Second order Lagrangian Twist systems: simple closed characteristics

We consider a special class of Lagrangians that play a fundamental role in the theory of second order Lagrangian systems: Twist systems. This subclass of Lagrangian systems is defined via a convenient monotonicity property that such systems share. This monotonicity property (Twist property) allows a finite dimensional reduction of the variational principle for finding closed characteristics in fixed energy levels. This reduction has some similarities with the method of broken geodesics for the geodesic variational problem on Riemannian manifolds. On the other hand, the monotonicity property can be related to the existence of local Twist maps in the associated Hamiltonian flow.

The finite dimensional reduction gives rise to a second order monotone recurrence relation. We study these recurrence relations to find simple closed characteristics for the Lagrangian system. More complicated closed characteristics will be dealt with in future work. Furthermore, we give conditions on the Lagrangian that guarantee the Twist property.

     

Sputtering of AlxGa1−x As semiconductor targets by Ar+ ions with energies of 2–14 keV

Investigations of the sputtering of Al_xGa_1−x As semiconductor solid solutions by Ar⁺ ions with energies of 2–14 keV are performed. The dependence of the sputtering yield on the energy and angle of incidence of the ions are determined and the character of the surface relief formed during the sputtering is investigated. A comparison with theory shows that the best agreement between theory and experiment is achieved when the Haff-Switkowski formula is used together with Yudin’s stopping cross section. It is shown that the surface binding energies obtained differ from the atomization energies by an amount approximately equal to the amorphization energy. Zh. Tekh. Fiz. 67, 113–117 (June 1997)     

Valence variations in the monolayer regime of Sm on the Nb(110) surface

Sm overlayers in the monolayer regime, deposited on a Nb(110) single-crystal surface at room temperature, have been studied by means of high-resolution photoelectron spectroscopy of the Nb 3d_5/2 core level and the Sm valence band. In the submonolayer regime, the Sm valence varies from mainly divalent for very low coverages to essentially trivalent close to a complete monolayer. Above 1 ML, a new divalent component appears in the Sm 4f spectra, corresonding to divalent Sm in the second layer. The mixed valence in this overlayer system is concluded to be heterogeneous (all Sm atoms have integer but site-dependent valence). Sm forms ordered overlayers on Nb(110) and the Sm growth is consistent with a layer-by-layer growth mode (Frank–van der Merwe growth).     

Eigenvalues and eigenfunctions of discontinuous Sturm--Liouville problems with eigenparameter-dependent boundary conditions

We extend some fundamental spectral properties of classic regular Sturm--Liouville problems to discontinuous boundary-value problems with eigenvalue-dependent boundary conditions. We suggest a new approach for investigation of such type discontinuous problems.     

Configuration space for random walk dynamics

Applied to statistical physics models, the random cost algorithm enforces a Random Walk (RW) in energy (or possibly other thermodynamic quantities). The dynamics of this procedure is distinct from fixed weight updates. The probability for a configuration to be sampled depends on a number of unusual quantities, which are explained in this paper. This has been overlooked in recent literature, where the method is advertised for the calculation of canonical expectation values. We illustrate these points for the 2d Ising model. In addition, we prove a previously conjectured equation which relates microcanonical expectation values to the spectral density. Received: 13 May 1998 / Received in final form and Accepted: 26 May 1998     

Exit and Return of a Simple Random Walk

Let V be a finite subset of Z^m. Estimates are obtained for the average probability that a simple random walk, starting at a point x in V, exits V before it returns to x. The average is taken over all points x in V. Mathematics Subject Classifications (2000) 60G50, 60J45     

Development and validation of a direct plasma injection LC-MS method for YM087 and YM440 and metabolites in human plasma

Summary A fully automated, direct plasma-injection technique using an LC coupled to a quadrupole mass spectrometric detector with an on-line, sample clean-up procedure for two new pharmaceutical products, YM087 and YM440, has been developed. Plasma samples containing YM440 were mixed with internal standard or plasma containing YM087 and were injected into a chromatographic system based on two coupled columns. An extraction column packed with alkyl-diol-silica (ADS) was used for online sample cleanup. Using a back-flush technique analytes were subsequently transferred to an analytical column, for separation. Detection was based on tandem mass spectrometry either in electronspray or in APCI mode. Despite the relatively small volumes of plasma injected, reasonably low limits of quantitation were achieved. Validation of both assays was performed using guidelines concerning method validation. All parameters studied were within acceptance criteria. The methods were successfully applied to clinical pharmacokinetic studies.     

Heat flow and Hardy inequality in complete Riemannian manifolds with singular initial conditions

Upper bounds are obtained for the heat content of an open set D with singular initial condition f on a complete Riemannian manifold, provided (i) the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and (ii) f satisfies an integrability condition. Precise asymptotic results for the heat content are obtained for an open bounded and connected set D in Euclidean space with C² boundary, and with initial condition f(x)=δ(x)^−α,0<α<2, where δ(x) is the distance from x to the boundary of D.     

Retrieval of aerosol optical depth in vicinity of broken clouds from reflectance ratios: Sensitivity study

We conducted a sensitivity study to better understand the potential of a new method for retrieving aerosol optical depth (AOD) under partly cloudy conditions. This method exploits ratios of reflectances in the visible spectral range and provides an effective way to avoid three-dimensional (3D) cloud effects. The sensitivity study is performed for different observational conditions and random errors in input data. The results of the sensitivity study suggest that this ratio method has the ability to detect clear pixels even in close proximity to clouds. Such detection does not require a statistical analysis of the two-dimensional (2D) horizontal distribution of reflected solar radiation, which makes it suitable for operational retrievals. In comparison with previously suggested approaches, the ratio method has the capability to increase the “harvest” of clear pixels. Similar to the traditional independent pixel approximation (IPA), the ratio method has a low computational cost for retrieving AOD. In contrast to the IPA method, the ratio method provides much more accurate estimations of the AOD values under broken cloud conditions: pixel-based and domain-averaged estimations of errors in AOD are about 25% and 10%, respectively. Finally, both the ratio-based cloud screening and the accuracy of domain-averaged ratio-based AOD values do not suffer greatly when 5% random errors are introduced in the reflectances.