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Schriftenreihe
Sonstige beteiligte Institutionen
- Helmholtz Institute for RNA-based Infection Research (HIRI) (7)
- Fraunhofer-Institut für Silicatforschung ISC (5)
- Technische Hochschule Nürnberg Georg Simon Ohm (3)
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ResearcherID
- B-1911-2015 (1)
- B-4606-2017 (1)
- C-2593-2016 (1)
- D-1250-2010 (1)
- I-5818-2014 (1)
- J-8841-2015 (1)
- M-1240-2017 (1)
- N-2030-2015 (1)
- N-3741-2015 (1)
EU-Project number / Contract (GA) number
- 311781 (1)
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Clinical evaluation of novel methods to determine dialysis parameters using conductivity cells
(2002)
Eine die letzten beiden Jahrzehnte anhaltende Diskussion über die erforderliche Dosis Dialyse, die ein Patient benötigt, ergab, daß der Harnstoff-basierte Kt/V-Wert signifikant mit der Morbidität von ‚end stage renal deasease' (ESRD)- Patienten korreliert. Wenn auch nicht vollständig akzeptiert, so scheint es doch zunehmende Übereinkunft zwischen Nephrologen, daß eine angemessene Dialysebehandlung von Patienten ohne Restdiurese im Rahmen eines 3x4 Stunden pro Woche- Schemas mindestens einen Kt/V-Wert von 1.2 bis 1.3 ergeben sollte, um auf lange Sicht die Lebensqualität zu sichern und die Morbidität und Mortalität niedrig zu halten. K ist die vom Dialysesystem erbrachte Clearance, t die Behandlungszeit und V das Harnstoff-Verteilungsvolumen, welches dem Gesamt-Körperwasser nahezu gleicht. Kt/V wird in der Dosiseinheit (ml Medikament pro ml Körperwasser) ausgedrückt und daher auch häufig als Dialyse-‚Dosis' bezeichnet, auch wenn darüber wegen der Zusammenfassung in nur einer Harnstoff-korrelierten Zahl konträr diskutiert wird. Diese Arbeit besitzt eine eher technische Prämisse und möchte sich nicht an dieser Diskussion beteiligen. Sie möchte dem interessierten Nephrologen lediglich eine patientenfreundliche, präzise, kostenneutrale und leicht zu handhabende technische Lösung an die Hand geben, um kontinuierlich die in Kt/V ausgedrückte Dialysedosis zu überwachen. Natürlich ist damit auch die Hoffnung verbunden, daß die Langzeit-Sterblichkeit verringert werden kann, wenn eine flächendeckende, zeitnahe Erfolgskontrolle der Dialyse ermöglicht wird. Die gewählte technische Lösung basiert auf der Äquivalenz der Diffusionskoeffizienten von gelöstem Harnstoff und Natriumchlorid. Es ist das zentrale Anliegen dieser Studie, festzustellen, ob das Diffusionsverhalten von NaCl und Harnstoff beim Durchtritt durch die Membran des Dialysefilters gleich ist. Der entscheidende Vorteil, der das Verfahren so leicht handhabbar macht, besteht darin, daß NaCl-Konzentrationen sehr genau durch die ohnehin in großer Zahl in Dialysegeräten verwendeten Leitfähigkeitsmeßzellen bestimmt werden können. Um die NaCl-Massenbilanz über den Dialysefilter zu bestimmen, benötigt man lediglich eine weitere Meßzelle, die stromab des Filters zu installieren ist. Die Messung von Harnstoff, die indirekt über die enzymatische Zerlegung in Ammonium-Ionen und das anschließende Erzeugen eines hoch zu verstärkenden elektrischen Potentials an einer Membran geschieht, ist komplizierter. Zudem ist eine geschlossene Kühlkette für das Enzym sicher zu stellen. Um eine leitfähigkeitsbasierte technische Lösung abzusichern, wurden zwei klinische Studien durchgeführt. In der ersten Studie wurde die Leitfähigkeit in Form von konstanten Stufenprofilen variiert. Sie wurde ausgehend von der Grundlinie für 7 min erhöht und anschließend für 7 min erniedrigt. Das Prinzip einer solchen Messung wurde erstmals 1982 in einer Patentschrift beschrieben. In einer Sequenz von 494 solchen Messungen in 206 automatisch aufgezeichneten Dialysesitzungen an 22 Patienten wurde gefunden, daß sich die Harnstoff- Clearance elektrolytisch mit einer Genauigkeit von -1.46+/-4.75% (Fehler+/-Standardabweichung) messen ließ. Die Messung von Kt/V gemäß dem Ein-Kompartment-Modell ergab eine ähnliche Genauigkeit von 2.88+/-4.15%. Obgleich diese Ergebnisse in Übereinstimmung mit anderen Studien stehen, wurde ein Effekt bemerkt, der nicht in Einklang mit der zunächst bestehenden Theorie zu bringen war. Dieser Effekt besteht darin, daß die Genauigkeit der elektrolytischen Clearancemessung vom beim Patienten vorhandenen Harnstoff-Verteilungsvolumen abhängig war. Weiter war es nicht bedeutungslos, welchen Teil des dreiteiligen Stufenprofils man zur Auswertung heranzog: Den Grundlinie-Hoch- Übergang, den von der Grundlinie zum Niedrig-Nieveau oder den Hoch-Niedrig- Übergang. Dies deutete auf einen Mangel an theoretischem Verständnis hin. Eine genaue weitere Untersuchung führte zu dem Ergebnis, daß unerwünschter NaCl-Transfer vom und zum Patienten die Ursache für die Abhängigkeit vom Verteilungsvolumen war. Es wurde daraufhin die Theorie dahingehend erweitert, daß dieser Effekt korrekt und plausibel beschrieben werden konnte. Aus dieser Erweiterung ergab sich die neue Forderung, den NaCl-Transfer bei der Messung weitestgehend zu minimieren. Die Benutzung von Stufenprofilen stellte hier jedoch an sich eine Limitierung dar, da in der zum Einnehmen eines stabilen Zustandes erforderlichen Zeit zuviel NaCl über die Membran transferiert wurde. Die Konsequenz war, von den Stufenprofilen auf kurze, dynamische Leitfähigkeitsboli überzugehen, die erlaubten, die NaCl-Gabe auf das Maß zu verringern, welches aufgrund der technischen Auflösung erforderlich war. Hierzu mußten jedoch die notwendigen mathematischen Algorithmen neu zugeschnitten werden. Nach diesem Schritt wurde eine weitere klinische Studie gestartet, die den Zweck verfolgte, das neue Verfahren am Patienten zu verifizieren. In dieser Studie mit 10 Patienten und 93 Dialysesitzungen, 264 Stufenprofil- und 173 Bolus-Dialysancemesssungen wurde gefunden, daß die Bolus-Messungen ihre zugehörigen blutseitigen Referenzmessungen mit außergewöhnlicher Genauigkeit von 0.06+/-4.76% trafen. Student's t-Test für gepaarte Daten ergab, daß sich die Datensätze nicht signifikant unterschieden (p=0.87). Die blutseitige Kt/V-Referenz auf der Basis des equilibrierten Einkompartment-Modells mit variablem Volumen wurde mit 5.32+/-3.9% getroffen, wobei eine Korrelation von 0.98 erzielt wurde. Die verbleibende Differenz von 5.32% wird der Vernachlässigung der Harnstoff-Erzeugung während der Messung zugeschrieben. Auch das Stufenprofil zeigte trotz seiner Abhängigkeit vom Verteilungsvolumen gegenüber dem gleichen Modell einen mittleren Fehler von 0.05+/-5% bei einer Korrelation von 0.96. Jedoch konnte es die Vernachlässigung der Harnstoff-Erzeugung nicht korrekt abbilden. Die kontinuierlich aufgenommenen Daten wurden auch nach dem 2-pool Modell untersucht, welches auch die Harnstoff-Erzeugung enthält sowie eine innere Kompartimentierung des Patienten annimmt und damit die tatsächlichen Verhältnisse besser beschreibt. Danach weicht das Bolus-Meßprinzip -3.04+/-14.3% von der Referenz ab (n.s.,p=0.13). Die relativ hohe Standardabweichung wird mit der Komplexität des Modells erklärt. Weiter ist aus der Theorie zum Na-Transfer eine vereinfachende Methode zur Messung des Na-Verteilungsvolumens abgeleitet worden. Diese Methode wurde in-vitro gegen ein Behältnis mit einer bekannten Menge an Dialysat geprüft. Es wurde ein mittlerer Fehler von -19.9+/-34% gefunden. Die Korrelation war 0.92 (n.s., p=0.916). Die gleiche Prüfung fand in-vivo gegen das Harnstoff-Verteilungsvolumen statt und ergab einen mittleren Fehler von -7.4+/-23.2% (r=0.71, n.s., p=0.39). Es hat den Anschein, als würden sich gemäß der Theorie der Dilution die Verteilungsvolumina für Natrium und für Harnstoff scheinbar nur wenig unterscheiden, obwohl sie sich absolut natürlich deutlich unterscheiden. In Anbetracht der erheblichen Vereinfachungen, die bei der Ableitung dieses Ansatzes gemacht wurden, scheint es ausgesprochen ermutigend, auf diesem Weg möglicherweise ein Verfahren entwickeln zu können, welches auf rein elektrolytischem Wege nun nicht mehr nur K, sondern auch V und damit alle zur Quantifizierung gesuchten Größen analytisch ermitteln kann. Weiter wurde im Rahmen dieser Arbeit anhand der analytisch ermittelten Volumina verglichen, ob man mit Hilfe anthropometrischer Formeln zur Ermittlung des Harnstoff-Verteilungsvolumens zu einer guten Abschätzung kommen kann. Es wurde gefunden, daß man das Ergebnis der Watson-Formel um ca. 13% vermindern kann und dann zu einem recht guten Wert für das tatsächliche Harnstoff-Verteilungsvolumen gelangt. Dies ist jedoch mit Vorsicht und Erfahrung zu tun, da sich damit Kt/V rechnerisch zum Nachteil des Patienten verändert. Auch ein elektrolytisches Verfahren mit empirischen Komponenten zur Ermittlung des Plasma-Natriums des Patienten wurde erprobt und konnte mit einer Genauigkeit von 4.3+/-1.2% den Laborwert vorhersagen. Zusammenfassend kann gesagt werden, daß sich im Rahmen dieser Arbeit die leitfähigkeitsbasierten Methoden zur Messung von einigen wichtigen Dialyseparametern als sehr nützlich für die klinische Praxis erwiesen haben und zudem mit keinem Zusatzaufwand für die Beteiligten verbunden sind. Das Ergebnis dieser Arbeit ist mittlerweile in größeren Stückzahlen in frei erhältliche Dialysegeräte implementiert worden. Die Erfahrung der ersten Zeit zeigt, daß das verwendete Prinzip von den Klinikern gut angenommen wird.
Previous work on Jurassic bivalves from the Iberian Range is reviewed, whereby emphasis is placed on Callovian-Kimmeridgian species. The taxonomy, distribution pattern and ecology of the bivalve fauna occurring in Middle and Upper Jurassic rocks of the Aragonian Branch of the Iberian Range have been analysed. For this purpose 14 sections and 5 additional outcrops, selected according to the abundance of bivalves, were measured in detail and sampled. The rocks studied belong to the Chelva, Yátova, Sot de Chera and Loriguilla formations of Callovian-Kimmeridgian age. The distribution of species of bivalves is given for each section. More than 3000 specimens of bivalves representing 83 species that belong to 46 genera and subgenera of the subclasses Palaeotaxodonta, Pteriomorphia, Isofilibranchia. Palaeoheterodonta, Heterodonta and Anomaldesmata have been used for the taxonomic analysis. One species is new: Plagiostoma fuersichi from the Callovian of the Chelva Fm. The autecology (trophic group and life habit) of each bivalve has been discussed. 49 samples of four sections habe been selected for a quantitative palaeoecological analysis of the bivalve fraction of the benthic fauna. Five bivalve associations and two assemblages are recognised by a Q-mode hierarchical cluster analysis (Ward method). The main environmental factors controlling bivalve associations are thought to be substrate, water energy and distribution of organic matter. The bivalves exhibit a distinct spatial and temporal distribution pattern within the Aragonian Branch. Four of the bivalve associations occur in the Upper Oxfordian (Sot de Chera Fm) and one association in the Lower Callovian (Chelva Fm). In the Sot de Chera and Loriguilla formations, the abundance of bivalves decreases from NW to SE i.e., from relatively close to the shore line towards the distal-most part of the carbonate platform. In the Chelva Fm. bivalves are abundant in the Ariño region, interpreted as a palaeogeographic high. The distribution of bivalves might have been largely controlled by the availability of nutrients.
The present studies which have been performed in the work-group C-2 (Prof. W. Kiefer) within the program of the Sonderforschungsbereichs 347, deal with the FT-Raman and –IR spectroscopy on new organometallic complexes, synthesized in the work-groups B-2 (Prof. W. Malisch), B-3 (Prof. W. A. Schenk), D-1 (Prof. H. Werner) and D-4 (Prof. D. Stalke). The FT-Raman spectra recorded at 1064 nm led to very useful and interesting information. Furthermore, the DFT calculations which are known to offer promise of obtaining accurate vibrational wavenumbers, were successfully used for the assignment of the vibrational spectra. For the first time it has been possible to ascribe exactly the n(RhC) stretching mode in the vinylidene rhodium(I) complex trans-[RhF(=C=CH2)(PiPr3)2] by using isotopic substitution, in conjunction with theoretical calculations. This is also true for the complexes trans-[RhF(CO)(PiPr3)2], trans-[RhF(C2H4)(PiPr3)2], trans-[RhX(=C=CHPh)(PiPr3)2] (X = F, Cl, Br, I, Me, PhCºC) and trans-[RhX(CN-2,6-xylyl)(PiPr3)2] (X = F, Cl, Br, I, CºCPh). In addition, the comparison between the n(RhC) wavenumbers of the complexes trans-[RhF(=13C=13CH2)(PiPr3)2] and trans-[RhF(CO)(PiPr3)2], containing the isoelectronic ligands 13C=13CH2 and CO, which have the same reduced mass, indicated that the Rh-C bond is stronger in the carbonyl than in the vinylidene complex. Besides, the n(RhF) stretching mode, which has been observed at higher wavenumbers in the FT-Raman and -IR spectra of trans-[RhF(CO)(PiPr3)2], showed that the carbonyl ligand is a better p-acceptor and a less effective s-donor than the vinylidene one. Moreover, the comparison of the n(CºC) and n(Rh-C) modes from the FT-Raman spectrum of the complexes trans-[Rh(CºCPh)(L)(PiPr3)2] (L = C=CHPh, CO, CN-2,6-xylyl) point out that the p-acceptor ability of the ligand trans to CºCPh should rise in the order C=CH2 < CO < CN-2,6-xylyl £ C=CHPh. The investigated sensitivity of the n(RhC), n(CC), n(CO) and n(CN) vibrational modes to the electronic modifications occuring in the vinylidene, carbonyl, ethylene and isonitrile complexes, should allow in the future the examination of the p-acceptor or p-donor properties of further ligands. Likewise, we were able to characterize the influence of various X ligands on the RhC bond by using the n(RhC) stretching mode as a probe for the weakening of this. The calculated wavenumbers of the n(RhC) for the vinylidene complexes trans-[RhX(=C=CHR)(PiPr3)2], where R = H or Ph, suggested that the strength of the Rh=C bond increases along the sequence X = CºCPh < CH3 < I < Br < Cl < F. For the series of carbonyl compounds trans-[RhX(CO)(PiPr3)2], where X = F, Cl, Br and I, analogous results have been obtained and confirmed from the model compounds trans-[RhX(CO)(PMe3)2]. Since, the calculated vibrational modes for the ethylene complex trans-[RhF(C2H4)(PiPr3)2] were in good agreement with the experimental results and supported the description of this complex as a metallacyclopropane, we were interested in getting more information upon this class of compounds. In this context, we have recorded the FT-Raman and -IR spectra of the thioaldehyde complexes mer-[W(CO)3(dmpe)(h2-S=CH2)] and mer-[W(CO)3(dmpe)(h2-S=CD2)] which have been synthezised by B-3. The positions of the different WL vibrational modes anticipated by the DFT calculations, were consistent with the experimental results. Indeed, the analysis of the band shifts in the FT-Raman and –IR spectra of the isotopomer mer-[W(CO)3(dmpe)(h2-S=CD2)] confirmed our assignment. The different stereoisomers of complex mer-[W(CO)3(dmpe)(h2-S=CH2)] were investigated too, since RMN and IR-data have shown that complex mer-[W(CO)3(dmpe)(h2-S=CH2)] lead in solution to an equilibrium. Since the information on the vibrational spectra of the molybdenum and tungsten complexes Cp(CO)2M-PR2-X (M = Mo, W; R = Me, tBu, Ph; X = S, Se) is very scarce, we extended our research work to this class of compounds. We have tried to elucidate the bonding properties in these chalcogenoheterocycle complexes by taking advantage of the mass effect on the different metal atoms (W vs. Mo). Thus, the observed band shifts allowed to assign most of the ML fundamental modes of these complexes. This project and the following one were a cooperation within the work-group B-2. The Raman and IR spectra of the matrix isolated photoproducts expected by the UV irradiation of the iron silyl complex Cp(CO)2FeSiH2CH3 have been already reported by Claudia Fickert and Volker Nagel in their PhD-thesis. Since no exact assignment was feasible for these spectra, we were interested in the study of the reaction products created by irradiation of the carbonyl iron silyl complex Cp(CO)2FeCH2SiH3. Although the calculated characteristic vibrational modes of the metal ligand unit for the various photoproducts are significantly different in constitution, they are very similar in wavenumbers, which did not simplify their identification. However, the theoretical results have been found to be consistent with the earlier experimental results. Finally, the last part of this thesis has been devoted to the (2-Py)2E- anions which exhibit a high selectivity toward metal-coordination. All di(2-pyridyl) amides and -phosphides which were synthesized by D-4, coordinate the R2Al+ fragment via both ring nitrogen atoms. This already suggests that the charge density in the anions is coupled into the rings and accumulated at the ring nitrogen atoms, but the Lewis basicity of the central nitrogen atom in Et2Al(2-Py)2N is still high enough to coordinate a second equivalent AlEt3 to form the Lewis acid base adduct Et2Al(2-Py)2NAlEt3. Due to the higher electronegativity of the central nitrogen atom in Me2Al(2-Py)2N, Et2Al(2-Py)2N and Et2Al(2-Py)2NAlEt3, compared to the bridging two coordinated phosphorus atom in Me2Al(2-Py)2P and Et2Al(2-Py)2P, the di(2-pyridyl)amide is the hardest Lewis base. In the phosphides merely all charge density couples into the rings leaving the central phosphorus atom only attractive for soft metals. These results were confirmed by using DFT and MP2 calculations. Moreover, a similar behaviour has been observed and described for the benzothiazolyl complex [Me2Al{Py(Bth)P}], where complementary investigations are to be continued. The DFT calculations carried out on the model compounds analysed in these studies supply very accurate wavenumbers and molecular geometries, these being in excellent agreement with the experimental results obtained from the corresponding isolated complexes.
The presented work shows the analysis of the correlation between the spatial and temporal expression pattern of NtAQP1 and its function in water relation in planta. In situ immunological studies indicated NtAQP1-protein accumulation in the root exodermis and endodermis, in the cortex, close to vascular bundles, in the xylem parenchyma and in cells of the stomatal cavities. The aquaporin was also found to be abundant in longitudinal cell-rows in the petioles. Expression studies with generated transgenic plants (Ntaqp1-promoter::gus or luc) confirmed the Ntaqp1 accumulation in the root, stem and petioles but also revealed further localization in pollen grains, adventitious roots and leaf glandular hairs. Ntaqp1-expression was induced during growth processes, like stem bending after gravistimulation or photostimulation, seed germination and hypocotyl elongation as well as during the comparatively fast circadian leaf movement. The expression was further stimulated by phytohormones, especially gibberellic acid (GA) and osmotic stress. Further analysis displayed a diurnal and even circadian expression of Ntaqp1 in roots and petioles. The functional analysis of the aquaporin was accomplished by reverse genetics and biophysical studies. The antisense technique was used to reduce NtAQP1-expression in tobacco plants. The antisense (AS) plants exhibited a severe reduction of Ntaqp1-mRNA, less reduction of the highly homologous NtPIP1a RNA and no effect on expression of other aquaporin family genes (PIP2, TIP). The function of NtAQP1 at the cellular level was investigated by a newly developed experimental setup to record the osmotically induced increase in protoplast volume. The reduction of NtAQP1 by the antisense expression decreased the overall cellular waterpermeability Pos for more than 50 %. Function of NtAQP1 at the whole plant level was e.g. measured by the “high-pressure flow meter method”. Those measurements revealed that the root hydraulic conductivity per unit root surface area (KRA) of roots from the AS-lines was reduced by more than 50 %. KRA displayed a strong diurnal and circadian variation with a maximum in the middle of the light period, similar to the expression pattern of Ntaqp1 in roots. Gas exchange-, stem (Ystem) and leaf (Yleaf) water potential measurement gave dissimilar values in AS and control plants under well-watered conditions. Under a water-limiting environment the Y of AS-plants remained at more negative water values, even though a further decrease in transpiration of AS-plants was detected. Quantitative analysis displayed a much stronger wilting reaction in the AS than in the control plants. Quantitative studies of the leaf movement in AS compared to control plants exhibited a dramatic reduction in velocity and also in the extent of the process. The following conclusions can be drawn. NtAQP1 was expressed at sites of anticipated high water fluxes from and to the apoplast or symplast. Additionally, the specific distribution pattern and temporal expression of NtAQP1 in petioles and the bending stem strongly indicate a role in transcellular movement of water. The reduction of NtAQP1 by the antisense expression decreased the overall cellular Pos. Conclusively, NtAQP1-function increases membrane water permeability of tobacco root protoplasts. The decrease of the specific root hydraulic conductivity (KRA) was in the same order of magnitude as the mean cellular water permeability reduction, indicating that aquaporin expression is essential in maintaining a natural root hydraulic conductance. Reduction of KRA in AS plants might be the first definitive proof that the pathway of water uptake from the root surface to the xylem involves passage across membranes. The absence of NtAQP1 resulted in a water stress signal, causing a certain stomatal closure. NtAQP1 seems to contribute to water stress avoidance in tobacco. NtAQP1 plays an essential role in fast plant movements and transcellular water shift.
Network planning has come to great importance during the past decades. Today's telecommunication, traffic systems, and logistics would not have been evolved to the current state without careful analysis of the underlying network problems and precise implementation of the results obtained from those examinations. Graphs with node and arc attributes are a very useful tool to model realistic applications, while on the other hand they are well understood in theory. We investigate network design problems which are motivated particularly from applications in communication networks and logistics. Those problems include the search for homogeneous subgraphs in edge labeled graphs where either the total number of labels or the reload cost are subject to optimize. Further, we investigate some variants of the dial a ride problem. On the other hand, we use node and edge upgrade models to deal with the fact that in many cases one prefers to change existing networks rather than implementing a newly computed solution from scratch. We investigate the construction of bottleneck constrained forests under a node upgrade model, as well as several flow cost problems under a edge based upgrade model. All problems are examined within a framework of multi-criteria optimization. Many of the problems can be shown to be NP-hard, with the consequence that, under the widely accepted assumption that P is not equal to NP, there cannot exist efficient algorithms for solving the problems. This motivates the development of approximation algorithms which compute near-optimal solutions with provable performance guarantee in polynomial time.
The thesis looks at the question asking for the computability of the dot-depth of star-free regular languages. Here one has to determine for a given star-free regular language the minimal number of alternations between concatenation on one hand, and intersection, union, complement on the other hand. This question was first raised in 1971 (Brzozowski/Cohen) and besides the extended star-heights problem usually refered to as one of the most difficult open questions on regular languages. The dot-depth problem can be captured formally by hierarchies of classes of star-free regular languages B(0), B(1/2), B(1), B(3/2),... and L(0), L(1/2), L(1), L(3/2),.... which are defined via alternating the closure under concatenation and Boolean operations, beginning with single alphabet letters. Now the question of dot-depth is the question whether these hierarchy classes have decidable membership problems. The thesis makes progress on this question using the so-called forbidden pattern approach: Classes of regular languages are characterized in terms of patterns in finite automata (subgraphs in the transition graph) that are not allowed. Such a characterization immediately implies the decidability of the respective class, since the absence of a certain pattern in a given automaton can be effectively verified. Before this work, the decidability of B(0), B(1/2), B(1) and L(0), L(1/2), L(1), L(3/2) were known. Here a detailed study of these classes with help of forbidden patterns is given which leads to new insights into their inner structure. Furthermore, the decidability of B(3/2) is proven. Based on these results a theory of pattern iteration is developed which leads to the introduction of two new hierarchies of star-free regular languages. These hierarchies are decidable on one hand, on the other hand they are in close connection to the classes B(n) and L(n). It remains an open question here whether they may in fact coincide. Some evidence is given in favour of this conjecture which opens a new way to attack the dot-depth problem. Moreover, it is shown that the class L(5/2) is decidable in the restricted case of a two-letter alphabet.
In this thesis we investigate near-isomorphism classes and isomorphism classes of almost completely decomposable groups. In Chapter 2 we introduce the concept of almost completely decomposable groups and sum up their most important facts. A local group is an almost completely decomposable group with a primary regulator quotient. A uniform group is a rigid local group with a homocyclic regulator quotient. In Chapter 3 a weakening of isomorphism, called type-isomorphism, appears. It is shown that type-isomorphism agrees with Lady's near-isomorphism. By the Main Decomposition Theorem and the Primary Reduction Theorem we are allowed to restrict ourselves on clipped local groups, namely groups without a direct rank-one summand. In Chapter 4 we collect facts of matrices over commutative rings with an identity element. Matrices over the local ring (Z / p^e Z) of residue classes of the rational integers modulo a prime power play an important role. In Chapter 5 we introduce representing matrices of finite essential extensions. Here a normal form for local groups is found by the Gauß algorithm. Uniform groups have representing matrices in Hermite normal form. The classification problems for almost completely decomposable groups up to isomorphism and up to near-isomorphism can be rephrased as equivalence problems for the representing matrices. In Chapter 6 we derive a criterion for the representing matrices of local groups in Gauß normal form. In Chapter 7 we formulate the matrix criterion for uniform groups. Two representing matrices in Hermite normal form describe isomorphic groups if and only if the rest blocks of the representing matrices are T-diagonally equivalent. Starting from a fixed near-isomorphism class in Chapter 8 we investigate isomorphism classes of uniform groups. We count groups and isomorphism classes. In Chapter 9 we specialize on uniform groups of rank 2r with a regulator quotient of rank r such that the rest block of the representing matrix is invertible and normed.
Complexity and Partitions
(2001)
Computational complexity theory usually investigates the complexity of sets, i.e., the complexity of partitions into two parts. But often it is more appropriate to represent natural problems by partitions into more than two parts. A particularly interesting class of such problems consists of classification problems for relations. For instance, a binary relation R typically defines a partitioning of the set of all pairs (x,y) into four parts, classifiable according to the cases where R(x,y) and R(y,x) hold, only R(x,y) or only R(y,x) holds or even neither R(x,y) nor R(y,x) is true. By means of concrete classification problems such as Graph Embedding or Entailment (for propositional logic), this thesis systematically develops tools, in shape of the boolean hierarchy of NP-partitions and its refinements, for the qualitative analysis of the complexity of partitions generated by NP-relations. The Boolean hierarchy of NP-partitions is introduced as a generalization of the well-known and well-studied Boolean hierarchy (of sets) over NP. Whereas the latter hierarchy has a very simple structure, the situation is much more complicated for the case of partitions into at least three parts. To get an idea of this hierarchy, alternative descriptions of the partition classes are given in terms of finite, labeled lattices. Based on these characterizations the Embedding Conjecture is established providing the complete information on the structure of the hierarchy. This conjecture is supported by several results. A natural extension of the Boolean hierarchy of NP-partitions emerges from the lattice-characterization of its classes by considering partition classes generated by finite, labeled posets. It turns out that all significant ideas translate from the case of lattices. The induced refined Boolean hierarchy of NP-partitions enables us more accuratly capturing the complexity of certain relations (such as Graph Embedding) and a description of projectively closed partition classes.
Starfree regular languages can be build up from alphabet letters by using only Boolean operations and concatenation. The complexity of these languages can be measured with the so-called dot-depth. This measure leads to concatenation hierarchies like the dot-depth hierarchy (DDH) and the closely related Straubing-Thérien hierarchy (STH). The question whether the single levels of these hierarchies are decidable is still open and is known as the dot-depth problem. In this thesis we prove/reprove the decidability of some lower levels of both hierarchies. More precisely, we characterize these levels in terms of patterns in finite automata (subgraphs in the transition graph) that are not allowed. Therefore, such characterizations are called forbidden-pattern characterizations. The main results of the thesis are as follows: forbidden-pattern characterization for level 3/2 of the DDH (this implies the decidability of this level) decidability of the Boolean hierarchy over level 1/2 of the DDH definition of decidable hierarchies having close relations to the DDH and STH Moreover, we prove/reprove the decidability of the levels 1/2 and 3/2 of both hierarchies in terms of forbidden-pattern characterizations. We show the decidability of the Boolean hierarchies over level 1/2 of the DDH and over level 1/2 of the STH. A technique which uses word extensions plays the central role in the proofs of these results. With this technique it is possible to treat the levels 1/2 and 3/2 of both hierarchies in a uniform way. Furthermore, it can be used to prove the decidability of the mentioned Boolean hierarchies. Among other things we provide a combinatorial tool that allows to partition words of arbitrary length into factors of bounded length such that every second factor u leads to a loop with label u in a given finite automaton.
A completely decomposable group is a direct sum of subgroups of the rationals. An almost completely decomposable group is a torsion free abelian group that contains a completely decomposable group as subgroup of finite index. Tight subgroups are maximal subgroups (with respect to set inclusion) among the completely decomposable subgroups of an almost completely decomposable group. In this dissertation we show an extended version of the theorem of Bezout, give a new criterion for the tightness of a completely decomposable subgroup, derive some conditions under which a tight subgroup is regulating and generalize a theorem of Campagna. We give an example of an almost completely decomposable group, all of whose regulating subgroups do not have a quotient with minimal exponent. We show that among the types of elements of a coset modulo a completely decomposable group there exists a unique maximal type and define this type to be -the- coset type. We give criteria for tightness and regulating in term of coset types as well as a representation of the type subgroups using coset types. We introduce the notion of reducible cosets and show their key role for transitions from one completely decomposable subgroup up to another one containing the first one as a proper subgroup. We give an example of a tight, but not regulating subgroup which contains the regulator. We develop the notion of a fully single covered subset of a lattice, show that V-free implies fully single covered, but not necessarily vice versa, and we define an equivalence relation on the set of all finite subsets of a given lattice. We develop some extension of ordinary Hasse diagrams, and apply the lattice theoretic results on the lattice of types and almost completely decomposable groups.