Monadische Erweiterungen von monadic NP

Fagin zeigt in seiner bahnbrechenden Arbeit, dass die Komplexitätsklasse NP mit der logischen Sprache 'existentielle Logik zweiter Ordnung' identifiziert werden kann. Ein einfaches und daher greifbares Fragment dieser Sprache ist monadic NP. Fagin bezeichnet monadic NP als '...training ground for attacking the problems in their full generality'. In dieser Arbeit werden zwei Arten von monadischen Erweiterungen von monadic NP untersucht. Der erste Teil beschäftigt sich mit schwachen built-in Relationen.Einebuilt-in Relation B heißt schwach, falls: monadic NP + B + polynomielles Padding neq NP.Es werden zwei neue Klassen schwacher built-in Relationen (unendlich teilbare-und verpackbare built-in Relationen) eingeführt. Hauptergebnis dieses Teils ist eine Klassifizierung aller bekannten schwachen built-in Relationen mittels dieser beiden Klassen. Im zweiten Teil dieser Arbeit werden monadische Abschlüsse von monadic NP betrachtet. Besonderes Interesse gilt dabei den positiven Abschluss erster Ordnung von monadic NP (kurz: PFO(monNP)). Hauptergebnis dieses Teils ist die Aussage, dass nicht-k-Färbbarkeit (k=>3) nicht ausdrückbar ist in PFO(monNP).

Synthesis and surface modification of semiconductor nanocrystals

The last decade has witnessed an exponential growth of activities in the field of nanoscience and nanotechnology worldwide, driven both by the excitement of understanding new science and by the potential hope for applications and economic impacts. The largest activity in this field up to date has been in the synthesis and characterization of new materials consisting of particles with dimensions in the order of a few nanometers, so-called nanocrystalline materials. [1-8] Semiconductor nanomaterials such as III/V or II/VI compound semiconductors exhibit strong quantum confinement behavior in the size range from 1 to 10 nm. Therefore, preparation of high quality semiconductor nanocrystals has been a challenge for synthetic chemists, leading to the recent rapid progress in delivering a wide variety of semiconducting nanomaterials. Semiconductor nanocrystals, also called quantum dots, possess physical properties distinctly different from those of the bulk material. Typically, in the size range from 1 to 10 nm, when the particle size is changed, the band gap between the valence and the conduction band will change, too. In a simple approximation a particle in a box model has been used to describe the phenomenon[9]: at nanoscale dimensions the degenerate energy states of a semiconductor separate into discrete states and the system behaves like one big molecule. The size-dependent transformation of the energy levels of the particles is called “quantum size-effect”. Quantum confinement of both the electron and hole in all three dimensions leads to an increase in the effective bandgap of the material with decreasing crystallite size. Consequently, both the optical absorption and emission of semiconductor nanaocrystals shift to the blue (higher energies) as the size of the particles gets smaller. This color tuning is well documented for CdSe nanocrystals whose absorption and emission covers almost the whole visible spectral range. As particle sizes become smaller the ratio of surface atoms to those in the interior increases, which has a strong impact on particle properties, too. Prominent examples are the low melting point [8] and size/shape dependent pressure resistance [10] of semiconductor nanocrystals. Given the size dependence of particle properties, chemists and material scientists now have the unique opportunity to change the electronic and chemical properties of a material by simply controlling the particle size. In particular, CdSe nanocrystals have been widely investigated. Mainly due to their size-dependent optoelectronic properties [11, 12] and flexible chemical processibility [13], they have played a distinguished role for a number of seminal studies [11, 12, 14, 15]. Potential technical applications have been discussed, too. [8, 16-27] Improvement of the optoelectronic properties of semiconductor nanocrystals is still a prominent research topic. One of the most important approaches is fabricating composite type-I core-shell structures which exhibit improved properties, making them attractive from both a fundamental and a practical point of view. Overcoating of nanocrystallites with higher band gap inorganic materials has been shown to increase the photoluminescence quantum yields by eliminating surface nonradiative recombination sites. [28] Particles passivated with inorganic shells are more robust than nanocrystals covered by organic ligands only and have greater tolerance to processing conditions necessary for incorporation into solid state structures or for other applications. Some examples of core-shell nanocrystals reported earlier include CdS on CdSe [29], CdSe on CdS, [30], ZnS on CdS, [31] ZnS on CdSe[28, 32], ZnSe on CdSe [33] and CdS/HgS/CdS [34]. The characterization and preparation of a new core-shell structure, CdSe nanocrystals overcoated by different shells (CdS, ZnS), is presented in chapter 4. Type-I core-shell structures as mentioned above greatly improve the photoluminescence quantum yield and chemical and photochemical stability of nanocrystals. The emission wavelengths of type-I core/shell nanocrystals typically only shows a small red-shift when compared to the plain core nanocrystals. [30, 31, 35] In contrast to type-I core-shell nanocrystals, only few studies have been conducted on colloidal type-II core/shell structures [36-38] which are characterized by a staggered alignment of conduction and valence bands giving rise to a broad tunability of absorption and emission wavelengths, as was shown for CdTe/CdSe core-shell nanocrystals. [36] The emission of type-II core/shell nanocrystals mainly originates from the radiative recombination of electron-hole pairs across the core-shell interface leading to a long photoluminescence lifetime. Type-II core/shell nanocrystals are promising with respect to photoconduction or photovoltaic applications as has been discussed in the literature.[39] Novel type-II core-shell structures with ZnTe cores are reported in chapter 5. The recent progress in the shape control of semiconductor nanocrystals opens new fields of applications. For instance, rod shaped CdSe nanocrystals can enhance the photo-electro conversion efficiency of photovoltaic cells, [40, 41] and also allow for polarized emission in light emitting diodes. [42, 43] Shape control of anisotropic nanocrystals can be achieved by the use of surfactants, [44, 45] regular or inverse micelles as regulating agents, [46, 47] electrochemical processes, [48] template-assisted [49, 50] and solution-liquid-solution (SLS) growth mechnism. [51-53] Recently, formation of various CdSe nanocrystal shapes has been reported by the groups of Alivisatos [54] and Peng, [55] respectively. Furthermore, it has been reported by the group of Prasad [56] that noble metal nanoparticles can induce anisotropic growth of CdSe nanocrystals at lower temperatures than typically used in other methods for preparing anisotropic CdSe structures. Although several approaches for anisotropic crystal growth have been reported by now, developing new synthetic methods for the shape control of colloidal semiconductor nanocrystals remains an important goal. Accordingly, we have attempted to utilize a crystal phase control approach for the controllable synthesis of colloidal ZnE/CdSe (E = S, Se, Te) heterostructures in a variety of morphologies. The complex heterostructures obtained are presented in chapter 6. The unique optical properties of nanocrystals make them appealing as in vivo and in vitro fluorophores in a variety of biological and chemical investigations, in which traditional fluorescence labels based on organic molecules fall short of providing long-term stability and simultaneous detection of multiple emission colours [References]. The ability to prepare water soluble nanocrystals with high stability and quantum yield has led to promising applications in cellular labeling, [57, 58] deep-tissue imaging, [59, 60] and assay labeling [61, 62]. Furthermore, appropriately solubilized nanocrystals have been used as donors in fluorescence resonance energy transfer (FRET) couples. [63-65] Despite recent progress, much work still needs to be done to achieve reproducible and robust surface functionalization and develop flexible (bio-) conjugation techniques. Based on multi-shell CdSe nanocrystals, several new solubilization and ligand exchange protocols have been developed which are presented in chapter 7. The organization of this thesis is as follows: A short overview describing synthesis and properties of CdSe nanocrystals is given in chapter 2. Chapter 3 is the experimental part providing some background information about the optical and analytical methods used in this thesis. The following chapters report the results of this work: synthesis and characterization of type-I multi-shell and type-II core/shell nanocrystals are described in chapter 4 and chapter 5, respectively. In chapter 6, a high–yield synthesis of various CdSe architectures by crystal phase control is reported. Experiments about surface modification of nanocrystals are described in chapter 7. At last, a short summary of the results is given in chapter 8.

Systematics and biogeography of Southeast Asian Senecioneae (Asteraceae): Revision of Cissampelopsis and Gynura and hybridisation in the introduced Crassocephalum

ZUSAMMENFASSUNG Die vorgelegte Dissertation enthält zwei Teile. Der erste beinhaltet eine Einführung in die Flora Südostasiens und die Untersuchungsgruppe Asteraceae-Senecioneae Cass. mit den Gattungen Cissampelopsis (DC.) Miq., Gynura Cass. und Crassocephalum Moench (Kapitel 1). Der zweite Teil besteht aus drei Manuskripten, die auf originalen Forschungsergebnissen basieren (Kapitel 2-4). In Kapitel 2 wird eine Revision der asiatischen Gattung Cissampelopsis vorgelegt. Die folgenden zwei Sektionen mit zehn Arten und zwei Varietäten werden anerkannt: sect. Buimalia C. Jeffrey & Y. L. Chen mit C. buimalia (Buch.-Ham. ex D. Don) C. Jeffrey & Y. L. Chen, C. erythrochaeta C. Jeffrey & Y. L. Chen und C. calcadensis (Ramasw.) C. Jeffrey & Y. L. Chen sowie sect. Cissampelopsis mit C. glandulosa C. Jeffrey & Y. L. Chen, C. walkeri (Arn.) C. Jeffrey & Y. L. Chen mit var. walkeri und var. floccosa Vanijajiva & Kadereit (var. nov.), C. corifolia C. Jeffrey & Y. L. Chen, C. volubilis (Bl.) Miq, C. ansteadii (Tadul. & Jacob) C. Jeffrey & Y. L. Chen, C. spelaeicola (Van.) C. Jeffrey & Y. L. Chen und C. corymbosa (Wall. ex DC.) C. Jeffrey & Y. L. Chen. Schlüssel, Artbeschreibungen, Fotographien von Blütenmerkmalen und Verbreitungskarten werden präsentiert. Kapitel 3 beinhaltet die Revision der paläotropischen Gattung Gynura. Vierundvierzig Arten werden anerkannt, darunter die folgenden drei Neubeschreibungen: G. davisii Vanijajiva & Kadereit, G. siamensis Vanijajiva & Kadereit und G. villosus Vanijajiva & Kadereit. Gynura dissecta (F. G. Davies) Vanijajiva & Kadereit, G. annua (F. G. Davies) Vanijajiva & Kadereit und G. aurantiaca (Bl) DC. subsp. parviflora (F. G. Davies) Vanijajiva & Kadereit sind Neukombinationen. Ein Schlüssel, Artbeschreibungen und Verbreitungskarten werden vorgelegt. In Kapitel 4 wird eine Analyse von Crassocephalum in Asien, einer aus Afrika eingeschleppten Gattung, präsentiert. Diese Untersuchung basiert auf umfangreicher Feldarbeit, Herbarstudien, Analysen der Pollen- und Samenfertilität, Chromosomenzählungen sowie ITS- und trnL-F-Sequenzen. Die Studie ergab, dass Crassocephalum in Asien mit zwei Arten und deren Hybrid vertreten ist. Die zwei Arten sind C. crepidioides (Benth.) S. Moore und C. rubens (Juss. ex Jacq.) S. Moore, wobei letztere einen Neufund für Asien darstellt. Der Hybrid aus diesen beiden Arten resultiert aus einer Kreuzung von C. crepidioides (2n=40) als weiblichem und C. rubens (2n=40) als männlichem Elter.

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions?

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions? The collapse of polyions in a poor solvent is a complex system and is an active research subject in the theoretical polyelectrolyte community. The complexity is due to the subtle interplay between hydrophobic effects, electrostatic interactions, entropy elasticity, intrinsic excluded volume as well as specific counter-ion and co-ion properties. Long range Coulomb forces can obscure single molecule properties. The here presented approach is to use just a small amount of screening salt in combination with a very high sample dilution in order to screen intermolecular interaction whereas keeping intramolecular interaction as much as possible (polyelectrolyte concentration cp ≤ 12 mg/L, salt concentration; Cs = 10^-5 mol/L). This is so far not described in literature. During collapse, the polyion is subject to a drastic change in size along with strong reduction of free counterions in solution. Therefore light scattering was utilized to obtain the size of the polyion whereas a conductivity setup was developed to monitor the proceeding of counterion collection by the polyion. Partially quaternized PVP’s below and above the Manning limit were investigated and compared to the collapse of their uncharged precursor. The collapses were induced by an isorefractive solvent/non-solvent mixture consisting of 1-propanol and 2-pentanone, with nearly constant dielectric constant. The solvent quality for the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of electrostatic interaction prior and during polyion collapse. Given that the Manning parameter M for QPVP4.3 is as low as lB / c = 0.6 (lB the Bjerrum length and c the mean contour distance between two charges), no counterion binding should occur. However the Walden product reduces with first addition of non solvent and accelerates when the structural collapse sets in. Since the dielectric constant of the solvent remains virtually constant during the chain collapse, the counterion binding is entirely caused by the reduction in the polyion chain dimension. The collapse is shifted to lower wns with higher degrees of quaternization as the samples QPVP20 and QPVP35 show (M = 2.8 respectively 4.9). The combination of light scattering and conductivity measurement revealed for the first time that polyion chains already collect their counter ions well above the theta-dimension when the dimensions start to shrink. Due to only small amounts of screening salt, strong electrostatic interactions bias dynamic as well as static light scattering measurements. An extended Zimm formula was derived to account for this interaction and to obtain the real chain dimensions. The effective degree of dissociation g could be obtained semi quantitatively using this extrapolated static in combination with conductivity measurements. One can conclude the expansion factor a and the effective degree of ionization of the polyion to be mutually dependent. In the good solvent regime g of QPVP4.3, QPVP20 and QPVP35 exhibited a decreasing value in the order 1 > g4.3 > g20 > g35. The low values of g for QPVP20 and QPVP35 are assumed to be responsible for the prior collapse of the higher quaternized samples. Collapse theory predicts dipole-dipole attraction to increase accordingly and even predicts a collapse in the good solvent regime. This could be exactly observed for the QPVP35 sample. The experimental results were compared to a newly developed theory of uniform spherical collapse induced by concomitant counterion binding developed by M. Muthukumar and A. Kundagrami. The theory agrees qualitatively with the location of the phase boundary as well as the trend of an increasing expansion with an increase of the degree of quaternization. However experimental determined g for the samples QPVP4.3, QPVP20 and QPVP35 decreases linearly with the degree of quaternization whereas this theory predicts an almost constant value.

57 Fe and 119 Sn Mössbauer studies on new Heusler compounds for spintronic applications

Seit der Entwicklung einer großen Vielfalt von Anwendungsmöglichkeiten der Spintronik auf Basis von Heusler Verbindungen innerhalb der letzten Dekade kann der Forschungsfortschritt an dieser Material Klasse in einer Vielzahl von Publikationen verfolgt werden. Eine typische Heusler Verbindung X2YZ besteht aus zwei Übergangsmetallen (X, Y) und einem Hauptgruppenelement (Z). Diese Arbeit berichtet von Heusler Verbindungen mit besonderem Augenmerk auf deren potentielle halbmetallische Eigenschaften und davon insbesondere solche, die eine richtungsabhängige magnetische Anisotropie (perpendicular magnetic anisotropy- PMA) zeigen könnten. PMA ist insbesondere für Spin transfer Torque (STT) Bauelemente von großem Interesse und tritt in tetragonalrnverzerrten Heusler Verbindungen auf. Bei STT-Elementen werden mittels spinpolarisierter Ströme die magnetische Orientierung von magnetischen Schichten beeinflusst.rnDie signifikantesten Ergebnisse dieser Arbeit sind: die Synthese neuer kubischen Heusler Phasen Fe2YZ, die theoretisch als tetragonal vorausgesagt wurden (Kapitel 1), die Synthese von Mn2FeGa, das in der tetragonal verzerrten Struktur kristallisiert und Potential für STT Anwendungen zeigt (Kapitel 2); die Synthese von Fe2MnGa, das einen magnetischen Phasenübergang mit exchange-bias (EB) Effekt zeigt, der auf einer Koexistenz von ferromagnetischen (FM) und antiferromagnetischen (AFM) Phasen beruht (Kapitel 3); Schlussendlich wird in Kapitel 4 die Synthese von Mn3−xRhxSn diskutiert, in welcher insbesondere tetragonales Mn2RhSn als potentielles Material für Anwendungen in derrnSpintronik vorgestellt wird.rnIn dieser Arbeit wurden hauptsächlich Heusler Verbindungen mit mößbaueraktiven Elementen 57Fe und 119Sn, synthetisiert und untersucht. Im Falle der hier untersuchten Heusler Verbindungen spielt die Charakterisierung durch Mößbauer Spektroskopie eine entscheidende Rolle, da Heusler Verbindungen meistens ein gewisses Maß an Fehlordnung aufweisen, welche deren magnetischen und strukturellen Eigenschaften beeinflussen kann. Die Art der Fehlordnung jedoch kann nur schwer durch standard Pulver-Röntgendiffraktion bestimmt werden, weshalb wir die Vorteile der Mößbauer Spektroskopie als lokale Methode nutzen, um den Typ und den Grad der Fehlordnung aufzuklären. rnDiese Arbeit ist wie folgt gegliedert:rnIn Kapitel 1 wurden die neuen, kubisch-weichferromagnetischen Heuslerphasen Fe2NiGe, Fe2CuGa und Fe2CuAl synthetisiert und charakterisiert. In vorangegangenen theoretischen Studien wurde für deren Existenz in tetragonaler Heuslerstruktur vorhergesagt.rnUngeachtet dessen belegten unsere experimentellen Untersuchungen, dass diese Verbindungen hauptsächlich in der kubischen invers Heusler(X-) struktur mit unterschiedlichen Anteilen an atomarer Fehlordnung kristallisieren. Alle Verbindungen sind weiche Ferromagneten mit hoher Curietemperatur bis zu 900K, weswegen alle als potentielle Materialien für magnetische Anwendungen geeignet sind. In Kapitel 2 wurde Mn2FeGa synthetisiert. Es zeigte sich, dass Mn2FeGa nach Temperatur Nachbehandlung bei 400°C die invers tetragonale Struktur (I4m2) annimmt. Theoretisch wurde die Existenz in der inversen kubischen Heuslerstruktur vorausgesagt. Abhängig von den Synthesebedingungen ändern sich die magnetischen und strukturellen Eigenschaften von Mn2FeGa eklatant. Deshalb ändert sich die Kristallstruktur von M2FeGa bei Temperung bei 800 °C zu einer pseudokubischen Cu3Au-artigen Struktur, in welcher Fe- und Mn-Atome statistisch verteilt vorliegen. Dieser Übergang der Kristallstrukturen wurde durch Mößbauer Spektroskopie anhand des Vorliegens oder Fehlens der Quadrupolaufspaltung im Falle der invers tetragonalen bzw. pseudokubischen Modifikation nachgewiesen. In Kapitel 3 wurde Fe2MnGa ebenfalls erfolgreich synthetisiert und durch verschiedene Methoden charakterisiert. Der Zusammenhang von Kristallstruktur und magnetischen Eigenschaften wurde durch verschiedene Temperungskonditionen und mechanischer Behandlung untersucht. Der Schwerpunkt lag auf einer geschmolzenen Probe ohne weitere Temperung, die einen FM-AFM Phasenübergang zeigte. Diese magnetische Phasenumwandlung führt zu einem starken EB-Verhalten, welches seinen Ursprung hauptsächlich in der Koexistenz von FM- und AFM-Phasen unterhalb der FMAFM- Übergangstemperatur hat. Kapitel 4 ist den neuen Mn-basierten Heusler-Verbindungen Mn3−xRhxSn gewidmet, bei denen wir versuchten, durch den Austausch von Mn durch das größere Rh eine Umwandlung zu einer tetragonalen Struktur von den hexagonalen Mn3Sn-Struktur zu erreichen. Als interessant stellten sich Mn2RhSn und Mn2.1Rh0.9Sn heraus, da sie aus nur einer Phase vorzuliegen scheinen, wohingegen die anderen Verbindungen aus gemischten Phasen mit gleichzeitiger starken Fehlordnung bestehen. Im abschließenden Anhang wurden die Fehlordnung und gelegentliche Mischphasen einer großen Auswahl von Mn3−xFexGa Materialien mit 1≤x≤3, dokumentiert.rn

Systematics, phylogeny and biogeography of Juncaginaceae

I investigated the systematics, phylogeny and biogeographical history of Juncaginaceae, a small family of the early-diverging monocot order Alismatales which comprises about 30 species of annual and perennial herbs. A wide range of methods from classical taxonomy to molecular systematic and biogeographic approaches was used. rnrnIn Chapter 1, a phylogenetic analysis of the family and members of Alismatales was conducted to clarify the circumscription of Juncaginaceae and intrafamilial relationships. For the first time, all accepted genera and those associated with the family in the past were analysed together. Phylogenetic analysis of three molecular markers (rbcL, matK, and atpA) showed that Juncaginaceae are not monophyletic. As a consequence the family is re-circumscribed to exclude Maundia which is pro-posed to belong to a separate family Maundiaceae, reducing Juncaginaceae to include Tetroncium, Cycnogeton and Triglochin. Tetroncium is weakly supported as sister to the rest of the family. The reinstated Cycnogeton (formerly included in Triglochin) is highly supported as sister to Triglochin s.str. Lilaea is nested within Triglochin s. str. and highly supported as sister to the T. bulbosa complex. The results of the molecular analysis are discussed in combination with morphological characters, a key to the genera of the family is given, and several new combinations are made.rnrnIn Chapter 2, phylogenetic relationships in Triglochin were investigated. A species-level phylogeny was constructed based on molecular data obtained from nuclear (ITS, internal transcribed spacer) and chloroplast sequence data (psbA-trnH, matK). Based on the phylogeny of the group, divergence times were estimated and ancestral distribution areas reconstructed. The monophyly of Triglochin is confirmed and relationships between the major lineages of the genus were resolved. A clade comprising the Mediterranean/African T. bulbosa complex and the American T. scilloides (= Lilaea s.) is sister to the rest of the genus which contains two main clades. In the first, the widespread T. striata is sister to a clade comprising annual Triglochin species from Australia. The second clade comprises T. palustris as sister to the T. maritima complex, of which the latter is further divided into a Eurasian and an American subclade. Diversification in Triglochin began in the Miocene or Oligocene, and most disjunctions in Triglochin were dated to the Miocene. Taxonomic diversity in some clades is strongly linked to habitat shifts and can not be observed in old but ecologically invariable lineages such as the non-monophyletic T. maritima.rnrnChapter 3 is a collaborative revision of the Triglochin bulbosa complex, a monophyletic group from the Mediterranean region and Africa. One new species, Triglochin buchenaui, and two new subspecies, T. bulbosa subsp. calcicola and subsp. quarcicola, from South Africa were described. Furthermore, two taxa were elevated to species rank and two reinstated. Altogether, seven species and four subspecies are recognised. An identification key, detailed descriptions and accounts of the ecology and distribution of the taxa are provided. An IUCN conservation status is proposed for each taxon.rnrnChapter 4 deals with the monotypic Tetroncium from southern South America. Tetroncium magellanicum is the only dioecious species in the family. The taxonomic history of the species is described, type material is traced, and a lectotype for the name is designated. Based on an extensive study of herbarium specimens and literature, a detailed description of the species and notes on its ecology and conservation status are provided. A detailed map showing the known distribution area of T. magellanicum is presented. rnrnIn Chapter 5, the flower structure of the rare Australian endemic Maundia triglochinoides (Maundiaceae, see Chapter 1) was studied in a collaborative project. As the morphology of Maundia is poorly known and some characters were described differently in the literature, inflorescences, flowers and fruits were studied using serial mictrotome sections and scanning electron microscopy. The phylogenetic placement, affinities to other taxa, and the evolution of certain characters are discussed. As Maundia exhibits a mosaic of characters of other families of tepaloid core Alismatales, its segregation as a separate family seems plausible.