Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

Group activity selection problem with approval preferences

We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents’ preferences are binary, i.e., each agent classifies all pairs of the form ‘(activity, group size)’ into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents’ preferences satisfy certain natural constraints.     

Precise mass measurement of a double-stranded 500 base-pair (309 kDa) polymerase chain reaction product by negative ion electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry

Electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI-FTICRMS) has been used to determine the mass of a double-stranded 500 base-pair (bp) polymerase chain reaction (PCR) product with an average theoretical mass of the blunt-ended (i.e. unadenylated) species of 308 859.35 Da. The PCR product was generated from the linearized bacteriophage Lambda genome which is a double-stranded template. Utilization of ethanol precipitation in tandem with a rapid microdialysis step to purify and desalt the PCR product was crucial to obtain a precise mass measurement. The PCR product (0.8 pmol/μL) was electrosprayed from a solution containing 75% acetonitrile, 25 mM piperidine, and 25 mM imidazole and was infused at a rate of 200 nL/min. The average molecular mass and the corresponding precision were determined using the charge-states ranging from 172 to 235 net negative charges. The experimental mass and corresponding precision (reported as the 95% confidence interval of the mean) was 309 406 +/- 27 Da (87 ppm). The mass accuracy was compromised due to the fact that the PCR generates multiple products when using Taq polymerase due to the non-template directed 3'-adenylation. This results in a mixture of three PCR products with nearly identical mass (i.e. blunt-ended, mono-adenylated and di-adenylated) with unknown relative abundances that were not resolved in the spectrum. Thus, the experimental mass will be a weighted average of the three species which, under our experimental conditions, reflects a nearly equal concentration of the mono- and di-adenylated species. This report demonstrates that precise mass measurements of PCR products up to 309 kDa (500 bp) can be routinely obtained by ESI-FTICR requiring low femtomole amounts. Copyright 1999 John Wiley & Sons, Ltd.     

Lithography potentials of UV-nanoimprint

In the past decade nanoimprint has been developed to a serious alternative for next generation lithography (NGL). In this work, the most recent developments of UV-nanoimprint Lithography (UV-NIL) with special emphasis to the work accomplished at AMO and the IHT-RWTH Aachen are reviewed and functional applications demonstrated. Further the potentials of various UV-NIL concepts are evaluated and possible interests in certain application areas are discussed.     

Experimental details of the Stopped Beam RISING campaign

The RISING (Rare ISotope INvestigations at GSI) project constitutes a major pan-european initiative to study nuclear structure in exotic nuclei. A brief outline of the technical details specific to studies of isomeric decays following relativistic projectile fragmentation reactions is presented.     

Influence of CF3 Substituents on the Spin Crossover Behavior of Iron(II) Coordination Polymers with Schiff Base-like Ligands

A Schiff base-like ligand bearing CF₃ substituents was synthesized and converted to iron(II) coordination polymers [{FeL(L_ax)}_n] using five different bridging ligands L_ax. The structure of the coordination polymers was investigated using powder X-ray diffraction and single-crystal X-ray diffraction in the case of [{FeL(bipy)}_n]. The later revealed an untypical ABAB pattern of alternating equatorial ligands rotated by 180° with regard to each other along the chain. The temperature-dependent magnetic behavior was investigated with a SQUID magnetometer and the spin states at room temperature were confirmed by ⁵⁷Fe-Mössbauer spectroscopy. Three out of five coordination polymers show spin crossover behavior in the temperature range between 50 and 400 K with different kind of curve progressions (abrupt, gradual, step-wise). The other two coordination polymers are either fully highspin or fully low spin.     

Intrinsic photorefractive effect of LiNbO3

The photorefractive effect of undoped LiNbO₃ crystals of high purity is studied by means of two-photon excitation of picosecond light pulses. We show that two-photon photorefractive recording is accompanied by characteristic changes of the optical absorption and electron spin resonance spectra due to the formation of color centers. The role of these centers for the photorefractive process in discussed.     

Water oxidation catalysed by manganese compounds: from complexes to 'biomimetic rocks'

One of the most fundamental processes of the natural photosynthetic reaction sequence is the light-driven oxidation of water to molecular oxygen. In vivo, this reaction takes place in the large protein ensemble Photosystem II, where a μ-oxido-Mn(4)Ca- cluster, the oxygen-evolving-complex (OEC), has been identified as the catalytic site for the four-electron/four-proton redox reaction of water oxidation. This Perspective presents recent progress for three strategies which have been followed to prepare functional synthetic analogues of the OEC: (1) the synthesis of dinuclear manganese complexes designed to act as water-oxidation catalysts in homogeneous solution, (2) heterogeneous catalysts in the form of clay hybrids of such Mn(2)-complexes and (3) the preparation of manganese oxide particles of different compositions and morphologies. We discuss the key observations from the studies of such synthetic manganese systems in order to shed light upon the catalytic mechanism of natural water oxidation. Additionally, it is shown how research in this field has recently been motivated more and more by the prospect of finding efficient, robust and affordable catalysts for light-driven water oxidation, a key reaction of artificial photosynthesis. As manganese is an abundant and non-toxic element, manganese compounds are very promising candidates for the extraction of reduction equivalents from water. These electrons could consecutively be fed into the synthesis of "solar fuels" such as hydrogen or methanol.