Angle theorems for the Lagrangian mean curvature flow

We prove that symplectic maps between Riemann surfaces L, M of constant, nonpositive and equal curvature converge to minimal symplectic maps, if the Lagrangian angle for the corresponding Lagrangian submanifold in the cross product space satisfies . If one considers a 4-dimensional K?hler-Einstein manifold of nonpositive scalar curvature that admits two complex structures J, K which commute and assumes that is a compact oriented Lagrangian submanifold w.r.t. J such that the K?hler form w.r.t.K restricted to L is positive and , then L converges under the mean curvature flow to a minimal Lagrangian submanifold which is calibrated w.r.t. . Received: 11 April 2001 / Published online: 29 April 2002     

Synthesis and antibody conjugation of magnetic nanoparticles with improved specific power absorption rates for alternating magnetic field cancer therapy

Bionized nanoferrite (BNF) particles with high specific power absorption rates were synthesized in the size range of 20–100 nm by high-pressure homogenization for targeted cancer therapy with alternating magnetic fields. Several strategies were used to conjugate antibodies to the BNF particles. These strategies were compared using an immunoassay to find optimal conditions to reach a high immunoreactivity of the final antibody–particle conjugate.     

The course scheduling problem at Lufthansa Technical Training

Lufthansa Technical Training GmbH (LTT) performs training courses for Lufthansa Technik AG as well as for several other international airlines. Courses of about 670 different types are offered of which several hundred take place each year. The course scheduling problem faced by LTT is to construct a yearly schedule which maximizes the profit margin incurred while meeting a variety of complex precedence, temporal, and resource-related constraints. A “good” operational schedule should also meet a number of additional subordinate objectives. We formalize the problem and develop a heuristic scheme along with several priority rules, as well as a local search algorithm to determine well-suited weights for weighted composite rules. The operational planning situation of 1996 served as our major test instance; additional test instances were constructed by modifying this data. Several computational experiments were carried out to evaluate the performance of the algorithms. It turned out that the best so-found schedule is substantially better in terms of the profit margin incurred than the solution manually constructed by LTT.     

On a problem proposed by H. Braß concerning the remainder term in quadrature for convex functions

Summary We prove that the error inn-point Gaussian quadrature, with respect to the standard weight functionw1, is of best possible orderO(n ^–2) for every bounded convex function. This result solves an open problem proposed by H. Braß and published in the problem section of the proceedings of the 2. Conference on Numerical Integration held in 1981 at the Mathematisches Forschungsinstitut Oberwolfach (Hämmerlin 1982; Problem 2). Furthermore, we investigate this problem for positive quadrature rules and for general product quadrature. In particular, for the special class of Jacobian weight functionsw _, (x)=(1–x)(1+x), we show that the above result for Gaussian quadrature is not valid precisely ifw _, is unbounded.Dedicated to Prof. H. Braß on the occasion of his 55th birthday     

Partial least-squares regression and fuzzy clustering — A joint approach

Chemical and physical analyses of malt, the main ingredient of beer, have been used to predict the concentration of certain volatile compounds in the finished beer.The prediction was done by means of the partial least squares regression (PLS2) in SIMCA. The total data set as well as individual malt clusters were submitted to PLS analysis. Best prediction was obtained by separating the total object matrix in classes according to similarity found by fuzzy pattern recognition (FCV). FCV was also used to separate the beer variables in classes and to select the subset of variables to be predicted.A joint approach of fuzzy pattern recognition to identify groups of samples and SIMCA-PLS2 to predict several dependent variables is suggested as a powerful tool in process-analytical chemistry.     

Atomic structure of Beta-tantalum nanocrystallites.

The structural properties of beta-phase tantalum nanocrystallites prepared by room temperature magnetron sputter deposition on amorphous carbon substrates are investigated at atomic resolution. For these purposes spherical aberration-corrected high-resolution transmission electron microscopy is applied in tandem with the numerical retrieval of the exit-plane wavefunction as obtained from a through-focus series of experimental micrographs. We demonstrate that recent improvements in the resolving power of electron microscopes enable the imaging of the atomic structure of beta-tantalum with column spacings of solely 0.127 nm with directly interpretable contrast features. For the first time ever, we substantiate the existence of grain boundaries of 30 degrees tilt type in beta-Ta whose formation may be well explained by atomic agglomeration processes taking place during sputter deposition.     

Evaluations of solid electrodes for use in voltammetric monitoring of heavy metals in samples from metallurgical nickel industry

Evaluation of different solid electrode systems for detection of zinc, lead, cobalt, and nickel in process water from metallurgical nickel industry with use of differential pulse stripping voltammetry has been performed. Zinc was detected by differential pulse anodic stripping voltammetry (DPASV) on a dental amalgam electrode as intermetallic Ni–Zn compound after dilution in ammonium buffer solution. The intermetallic compound was observed at –375 mV, and a linear response was found in the range 0.2–1.2 mg L^–1 (r²=0.98) for 60 s deposition time. Simultaneous detection of nickel and cobalt in the low g L^–1 range was successfully performed by use of adsorptive cathodic stripping voltammetry (AdCSV) of dimethylglyoxime complexes on a silver–bismuth alloy electrode, and a good correlation was found with corresponding AAS results (r²=0.999 for nickel and 0.965 for cobalt). Analyses of lead in the g L^–1 range in nickel-plating solution were performed with good sensitivity and stability by DPASV, using a working electrode of silver together with a glassy carbon counter electrode in samples diluted 1:3 with distilled water and acidified with H₂SO₄ to pH 2. A new commercial automatic at-line system was tested, and the results were found to be in agreement with an older mercury drop system. The stability of the solid electrode systems was found to be from one to several days without any maintenance needed.     

Detection of Trace concentrations of gases with coated piezoelectric quartz crystals

Coated piezoelectric crystal sensors for determination of trace constituents in gases are very sensitive. Detection limits down to the sub-ppb range have been reported, using injection techniques. From previous and presented data, this high sensitivity is found to be in disagreement with Sauerbrey's eqn., which allows a maximum sensitivity of about 1 ppm. By considering the adsorption of the gases on the coated surface and the calibration procedures used, the validity of Sauerbrey's eqn. is discussed.     

Asymptotics for the remainder of a class of positive quadratures for integrands with an interior singularity

Summary For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler Euler-Maclaurin type formulae. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u| , where >–1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type.