Parametric identification of transient electromagnetic systems

Data into and out of a transient eletromagnetic system are considered in the framework of modern system identification. System solutions that take the form of a complex exponential series are discussed. Since the identification of the parameters in the series is non-linear, emphasis shifts to the identification of the parameters in the difference equation whose solution is the exponential series. The subject is cast in the formalism of system identification with generalizations to more complex systems. Two examples are given, one involving an actual electromagnetic experiment.     

On the interaction between the input signal and the singularity expansion method

For transient excitation, it is well known that the Singularity Expansion Method (SEM) is a late time technique that is not in general suitable for early time. Lossy dielectric slab studies, with bounded integrable finite-duration input signal, have shown that the SEM representation for early time requires an additional branch cut contribution and a modification of the SEM series for completeness. Other researchers indicated that the SEM representation is not complete for most cases of practical interest and that it may not converge for early time. In this paper, we present an approach, using the input signal, to obtain a convergent SEM series that is valid for early as well as for late time. In this approach the branch cut contribution is not needed and instead we have pole contributions form the input signal and a modified SEM series. In addition, two forms of SEM representations will be presented, the traditional form and the time varying coupling coefficient form. Furthermore, the interaction and the effect of the input signal choice on the SEM representation will be clarified. This will be done for a dielectric slab backed by a perfect conductor.     

Extreme events in optics: Challenges of the MANUREVA project

In this contribution we describe and discuss a series of challenges and questions relating to understanding extreme wave phenomena in optics. Many aspects of these questions are being studied in the framework of the MANUREVA project: a multidisciplinary consortium aiming to carry out mathematical, numerical and experimental studies in this field. The central motivation of this work is the 2007 results from optical physics [D. Solli et al., Nature 450, 1054 (2007)] that showed how a fibre-optical system can generate large amplitude extreme wave events with similar statistical properties to the infamous hydrodynamic rogue waves on the surface of the ocean. We review our recent work in this area, and discuss how this observation may open the possibility for an optical system to be used to directly study both the dynamics and statistics of extreme-value processes, a potential advance comparable to the introduction of optical systems to study chaos in the 1970s.     

The Edge Correlation of Random Forests

The conjecture was made by Kahn that a spanning forest F chosen uniformly at random from all forests of any finite graph G has the edge-negative association property. If true, the conjecture would mean that given any two edges ε₁ and ε₂ in G, the inequality \mathbbP(e₁ ? F, e₂ ? F) ￡ \mathbbP(e₁ ? F)\mathbbP(e₂ ? F){{\mathbb{P}(\varepsilon_{1} \in \mathbf{F}, \varepsilon_{2} \in \mathbf{F}) \leq \mathbb{P}(\varepsilon_{1} \in \mathbf{F})\mathbb{P}(\varepsilon_{2} \in \mathbf{F})}} would hold. We use enumerative methods to show that this conjecture is true for n large enough when G is a complete graph on n vertices. We derive explicit related results for random trees.     

Akhmediev breather evolution in optical fiber for realistic initial conditions

We study numerically Akhmediev breather dynamics in optical fibers under initial conditions that do not correspond to an ideal infinitesimal modulation on a plane wave. We examine two modifications that are commonly encountered in realistic experiments: (i) a finite-amplitude (not necessarily weak) initial modulation; (ii) the use of pulsed excitation. In the first case, we derive an expression for the propagation distance required to generate a train of compressed breather pulses. In the second case, we show that breather dynamics with pulsed excitation can be interpreted in terms of local breather states at different points on the pulse envelope.     

Microwave Synthesis of 5-Substituted 1H-Tetrazoles Catalyzed by Bismuth Chloride in Water

Bismuth chloride was used to catalyze the [2 + 3] cycloaddition between sodium azide with aryl nitriles, aliphatic nitriles, and vinyl nitriles. A number of 5-substituted 1H-tetrazoles were synthesized in water or isopropanol/water mixtures using microwave heating. Good yields were obtained for these reactions when heated for 1 h at 120–160 °C in a 3:1 isopropanol/water mixture. A few of the less reactive nitriles required longer reaction times for good yields.     

A Meinardus Theorem with Multiple Singularities

We solve the quantum version of the A ₁ T-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum A ₁ Q-system and generalize it to the fully non-commutative case. We give the relation between the quantum T-system and the quantum lattice Liouville equation, which is the quantized Y-system.     

Investigation of uremic analytes in hemodialysate and their structural elucidation from accurate mass maps generated by a multi‐dimensional liquid chromatography/mass spectrometry approach

Historically, structural elucidation of unknown analytes by mass spectrometry alone has involved tandem mass spectrometry experiments using electron ionization. Most target molecules for bioanalysis in the metabolome are unsuitable for detection by this previous methodology. Recent publications have used high‐resolution accurate mass analysis using an LTQ‐Orbitrap with the more modern approach of electrospray ionization to identify new metabolites of known metabolic pathways. We have investigated the use of this methodology to build accurate mass fragmentation maps for the structural elucidation of unknown compounds. This has included the development and validation of a novel multi‐dimensional LC/MS/MS methodology to identify known uremic analytes in a clinical hemodialysate sample. Good inter‐ and intra‐day reproducibility of both chromatographic stages with a high degree of mass accuracy and precision was achieved with the multi‐dimensional liquid chromatography/tandem mass spectrometry (LC/MS/MS) system. Fragmentation maps were generated most successfully using collision‐induced dissociation (CID) as, unlike high‐energy CID (HCD), ions formed by this technique could be fragmented further. Structural elucidation is more challenging for large analytes >270 Da and distinguishing between isomers where their initial fragmentation pattern is insufficiently different. For small molecules (<200 Da), where fragmentation data may be obtained without loss of signal intensity, complete structures can be proposed from just the accurate mass fragmentation data. This methodology has led to the discovery of a selection of known uremic analytes and two completely novel moieties with chemical structural assignments made. Copyright © 2009 John Wiley & Sons, Ltd.     

Eine neue Reaction auf Galluss?ure

Ohne Zusammenfassung