Determination of aromatic sulfonic acids in industrial waste water by ion-pair chromatography

A method for the identification and quantification of aromatic sulfonic acids in industrial waste water has been developed. The preparation of the samples comprises a clean-up step and an enrichment step, utilizing i) reversed-phase extraction and ii) ion-pair solid phase extraction. The aromatic sulfonic acids are separated by ion-pair chromatography with diode-array detection. An advantage of the developed ion-pair chromatographic method is the separation of linear alkylbenzenesulfonic acids (LAS), lignosulfonic acids and aromatic sulfonic acids in one chromatographic run. Also described is an optimized clean-up procedure for collected fractions of a preparative chromatographic run to identify monosulfonic acids with GC/MS after methylation. The detection limits for aromatic sulfonic acids in industrial waste waters are at the g/l level.     

The limit of detection in transversal photothermal deflection spectroscopy with light scattering samples

The limit of detection for the 4,6 dinitro-orthocresol (DNOC) pesticide, including small latex particles as light scattering samples in water as suspending medium, has been determined for the transversal photothermal deflection technique. The results where compared to conventional spectrophotometry. In the photothermal deflection experiments performed with a continuous Ar⁺-excitation beam (=363.8 nm) a LOD of 0.8 g/l is achieved for the DNOC in water.Awarded poster prize     

Analytical solution for a steady flow of enclosed rotating disks

Low-Reynolds-number flow plays an important role in the centrifugal separation of fluid particles under microgravity conditions and also in micromechanics due to the miniaturization of fluid mechanical parts. In this situation, the governing equations may be simplified. Here an analytical solution is presented for the steady flow of an incompressible viscous fluid between two finite disks enclosed by a cylindrical container for small Reynolds number (Re 10). The general solution is valid for all choices of the aspect ratio () and different cases of disk to cylinder rotation rates (s). An expression for the torque acting on the disk is obtained. The tangential velocity distribution is calculated and presented graphically for different values of ands. Known results in the literature for a single rotating disk and similar problems follow as a particular case of the general solution presented.

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Zusammenfassung Zahlreiche hydrodynamische Vorgänge unter der Bedingung verminderter Schwerkraft aber auch Vorgänge in der Mikromechanik finden im Bereich kleiner Reynoldszahlen statt. In solchen Situationen können die Bewegungsgleichungen vereinfacht und eventuell analytische Lösungen gefunden werden. In dieser Arbeit wird die stationäre Strömung einer viskosen, inkompressiblen Flüssigkeit für kleine Reynolds- und unterschiedliche Aspektzahlen untersucht. Die Flüssigkeit ist zwischen zwei rotierenden Scheiben und einem zylindrischen Behälter eingeschlossen. Eine analytische Lösung für die Tangentialkomponente des Geschwindigkeitsvektors ist für den allgemeinen Fall, dass die Scheiben und der Behälter unterschiedliche Winkelgeschwindigkeiten besitzen können, dargestellt. Des weiteren wurde eine Beziehung für das Widerstandsmoment der rotierenden Scheibe angegeben. Der Verlauf der Tangentialgeschwindigkeiten für verschiedene Rotations- und Aspektverhältnisse wird graphisch dargestellt und diskutiert. Bereits angegebene Lösungen in der Literatur bezüglich dieser Geometrie können als Sonderfall der hier dargestellten Lösung entwickelt werden.

     

On some inequalities involving (n!)1/n,II

We prove: IfG(n) denotes the geometric mean of the firstn positive integers, then $$1< 1 + \frac{{G(n)}}{{G(n - 1)}} - \frac{{G(n + 1)}}{{G(n)}}< 1 + \frac{1}{n} - \frac{1}{{n + 1}}< n\frac{{G(n + 1)}}{{G(n)}} - (n - 1)\frac{{G(n)}}{{G(n - 1)}}$$ holds for alln≥3.     

On input/output stabilization of singular integrodifferential systems

In this paper we consider a class of systems described by singular integrodifferential equations. This type of systems appear, for example, in the modeling of certain aeroelastic control problems. We study these systems in frequency domain framework and show the existence of finite-dimensional stabilizing controllers. An algorithmic procedure is outlined for the construction of such controllers. In order to illustrate the numerical aspects of this algorithm, we present an example involving the classical Theodorsen model of an airfoil, which fits in the class of systems considered here.This work was supported in part by the National Science Foundation under Grants DMS-8907019 and MSS-9203418.     

Poles and zeros of best rational approximants of |x|

The asymptotic distribution (forn→∞) of poles and zeros of best rational approximantsr _n ^* ∈R _nn of the function |x| on [?1, 1] as well as the asymptotic distribution of extreme points of the error function |x|?r _n ^* (x) on [?1, 1] is investigated. The precision of the asymptotic formulae corresponds to that of the strong error formula $\lim _{n \to \infty } e^{\pi \sqrt n } E_{nn} (|x|,[ - 1,1]) = 8$ , which has been proved in [St1]. Here,E _nn (|x|, [?1, 1]) denotes the minimal approximation error in the uniform norm on [?1, 1]. The accuracy of the asymptotic distribution functions is so high that the location of individual poles, zeros, and extreme points can be distinguished forn sufficiently large.     

Series-parallel posets and relative Ockham lattices

A study is undertaken of order-reversing maps on series-parallel posets and structural characterisations are obtained of various subclasses of such ordered sets. The results are applied to complete the authors' earlier investigation of classes of finite relate lattices, where is a variety of Ockham lattices and the distributive lattice duals of the algebras in are required to be series-parallel.     

Fastiterative methods for least squares estimations

Least squares estimations have been used extensively in many applications, e.g. system identification and signal prediction. When the stochastic process is stationary, the least squares estimators can be found by solving a Toeplitz or near-Toeplitz matrix system depending on the knowledge of the data statistics. In this paper, we employ the preconditioned conjugate gradient method with circulant preconditioners to solve such systems. Our proposed circulant preconditioners are derived from the spectral property of the given stationary process. In the case where the spectral density functions() of the process is known, we prove that ifs() is a positive continuous function, then the spectrum of the preconditioned system will be clustered around 1 and the method converges superlinearly. However, if the statistics of the process is unknown, then we prove that with probability 1, the spectrum of the preconditioned system is still clustered around 1 provided that large data samples are taken. For finite impulse response (FIR) system identification problems, our numerical results show that annth order least squares estimator can usually be obtained inO(n logn) operations whenO(n) data samples are used. Finally, we remark that our algorithm can be modified to suit the applications of recursive least squares computations with the proper use of sliding window method arising in signal processing applications.Research supported in part by HKRGC grant no. 221600070, ONR contract no. N00014-90-J-1695 and DOE grant no. DE-FG03-87ER25037.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

Monotone path systems in simple regions

A monotone path system (MPS) is a finite set of pairwise disjoint paths (polygonal areas) in thexy-plane such that every horizontal line intersects each of the paths in at most one point. A MPS naturally determines a pairing of its top points with its bottom points. We consider a simple polygon in thexy-plane wich bounds the simple polygonal (closed) regionD. LetT andB be two finite, disjoint, equicardinal sets of points ofD. We give a good characterization for the existence of a MPS inD which pairsT withB, and a good algorithm for finding such a MPS, and we solve the problem of finding all MPSs inD which pairT withB. We also give sufficient conditions for any such pairing to be the same.The first author's research is supported by the Natural Sciences and Engineering Research Council of Canada