Exact one-particle theory of a free electron laser

From a semiclassical discussion of the one-particle quantized model we demonstrate that the free electron dynamics exhibits a phase transition in correspondence to a threshold value of the wiggler magnetic field. Below threshold the FEL can work as a small gain amplifier and can be described by the well-known pendulum analogy and gain-spread expressions. Above threshold the analogy is broken and the FEL works as a large gain amplifier which goes from spontaneous to stimulated emission regime.     

Permanganate oxidation of 3-methyl-4-nitro-5-styrilisoxazole: a correction

In contrast with a previous report, permanganate oxidation of the title compound $\text{3}$ gives the nitroisoxazolone $\text{8}$ and not 3-methyl-4- nitroisoxazole-5-carboxylic acid $\text{2}$; a reaction pathway, involving the spirocyclisation of the carboxylate $\text{10}$, is suggested.     

Autour des algèbres de Bernstein

Sans résuméTravail subventionné par Dirección de Investigación, Universidad de La Frontera, Temuco. Chile et CONICYT.     

Transverse effects in superfluorescence

We demonstrate that off-axial emission can be responsible for the pulse envelope ringing, transverse effects, and large shot-to-shot pulse shape fluctuations observed in recent superfluorescence experiments.     

Synthesis and crystal structure of bis(dimethylthioacetonedicarboxylate)nickel(II)

Summary The title compound has been synthesized and characterized. The crystal structure has been determined by single-crystal x-ray analysis from diffractometer data, and refined to R= 0.063 for 1889 observed reflections. Crystals are monoclinic, space group P2₁/n, witha=21.97(2),b=8.21(1),c=10.44(1) A, and =101.87(3), and Z=4. Both ligands are coordinated to nickel through sulphur and one oxygen atom to realize thecis form of the complex in the square planar coordination geometry. Bond distances are: Ni-S, 2.14(1), Ni-O, 1.87(1) and 1.90(1) Å. Each nickel atom also forms two close contacts with oxygen atoms from adjacent molecules.     

Decision support systems for water management: The Lake Como case study

We review an application-oriented study on the management of Lake Como, a natural multipurpose reservoir in Northern Italy. The emphasis is on the Decision Support System that resulted from this study and which is now being used by the manager to take his decisions on the amount of water to be released each day from the lake. The decision support system is based on the optimal solutions of complex multiobjective mathematical programming problems.     

Towards sympathetic cooling of trapped ions with laser-cooled Mg + ions for mass spectrometry and laser spectroscopy

Sympathetic cooling by laser cooled Mg ions has been proposed as a method for fast cooling of highly charged ions to a very low temperature. The paper describes the construction of the solid state laser system at 279.63 nm required for laser cooling of the Mg ions. The laser system is composed of a fiber laser at 1,118.54 nm and two successive second harmonic generation (SHG) ring cavities for frequency quadrupling. In the first SHG cavity, non-critical phase matching of a lithium triborate (LBO) crystal is used for doubling from 1,118.54 to 559.27 nm. The second SHG cavity uses critical phase matching of a β-barium borate (BBO) crystal for doubling from 559.27 to 279.63 nm. With the aid of Boyd–Kleinmann theory, optimum experimental parameters are calculated and used for an efficient SHG. Besides this, the paper intends to be a shortcut for practical applications of the Boyd–Kleinmann theory for SHG.     

Bilinear paraproducts revisited

Boundedness properties for bilinear paraproducts on several function spaces are presented. The methods are based on the realization of paraproducts as bilinear Calderón‐Zygmund operators and the molecular character‐ization of function spaces. This provides a unified approach for the study of paraproducts, recovering some know results and establishing several new (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Hörmander Classes of Bilinear Pseudodifferential Operators

Bilinear pseudodifferential operators with symbols in the bilinear analog of all the Hörmander classes are considered and the possibility of a symbolic calculus for the transposes of the operators in such classes is investigated. Precise results about which classes are closed under transposition and can be characterized in terms of asymptotic expansions are presented. This work extends the results for more limited classes studied before in the literature and, hence, allows the use of the symbolic calculus (when it exists) as an alternative way to recover the boundedness on products of Lebesgue spaces for the classes that yield operators with bilinear Calderón–Zygmund kernels. Some boundedness properties for other classes with estimates in the form of Leibniz’ rule are presented as well.