lorentz force can never close or self-intersect. This means that for these observers causality is preserved, which is an instance of our weak chronology protection criterion.     

95 GHz millimeter wave signal generation using an arrayed waveguide grating dual wavelength semiconductor laser

We report the generation of a 95?GHz carrier frequency by optical heterodyning of two wavelengths from adjacent channels from an arrayed waveguide grating-based multiwavelength laser. The extended cavity structure of the device provides low phase noise and narrow optical linewidth, further enhanced by the intracavity filter effect of the arrayed waveguide grating. We demonstrate that the generated RF beat note, at 95?GHz, has a -3 dB linewidth of 250?kHz. To the best of our knowledge, this is the narrowest RF linewidth generated from a free-running dual-wavelength semiconductor laser. The device is realized as a photonic integrated circuit using active-passive integration technology, and fabricated on a multiproject wafer run, constituting a novel approach for a compact, low-cost dual-wavelength heterodyne source.     

Two additional 1,9-diarylnonanoid 3-glucosides from Erica cinerea among which an unusual α-dione in conformational equilibrium

Continuation of the phytochemical analysis of Erica cinerea fresh aerial parts resulted in the isolation of two new compounds with a very close chromatographic behavior. On the basis of spectroscopic evidence (UV, MS and NMR), the structures were established as (−)-(3S,6E)-1,9-bis(p-hydroxyphenyl)-3-hydroxynon-6-en-5-one 3-O-β-d-glucoside named 6,7-anhydroericaone 3-O-β-d-glucoside and (−)-(3S)-1,9-bis(p-hydroxyphenyl)-3-hydroxynonan-5,6-dione 3-O-β-d-glucoside named α-ericadione 3-O-β-d-glucoside. Unanticipated by its α-alkadione type structure —a very unusual feature in the plant kingdom— the latter metabolite was found as a mixture of the minor s-cis and the major s-trans conformers. Moreover, the GC-MS analysis of the aglycone moieties of such glucosides, pointed out the permanent absence of the molecular ion and the constant hydroxybenzylium base peak, as well as the conversion of the α-dione into the major α-keto-enol tautomer.     

On the gentle properties of anisotropic Besov spaces

In this paper, we prove that anisotropic homogeneous Besov spaces ${\stackrel{?}{B}}_{p,q}^{s,u}\left({\mathbb{R}}^d\right)$ are gentle spaces, for all parameters $s,p,q$ and all anisotropies $u$. Using the Littlewood–Paley decomposition, we study their completeness, separability, duality and homogeneity. We then define the notion of anisotropic orthonormal wavelet basis of $L^2\left({\mathbb{R}}^d\right)$, and we show that the homogeneous version of Triebel families of anisotropic orthonormal wavelet bases associated to the tensor product of Lemarié–Meyer (resp. Daubechies) wavelets are particular examples. We characterize the ${\stackrel{?}{B}}_{p,q}^{s,u}\left({\mathbb{R}}^d\right)$ spaces using Lemarié–Meyer wavelets. In fact, we show that these bases will be either unconditional bases or unconditional $1$-weak bases of ${\stackrel{?}{B}}_{p,q}^{s,u}\left({\mathbb{R}}^d\right)$, depending on whether ${\stackrel{?}{B}}_{p,q}^{s,u}\left({\mathbb{R}}^d\right)$ is separable or not. By introducing an anisotropic version of the class of almost diagonal matrices related to anisotropic orthonormal wavelet bases, we prove that these spaces are stable under changes of anisotropic orthonormal wavelet bases. As a consequence, we extend the characterization of ${\stackrel{?}{B}}_{p,q}^{s,u}\left({\mathbb{R}}^d\right)$ using Daubechies wavelets.     

The stable admissions polytope

The stable admissions polytope– the convex hull of the stable assignments of the university admissions problem – is described by a set of linear inequalities. It depends on a new characterization of stability and arguments that exploit and extend a graphical approach that has been fruitful in the analysis of the stable marriage problem. Received: April 10, 1998 / Accepted: June 3, 1999?Published online January 27, 2000