Über eine Abschätzung der Amplituden in freien Schwingungs-problemen veränderlicher Kreisfrequenz

Summary Consider any differential equation of the form given under (1) below and, ifx(t) is any solution of (1) which is real-valued and does not vanish identically, letC be a half-waveatb of the curvex=x(t) in a (t, x)-plane [by this is meant thatx(a)=0 andx(b)=0 but |x(t)|>0 ifa<t<b]. Then ana priori upper limitation, involving the moments of the coefficient function of (1) [cf. the three integrals in formula (2) of the text, wherea=0 andb=h], is obtained for the ratiom/f. Herem denotes the maximum amplitude occurring inC, andf the area of the region surrounded by the segmentatb on thet-axis and the graph ofC in the (t, x)-plane (this region is always convex).     

Effective radii and volumes for elements in A15 compounds

Atomic sized measured by radii and volumes are compared for elements in the A15 structures.     

Improving the beam propagation method for TM polarization

The beam propagation method (BPM) has been widely used in numerical simulations of optical waveguides that vary slowly in the propagation direction. However, when BPM is used over a large propagation distance, a significant amplitude error in the coefficient of the leading propagating mode can be observed. Energy-conserving corrections and the single scatter approximation have been used to improve the accuracy of the BPM.     

Calibration and numerical simulation of Nanoparticle Surface Area Monitor (TSI Model 3550 NSAM)

TSI Nanoparticle Surface Area Monitor (NSAM) Model 3550 has been developed to measure the nanoparticle surface area deposited in different regions of the human lung. It makes use of an adjustable ion trap voltage to match the total surface area of particles, which are below 100 nm, deposited in tracheobronchial (TB) or alveolar (A) regions of the human lung. In this paper, calibration factors of NSAM were experimentally determined for particles of different materials. Tests were performed using monodisperse (Ag agglomerates and NaCl, 7–100 nm) and polydisperse particles (Ag agglomerates, number count mean diameter below 50 nm). Experimental data show that the currents in NSAM have a linear relation with a function of the total deposited nanoparticle surface area for the different compartments of the lung. No significant dependency of the calibration factors on particle materials and morphology was observed. Monodisperse nanoparticles in the size range where the response function is in the desirable range can be used for calibration. Calibration factors of monodisperse and polydisperse Ag particle agglomerates are in good agreement with each other, which indicates that polydisperse nanoparticles can be used to determine calibration factors. Using a CFD computer code (Fluent) numerical simulations of fluid flow and particle trajectories inside NSAM were performed to estimate response function of NSAM for different ion trap voltages. The numerical simulation results agreed well with experimental results.     

Nanostructuring of CyPLOS (Cyclic Phosphate-Linked OligoSaccharides), novel saccharide-based synthetic ion transporters

Ionophores are an important class of synthetic molecules which mimic natural ion channels or carriers. Here we report the aggregation behavior in pseudo-physiological environment of three Cyclic Phosphate-Linked Oligosaccharides (CyPLOS) derivatives, synthetic ion transporters based on cyclic, phosphate-linked disaccharide skeleton differing for the nature of the tails (tetraethylene-TEG glycol and/or n-undecyl chains) attached to the C-2 and C-3 of the constitutive monosaccharides. Their aggregation behavior has been studied by a combined use of dynamic light scattering (DLS), electron paramagnetic resonance spectroscopy (EPR) and Small Angle Neutron Scattering (SANS). DLS measurements were performed to reveal the formation and size distribution of the CyPLOS aggregates. EPR measurements, by using 5-doxyl stearic acid (5-DSA) as spin-probe, showed that the aggregates are mainly due to the formation of double layers and allowed to analyze the local fluidity. Finally, SANS measurements allowed estimating the layer thickness of the double layers. Our results indicate that the three CyPLOS analogs show self-aggregation properties that depend on the different nature of the inserted tails.