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Ohne Zusammenfassung     

A degenerate Newton’s map in two complex variables: Linking with currents

Little is known about the global structure of the basins of attraction of Newton’s method in two or more complex variables. We make the first steps by focusing on the specific Newton mapping to solve for the common roots of P(x, y) = x(1−x) and Q(x, y) = y² + Bxy − y. There are invariant circles S₀ and S₁ within the lines x = 0 and x = 1 which are superattracting in the x-direction and hyperbolically repelling within the vertical line. We show that S₀ and S₁ have local super-stable manifolds, which when pulled back under iterates of N form global super-stable spaces W₀ and W₁. By blowing-up the points of indeterminacy p and q of N and all of their inverse images under N we prove that W₀ and W₁ are real-analytic varieties. We define linking between closed 1-cycles in W_i (i = 0, 1) and an appropriate closed 2 current providing a homomorphism lk: H₁ (W_i, ℤ) → ℚ. If W_i intersects the critical value locus of N, this homomorphism has dense image, proving that H₁ (W_i, ℤ) is infinitely generated. Using the Mayer-Vietoris exact sequence and an algebraic trick, we show that the same is true for the closures of the basins of the roots      

Positive Semidefinite Rank-Based Correlation Matrix Estimation With Application to Semiparametric Graph Estimation

Many statistical methods gain robustness and flexibility by sacrificing convenient computational structures. In this article, we illustrate this fundamental tradeoff by studying a semiparametric graph estimation problem in high dimensions. We explain how novel computational techniques help to solve this type of problem. In particular, we propose a nonparanormal neighborhood pursuit algorithm to estimate high-dimensional semiparametric graphical models with theoretical guarantees. Moreover, we provide an alternative view to analyze the tradeoff between computational efficiency and statistical error under a smoothing optimization framework. Though this article focuses on the problem of graph estimation, the proposed methodology is widely applicable to other problems with similar structures. We also report thorough experimental results on text, stock, and genomic datasets.     

Nearest Neighbor Distances on a Circle: Multidimensional Case

We study the distances, called spacings, between pairs of neighboring energy levels for the quantum harmonic oscillator. Specifically, we consider all energy levels falling between E and E+1, and study how the spacings between these levels change for various choices of E, particularly when E goes to infinity. Primarily, we study the case in which the spring constant is a badly approximable vector. We first give the proof by Boshernitzan-Dyson that the number of distinct spacings has a uniform bound independent of E. Then, if the spring constant has components forming a basis of an algebraic number field, we show that, when normalized up to a unit, the spacings are from a finite set. Moreover, in the specific case that the field has one fundamental unit, the probability distribution of these spacings behaves quasiperiodically in logE. We conclude by studying the spacings in the case that the spring constant is not badly approximable, providing examples for which the number of distinct spacings is unbounded.     

Tensile Testing of Single Regenerated Cellulose Fibres

Summary: A tensile testing set-up was developed for the determination of the elastic modulus, tensile strength, and failure strain of single regenerated cellulose fibres. Since the accuracy of strain measurement is crucial for the measured elastic modulus and failure strain, strain measurements were performed mechanically and with a non-contacting optical method in parallel. The optical validation of mechanical strain measurement showed an agreement of measured strain >99%, confirming the accuracy and usefulness of the set-up and sample geometry developed for the test series.     

Fast-Beam Laser Spectroscopy of Helium-like Silicon

We have characterized a system of maghemite, γ-Fe₂O₃, nanosized particles prepared by a microemulsion method using an ionic surfactant. The Mössbauer spectra from 21 to 298 K evolve from a totally magnetically split signal at low temperatures to a single superparamagnetic (sp) doublet at 298 K with a blocking temperature of ≈150 K. The real component of the AC susceptibility (5≤ν≤10⁴ Hz) displays a behavior characteristic of a system of interacting particles. A broad distribution of the particle sizes is revealed by the much higher average energy barrier obtained by AC susceptibility than Mössbauer.

     

Quantitative photometrische Bestimmung der Pyrrolizidinalkaloide in Symphity Radix

Zusammenfassung Eine bereits in der Literatur beschriebene Farbreaktion für 1,2-ungesättigte Pyrrolizidinalkaloide (PAs) wird zur Gehaltsbestimmung der toxischen PAs in Symphyti Radix herangezogen. Durch Veränderung einiger Versuchsparameter konnte die Erfassungsgrenze auf 1 Mikrogramm herabgesetzt und die Reproduzierbarkeit der Messung erheblich verbessert werden. Für die alkaloidreichen Beinwellwurzeln wurde eine einfache Extraktionsmethode validiert, die einen Nachweis von 10 ppm in einem Gramm getrockneter Droge gestattet (0,001%).

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Quantitative photometric determination of pyrrolizidine alkaloids in Symphyti Radix

Summary A colour reaction for unsaturated pyrrolizidine alkaloids (PAs), which has already been published, is used for spectrophotometric determination of the toxic PAs in Symphyti Radix (Symphytum officinale L., Boraginaceae). By changing several parameters it was possible to reduce the detection limit to 1 microgram and to improve significantly the reproducibility of the quantitative determination. For Symphyti Radix a simple extraction method allowing the detection of 10 ppm PAs in 1 gram dried drug (0.001%) was validaded.

     

Dimeric Cyclodextrin Carriers with High Binding Affinity to Porphyrinoid Photosensitizers

The aim of our investigation was to develop carrier systems for an application of inert drugs in photodynamic cancer therapy. -Cyclodextrin dimers linked at their primary and secondary faces by spacers of varying lengths were synthesized as carrier systems. The binding constants of the inclusion complexes of these cyclodextrin dimers and porphyrinoid photosensitizers were determined by competitive spectrofluorometry. Particularly the secondary face linked dimers exhibited extremely high binding constants with values of 106-107 L/mol. Theoretical studies were carried out on these inclusion complexes to confirm the influence of spacer length and connecting side on complex stability.     

Quantitation in miniaturized GC and SFC systems

Separations of high efficiency and/or speed can be achieved in capillary GC by capillary columns of lower internal diameter (< 50 μm). Sampling techniques for the analytical application of narrow bore fused silica columns have been evaluated with regard to quantitation. On-column injection cannot be applied. Therefore liquid samples have to be vaporized in external devices before they enter the chromatographic system. Sample introduction by syringe with subsequent splitting must and can be applied but requires special syringes with perfect piston sealing because of the high inlet pressures needed even with hydrogen as carrier gas. For general analytical applications, valve systems should be developed to eliminate both the syringe and the septum from instrumental GC set-up's. In SFC using either narrow bore capillary or packed microbore columns, time-controlled valve sampling with partial displacement of the sample from the loop seems to be an adequate technique because of the very high inlet pressures involved. Splitting in combination with valve operation can also be applied in capillary SFC at least to samples of good solubility in the mobile phase. A disadvantage of splitting in SFC is that another restriction for the adjustment of the split flow is necessary.