Logarithmic stability in the dynamical inverse problem for the Schrödinger equation by arbitrary boundary observation

In this paper, we investigate the inverse problem of determining the potential of the dynamical Schrödinger equation in a bounded domain from the data of the solution in a subboundary over a time interval. Assuming that in a neighborhood of the boundary of the spatial domain, the potential is known and without any assumption on the dynamics (i.e. without the geometric optics condition for the observability), we prove a logarithmic stability estimate for the inverse problem with a single measurement on an arbitrarily given subboundary.     

Suppression of hysteresis in a forced van der Pol–Duffing oscillator

This paper examines the suppression of hysteresis in a forced nonlinear self-sustained oscillator near the fundamental resonance. The suppression is studied by applying a rapid forcing on the oscillator. Analytical treatment based on perturbation analysis is performed to capture the entrainment zone, the quasiperiodic modulation domain and the hysteresis area as well. The analysis leads to a strategy for the suppression of hysteresis occurring between 1:1 frequency-locked motion and quasiperiodic response. This hysteresis suppression causes the disappearance of nonlinear effects leading to a smooth transition between the quasiperiodic and the frequency-locked responses. Specifically, it appears that a rapid forcing introduces additional apparent nonlinear stiffness which can effectively suppress hysteresis in a certain range of the rapid excitation frequency. This work was motivated by the important issue of controlling and eliminating hysteresis often undesirable in mechanical systems, in general, and in application to microscale devices, especially.     

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.     

On the design of active inductors with current-controlled voltage sources

This paper presents a novel method of designing active inductors using current-controlled voltage sources (CCVSs). The basic idea consists of designing an equivalent inductor, using only capacitors and CCVSs. The signal-flow graph technique is used for this purpose. The CCVSs are emulated by means of nullator/norator pairs. These elements are then realized using second generation current conveyors (CCIIs), and a combination of CCIIs and operational transconductance amplifiers. In addition, a novel design of simulated inductors using operational transresistance amplifiers is presented. The proposed inductors were used to design filters. SPICE simulations are given to highlight viability and to show good reached results.     

Multi-dimensional Capon spectral estimation using discrete Zhang neural networks

The minimum variance spectral estimator, also known as the Capon spectral estimator, is a high resolution spectral estimator used extensively in practice. In this paper, we derive a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimator. To avoid the direct computation of the inverse covariance matrix used to estimate the Capon spectrum which can be computationally very expensive, particularly when the dimension of the matrix is large, we propose to use the discrete Zhang neural network for the online covariance matrix inversion. The computational complexity of the proposed algorithm for one-dimensional (1-D), as well as for two-dimensional (2-D) and three-dimensional (3-D) data sequences is lower when a parallel implementation is used.     

Outage Probability Analysis of Cooperative Diversity Networks Over Weibull and Weibull-Lognormal Channels

This paper presents the analysis of outage probability for a cooperative diversity wireless network using amplify-and-forward relays over independent non-identical distributed Weibull and Weibull-lognormal fading channels for single as well as multiple relays. To reach that end, a closed-from expression for the moment-generating function of the total signal-to-noise-ratio (SNR) at the destination is derived in terms of the tabulated Meijer’s G-function. Since it is hard to determine the exact probability distribution function of the SNR, a tight lower bound approximation is proposed. Simulation results are presented that show that the outage probability lower bound tends to be tight at high SNR values thus verifying the analytical results. The results also show the potential gain of relaying on the outage probability.