The mathematics of playing golf, or: a new class of difficult non-linear mixed integer programs

We consider a class of non-linear mixed integer programs with n integer variables and k continuous variables. Solving instances from this class to optimality is an NP-hard problem. We show that for the cases with k=1 and k=2, every optimal solution is integral. In contrast to this, for every k≥3 there exist instances where every optimal solution takes non-integral values. Received: August 2001 / Accepted: January 2002?Published online March 27, 2002     

Study of thermal aging effect on space charge in poly(methyl methacrylate)

Charges evolution in poly(methyl methacrylate) (PMMA) samples under thermal aging effect has been studied by means of two complementary techniques, thermal step method (TSM) and thermally stimulated depolarization current (TSDC). For the first method, measurements reveal that injected charges, whose quantity is found depending on the number of applied temperature cycles, remain close to the surface sample. TSDC measurements have been carried out for different temperatures ranging from 25 °C to 140 °C. Three distinguishable dipolar relaxations (β₁, β₂ and α) have been highlighted. In the same way, the presence of polarization and injected charges has been confirmed. In support of electric characterization, X-ray reflectometry has been used. The obtained results equally emphasized the thermal aging effect on the material.     

Existence and Nonlinear Stability of Stationary States of the Schrödinger–Poisson System

We consider the Schrödinger–Poisson system in the repulsive (plasma physics) Coulomb case. Given a stationary state from a certain class we prove its nonlinear stability, using an appropriately defined energy-Casimir functional as Lyapunov function. To obtain such states we start with a given Casimir functional and construct a new functional which is in some sense dual to the corresponding energy-Casimir functional. This dual functional has a unique maximizer which is a stationary state of the Schrödinger–Poisson system and lies in the stability class. The stationary states are parameterized by the equation of state, giving the occupation probabilities of the quantum states as a strictly decreasing function of their energy levels.     

Polyethylene compounds with antimicrobial surface properties

The present study aims at antimicrobial polyethylene surfaces. To achieve this, LLDPE was compounded with the polymeric biocide poly(2-tert-butylaminoethyl) methacrylate TBAM (bulk modification with 1.5-5.0 wt.% of TBAM). Surfaces of these polymer compounds were then subjected to microbial assays. Using standard methods the colony forming units (CFU) for Escherichia coli and Staphylococcus aureus were determined on these surfaces. In all cases, polyethylene surfaces with highly antimicrobial properties were achieved. An average reduction of 10⁴ CFU ml⁻¹ compared to neat LLDPE was achieved. The surfaces of these LLDPE/TBAM compounds were assessed by electrokinetic (zeta potential) measurements. The results indicate a relation between the antimicrobial activity and the zeta-potential of the polymer compounds. Moreover, the antimicrobial compounds were investigated towards biofilm formation. Compared to pristine LLDPE, the surfaces of the polymer compounds showed less adhering biofilm after a testing period of 16 weeks.     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

Nachweise verwandter Elemente nebeneinander in einem Tropfen. II. Mitteilung: Der mikrochemische Nachweis von Aluminium und Beryllium mittels Ammoniummolybdats

Zusammenfassung Entgegen den Auffassungen von van Zijp über den von ihm veröffentlichten Nachweis des Aluminiums mit Ammoniummolybdat wurde gezeigt, daß ein derartiger Nachweis Empfindlichkeit und Störungsfreiheit in hohem Grade vereint.Der Nachweis durch Ammoniummolybdat konnte auf Beryllium ausgedehnt werden. Eine Reihe von Versuchen zeigte, daß Aluminium- und Berylliummolybdat in zwei verschiedenen Krystallformen ohne gegenseitige Beeinträchtigung selbst nebeneinander auszukrystallisieren vermögen.Es ist mir eine angenehme Pflicht, Herrn Prof. Dr. Wilhelm Böttger für sein stets färderndes Interesse und für die mikrochemische Arbeitsmäglichkeit überhaupt zu danken. Zu Dank verpflichtet bin ich auch der Fa. Otto Perutz, München für die freundliche überlassung von Pervola-Platten zu den Mikrophotographien.     

Photochemical expulsion of the neutral monodentate ligand L in Ru(terpy*)(diimine)(L)2+: a dramatic effect of the steric properties of the spectator diimine ligand

A series of photoreactive complexes of the type Ru(terpy*)(N-N)(L)(2+), where terpy* is 4'-(3,5-ditertiobutylphenyl)-2,2':6',2' '-terpyridine, N-N is the bidentate chelate phen or dmp (phen = 1,10-phenanthroline, dmp = 2,9-dimethyl-1,10-phenanthroline), and L is the monodentate ligand dms, MeBN, or MeOBN (dms = dimethyl sulfide, MeBN = 2,6-dimethyl benzonitrile, MeOBN = 2,6-dimethoxybenzonitrile), has been synthesized and fully characterized by proton NMR spectroscopy, electrospray mass spectrometry, and UV-vis spectroscopy. The X-ray structures of four complexes were also obtained. In neat pyridine, the quantum yields for the photosubsitution of L by pyridine were measured and showed dramatic variations depending on the steric interactions between the spectator bidentate ligand and the leaving monodentate ligand L. The use of dmp instead of phen multiplied the photosubstitution efficiency by a factor of 20-50, depending on L. This effect could be qualitatively correlated to the distortions observed in the X-ray structures of the corresponding complexes. The highly distorted structure of Ru(terpy)(dmp)(dms)(PF(6))(2) showed a very high photosubsitution quantum yield phi = 0.36 in neat pyridine. The high photoreactivity of some of the compounds makes them particularly promising as components of future light-driven molecular machines.     

MDGC–MS: A powerful tool for enantioselective flavor analysis

This paper reports the differentiation between the enantiomers of theaspiranes and theaspirones, potent flavor compounds widely used in the flavor industry. Optically pure reference compounds of isomeric theaspiranes were obtained by enantioselective synthesis. Enantiomerically pure reference theaspirones were isolated from quince fruit; their absolute stereochemistry was assigned by CD spectroscopy. For both types of compounds the order of elution was elucidated by using authentic reference compounds. These data enabled the determination of the enantiomeric distribution of both types of compounds in a variety of plant tissues. Because of the complexity of the natural flavor isolates, compounds were identified by mass spectrometry after multidimensional gas chromatography employing a Sichromat 2 double oven chromatograph. After separation of the target compounds on the first, achiral, column (DB-5), they were transferred to a chiral column (C-Dex B) for determination of the enantiomeric distribution. Multiple ion detection (MID) enabled the determination of the enantiomeric distribution even for complex mixtures containing the target compounds at extremely low levels.