Search results for "LIMIT"
showing 10 items of 2826 documents
The 0-Parameter Case
1998
As an introduction to the theory of bifurcations, in this chapter we want to consider individual vector fields, i.e., families of vector fields with a 0-dimensional parameter space. We will present two fundamentals tools: the desingularization and the asymptotic expansion of the return map along a limit periodic set. In the particular case of an individual vector field these techniques give the desired final result: the desingularization theorem says that any algebraically isolated singular point may be reduced to a finite number of elementary singularities by a finite sequence of blow-ups. If X is an analytic vector field on S 2, then the return map of any elementary graphic has an isolate…
$O^\star$-algebras and quantum dynamics: some existence results
2008
We discuss the possibility of defining an algebraic dynamics within the settings of O -algebras. Compared to our previous results on this subject, the main improvement here is that we are not assuming the existence of some Hamiltonian for the full physical system. We will show that, under suitable conditions, the dynamics can still be defined via some limiting procedure starting from a given regularized sequence. © 2008 American Institute of Physics.
Approximations of positive operators and continuity of the spectral radius III
1994
AbstractWe prove estimates on the speed of convergence of the ‘peripheral eigenvalues’ (and principal eigenvectors) of a sequence Tn of positive operators on a Banach lattice E to the peripheral eigenvalues of its limit operator T on E which is positive, irreducible and such that the spectral radius r(T) of T is a Riesz point of the spectrum of T (that is, a pole of the resolvent of T with a residuum of finite rank) under some conditions on the kind of approximation of Tn to T. These results sharpen results of convergence obtained by the authors in previous papers.
Jacobian of weak limits of Sobolev homeomorphisms
2016
Abstract Let Ω be a domain in ℝ n {\mathbb{R}^{n}} , where n = 2 , 3 {n=2,3} . Suppose that a sequence of Sobolev homeomorphisms f k : Ω → ℝ n {f_{k}\colon\Omega\to\mathbb{R}^{n}} with positive Jacobian determinants, J ( x , f k ) > 0 {J(x,f_{k})>0} , converges weakly in W 1 , p ( Ω , ℝ n ) {W^{1,p}(\Omega,\mathbb{R}^{n})} , for some p ⩾ 1 {p\geqslant 1} , to a mapping f. We show that J ( x , f ) ⩾ 0 {J(x,f)\geqslant 0} a.e. in Ω. Generalizations to higher dimensions are also given.
Analytic Bergman operators in the semiclassical limit
2018
Transposing the Berezin quantization into the setting of analytic microlocal analysis, we construct approximate semiclassical Bergman projections on weighted $L^2$ spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic expansions of the Bergman kernel on $\mathbb{C}^n$ and for high powers of ample holomorphic line bundles over compact complex manifolds.
Nanomolar pyrophosphate detection in water and in a self-assembled hydrogel of a simple terpyridine-Zn2+ complex.
2014
A simple terpyridine-Zn(II) complex is shown to act as an efficient and highly selective fluorescent sensor for pyrophosphate in water at physiological pH. The sensor complex showed an unprecedented fluorescence response (∼500 fold increase) and a record nanomolar sensitivity (detectable fluorescent response at 20 nM and LOD ∼ 0.8 nM). It has successfully been used to stain and record confocal fluorescence microscopy images of HeLa cells. Moreover, the complex was found to self-assemble into a hydrogel which was subsequently used to coat disposable paper strips for easy, low-cost detection of pyrophosphate.
Low-Noise Amplification and Frequency Conversion with a Multiport Microwave Optomechanical Device
2016
High-gain amplifiers of electromagnetic signals operating near the quantum limit are crucial for quantum information systems and ultrasensitive quantum measurements. However, the existing techniques have a limited gain-bandwidth product and only operate with weak input signals. Here we demonstrate a two-port optomechanical scheme for amplification and routing of microwave signals, a system that simultaneously performs high-gain amplification and frequency conversion in the quantum regime. Our amplifier, implemented in a two-cavity microwave optomechanical device, shows 41 dB of gain and has a high dynamic range, handling input signals up to $10^{13}$ photons per second, three orders of magn…
Sensitive Monoclonal Antibody-Based Immunoassays for Kresoxim-methyl Analysis in QuEChERS-Based Food Extracts
2014
Kresoxim-methyl is nowadays widely used to combat a diversity of common diseases affecting high-value crops. In this article, we report the development and characterization of two novel immunoassays for the analysis of this pioneer strobilurin fungicide, and for the first time, a validation study with food samples was performed. A direct and an indirect competitive immunoassay based on a new anti-kresoxim-methyl monoclonal antibody were developed for sensitive and specific chemical analysis. Optimized assays showed limits of detection of 0.1 μg/L. Fruit and vegetable samples were extracted with acetonitrile by the QuEChERS procedure and analyzed by the developed immunoassays after a simple …
Optimization of large-volume injection for the determination of polychlorinated biphenyls in children's fast-food menus by low-resolution mass spectr…
2008
International audience; This study includes the determination of five indicator polychlorinated biphenyls (PCBs) (52, 101, 153, 138, and 180), six non-ortho PCBs (35, 80, 81, 77, 126, and 169), and two mono-ortho PCBs (28 and 118) in fast food for children. A freeze-dried sample of 10 g is extracted by using pressurized n-hexane in two 5 min cycles at 120 degrees C and 100 mbar. Fatty extracts were cleaned up by means of acetonitrile/n-hexane partitioning and gel-permeation chromatography. The fractionation of non-ortho, mono-ortho, and indicator PCBs was made on graphitized carbon solid-phase extraction cartridges by using n-hexane, n-hexane/toluene (99:1, v/v), and toluene as elution solv…
Determination of ultratrace bismuth in milk samples by atomic fluorescence spectrometry.
2003
Abstract A sensitive procedure was developed for determination of bismuth (Bi) in milk samples by hydride generation atomic fluorescence spectrometry (HG–AFS) after microwave-assisted sample digestion with HNO3 and H2O2. The method provides a sensitivity of 1832 fluorescence units (ng/mL) with a detection limit of 0.01 ng/mL, which corresponds to 20 pg absolute limit of detection, equivalent to 0.50 ng/g in the original sample. Application of the methodology to cow milk samples from the Spanish market showed the presence of Bi at a concentration of 11.8–28.8 ng/g, which compared well with data obtained after dry ashing of samples and with data obtained by inductively coupled plasma–mass spe…