Compact tunable mid-infrared laser source by difference frequency generation of two diode-lasers

Two continuous-wave single mode diode-lasers (Hitachi HL 7851G and Toshiba TOLD 9150) are applied as signal and pump sources for difference frequency generation (DFG) in an AgGaS2 crystal with a length of 30 mm. For 90° type I phase matching tunable mid-infrared laser radiation around 5 µm is obtained with an output power of up toP _DFG = 0.2 µW while the diode lasers are operated with powers of 30 and 50 mW at the center wavelengths 682 and 791 nm, respectively. The performance of the diode-laser-DFG system is shown as the absorption spectrum of CO for the P(28) rotational line around 2023 cm^–1 is probed in a 10cm long cell and in the exhaust of an engine.This research was supported by the Technologiestiftung Schleswig-Holstein under contract 94-35i.     

Determination of 13CO2/12CO2 Ratio by IRMS and NDIRS

Abstract

Breath tests using ¹³C-labelled substrates require the measurement of ¹³CO₂/¹²CO₂ ratio in breath gas samples. Next to isotope ratio mass spectrometry (IRMS), which is very sensitive but also complex and expensive, alternatively isotope selective nondispersive infrared spectrometry (NDIRS) can be used to determine the ¹³CO₂/¹²CO₂ ratio in expired breath. In this study we compared NDIRS- with IRMS-results to investigate whether the less expensive and very simply to operate NDIRS works as reliable as IRMS. For this purpose we applicated 1-¹³C-Phenylalanine to patients with advanced liver cirrhosis and healthy volunteers and took duplicated breath samples for IRMS and NDIRS at selected time points. Our data show a good correlation between these two methods for a small number of samples as required for simple breath tests. Longer series, where repeated measurements are required on the NDIRS instrument lead to a decreasing correlation. This indicates the superiority of IRMS concerning ¹³CO₂-kinetics over longer time periods.     

Exact Solution of a Generalized ANNNI Model on a Cayley Tree

We consider the Ising model on a rooted Cayley tree of order two with nearest neighbor interactions and competing next nearest neighbor interactions restricted to spins belonging to the same branch of the tree. This model was studied by Vannimenus who found a new modulated phase, in addition to the paramagnetic, ferromagnetic, antiferromagnetic phases and a (+ + - -) periodic phase. Vannimenus’s results are based on an analysis of the recurrence equations (relating the partition function of an n ? generation tree to the partition function of its subsystems containing (n ?1) generations) and most results are obtained numerically. In this paper we analytically study the recurrence equations and obtain some exact results: critical temperatures and curves, number of phases, partition function.     

Ion-isotopic exchange reaction kinetics using Duolite ARA-9366B and Indion-AGR resins

Radiotracer isotopic technique as an effective analytical tool was used to study the kinetics of ion-isotopic exchange reactions in the nuclear- and nonnuclear-grade anion exchange resins Duolite ARA-9366B and Indion-AGR. On the basis of kinetic data, specific reaction rate (per minute), amount of ion exchanged (millimoles), initial rate of iodide ion exchange (millimoles per minute), and log K _d values were calculated for the two resins. It was observed that under identical experimental conditions of 35.0 °C, 1.000 g of ion exchange resins, and 0.002 mol/L of labeled iodide ion solution, the values calculated were 0.200 min^?1, 0.278 mmol, 0.056 mmol/min, and 9.6, respectively, for Duolite ARA-9366B resin, which were higher than 0.102 min^?1, 0.216 mmol, 0.022 mmol/min, and 5.7, respectively, for Indion-AGR resins. An identical trend was observed for the two resins during bromide ion-isotopic exchange reaction. The overall results indicate that under identical experimental conditions, Duolite ARA-9366B resins show superior performance than Indion-AGR resins. The results of the present experimental work have demonstrated that the radioanalytical technique used here can be successfully applied for the characterization of different ion exchange resins so as to evaluate their performance under various process parameters.     

Conformally Flat Hypersurfaces of E4

We consider 3-dimensional conformally flat hypersurfaces of E ⁴ with 2 different principal curvatures such that the coordinate directions are principal directions. We describe explicitly those which allow an immersion with constant mean curvature. They are shown to be in close correspondence with solutions of the nonlinear integrable sine-Gordon and sinh-Gordon equations. Conversely, this provides a geometrical characterization for this particular class of conformally flat hypersurfaces of E ⁴.     

Non-parametric identification of non-linear oscillating systems

The problem of system identification from a time series of measurements is solved by using non-parametric additive models. Having only few structural information about the system, a non-parametric approach may be more appropriate than a parametric one for which detailed prior knowledge is needed. Based on non-parametric regression, the functions in the additive models are estimated by a penalized least-squares approach using backfitting. The optimal smoothing parameters are determined via generalized cross-validation, making this approach completely adaptive to the data. The procedure is applied to identify the non-linear restoring force of vibrationally excited helical wire rope isolators.     

Almost Everywhere Convergence of Strong Nörlund Logarithmic Means of Walsh-Fourier Series

In this paper we study the maximal operator for a class of subsequences of strong Nörlund logarithmic means of Walsh-Fourier series. For such a class we prove the almost everywhere strong summability for every integrable function f.     

Use of carbon-containing materials for efficient high-order harmonic generation of laser radiation

A systematic study of the high-order harmonic generation (HHG) of laser radiation in various carbon-containing plasma plumes (CCPPs) is presented. The materials studied are: graphite, boron carbide, C₆₀, polytetrafluoroethylene, polyethylene, carbon nanotubes, and soot. These studies show that CCPPs present the best plasma media for efficient lower order (from 9th to 19th) harmonic generation, while the harmonic cutoff restricted to the 29th order. The advantages of CCPPs for the harmonic generation are confirmed by comparison of the HHG conversion efficiency with that in Ag and In plasma plumes, where the highest conversion efficiency was reported. Use of two-color pump scheme allows further enhancement of harmonic yield from the CCPPs.     

A description of harmonic functions via properties of the group representation of the Cayley tree

We introduce a natural generalization of the notion of harmonic functions on a Cayley tree and use some properties of the group representation of the Cayley tree to describe the set of harmonic functions periodic with respect to normal subgroups of finite index.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.