Counting singularities via fitting ideals

The stable singularities of differential map germs constitute the main source of studying the geometric and topological behavior of these maps. In particular, one interesting problem is to find formulae which allow us to count the isolated stable singularities which appear in the discriminant of a stable deformation of a finitely determined map germ. Mond and Pellikaan showed how the Fitting ideals are related to such singularities and obtain a formula to count the number of ordinary triple points in map germs from C-2 to C-3, in terms of the Fitting ideals associated with the discriminant. In this article we consider map germs from (Cn+m, 0) to (C-m, 0), and obtain results to count the number of isolated singularities by means of the dimension of some associated algebras to the Fitting ideals. First in Corollary 4.5 we provide a way to compute the total sum of these singularities. In Proposition 4.9, for m = 3 we show how to compute the number of ordinary triple points. In Corollary 4.10 and with f of co-rank one, we show a way to compute the number of points formed by the intersection between a germ of a cuspidal edge and a germ of a plane. Furthermore, we show in some examples how to calculate the number of isolated singularities using these results.

delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras

In the paper, a complete description of the delta-derivations and the delta-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p not equal 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

Partial projective representations and partial actions II

This paper is a continuation of Dokuchaev and Novikov (2010) [8]. The interaction between partial projective representations and twisted partial actions of groups considered in Dokuchaev and Novikov (2010) [8] is treated now in a categorical language. In the case of a finite group G, a structural result on the domains of factor sets of partial projective representations of G is obtained in terms of elementary partial actions. For arbitrary G we study the component pM'(G) of totally-defined factor sets in the partial Schur multiplier pM(G) using the structure of Exel's semigroup. A complete characterization of the elements of pM'(G) is obtained for algebraically closed fields. (C) 2011 Elsevier B.V. All rights reserved.

U-Pb zircon in situ dating with LA-MC-ICP-MS using a mixed detector configuration

The LA-MC-ICP-MS method applied to U-Pb in situ dating is still rapidly evolving due to improvements in both lasers and ICP-MS. To test the validity and reproducibility of the method, 5 different zircon samples, including the standard Temora-2, ranging in age between 2.2 Ga and 246 Ma, were dated using both LA-MC-ICP-MS and SHRIMP. The selected zircons were dated by SHRIMP and, after gentle polishing, the laser spot was driven to the same site or on the same zircon phase with a 213 nm laser microprobe coupled to a multi-collector mixed system. The data were collected with a routine spot size of 25 μm and, in some cases, of 15 and 40 μm. A careful cross-calibration using a diluted U-Th-Pb solution to calculate the Faraday reading to counting rate conversion factors and the highly suitable GJ-1 standard zircon for external calibrations were of paramount importance for obtaining reliable results. All age results were concordant within the experimental errors. The assigned age errors using the LA-MC-ICP-MS technique were, in most cases, higher than those obtained by SHRIMP, but if we are not faced with a high resolution stratigraphy, the laser technique has certain advantages.

Morphology, mineralogy and micromorphology of soils associated to summit depressions of the Northeastern Brazilian Coastal Plains

The scarcity of comprehensive characterizations of soils associated to gentle summit depressions of the Northeastern Brazilian Coastal Plains justifies this work, which had as objective to provide basic information for the more diverse agricultural and non-agricultural uses. For that, representative soils (Spodosols or similar soils) from these environments were selected in Alagoas, Sergipe and Bahia states. This approach included characterization of morphological, mineralogical and micromorphological properties of the soil profiles, employing standard procedures. The morphological characterization corroborated the effect of the podzolization process during the formation of these soils. The mineralogy of the clay fraction of these soils was basically composed of kaolinite and quartz, which, associated to the very sandy texture, helped in the understanding of the obtained data. The soil micromorphological study, besides confirming the field morphology, mainly in regard to the strong cementation, aggregated value to the work in terms of the secure identification of the clay illuviation process (non-identified in the field), in association with the dominant podzolization process.

Conceptual problem for noncommutative inflation and the new approach for nonrelativistic inflationary equation of state

In a previous paper, we connected the phenomenological noncommutative inflation of Alexander, Brandenberger and Magueijo [ Phys. Rev. D 67 081301 (2003)] and Koh and Brandenberger [ J. Cosmol. Astropart Phys. 2007 21 ()] with the formal representation theory of groups and algebras and analyzed minimal conditions that the deformed dispersion relation should satisfy in order to lead to a successful inflation. In that paper, we showed that elementary tools of algebra allow a group-like procedure in which even Hopf algebras (roughly the symmetries of noncommutative spaces) could lead to the equation of state of inflationary radiation. Nevertheless, in this paper, we show that there exists a conceptual problem with the kind of representation that leads to the fundamental equations of the model. The problem comes from an incompatibility between one of the minimal conditions for successful inflation (the momentum of individual photons being bounded from above) and the Fock-space structure of the representation which leads to the fundamental inflationary equations of state. We show that the Fock structure, although mathematically allowed, would lead to problems with the overall consistency of physics, like leading to a problematic scattering theory, for example. We suggest replacing the Fock space by one of two possible structures that we propose. One of them relates to the general theory of Hopf algebras (here explained at an elementary level) while the other is based on a representation theorem of von Neumann algebras (a generalization of the Clebsch-Gordan coefficients), a proposal already suggested by us to take into account interactions in the inflationary equation of state.

Analysis of Electrostatic Turbulence Drive in Texas Helimak.

Plasma turbulence and particle transport in Texas Helimak change with the radial electric field profile modified by an external voltage bias. When the bias is positive, the turbulence shows enhanced level and broadband spectra with extreme events, similar to the turbulence in tokamak scrape-‐off layer. However, negative bias reduces the turbulence level and decreases the spectrum widths. Moreover, for negative biased shots, the particle transport is strongly affected by a wave particle resonant interaction. On the other hand, for positive bias values, the plasma presents a transport barrier in the reversed shear flow region.

A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

Rappresentazioni lineari di SL3(C)

Espongo i fatti di base della teoria delle rappresentazioni con lo scopo di indagare i possibili modi in cui un dato gruppo di Lie o algebra di Lie agisce su uno spazio vettoriale di dimensione finita. Tali risultati verranno applicati all'algebra di Lie del gruppo speciale lineare.

Methodische Entwicklung der MALDI-TOF-Massenspektrometrie für Grenzbereiche der Polymeranalytik

Zusammenfassung der DoktorarbeitDie MALDI-TOF-Massenspektrometrie (Matrix Assisted Laser Desorption and Ionisation–Time Of Flight) ist in der Lage, Moleküle mit einem Molekulargewicht bis zu mehreren Hunderttausend Da intakt in die Gasphase zu überführen. Dabei wird die Fragmentierung des Analyten stark eingeschränkt bzw. gänzlich vermieden. Diese Methode findet daher zunehmend Verwendung für die Charakterisierung von Biopolymeren und synthetischen Polymeren. Ziel dieser Arbeit war, die MALDI-TOF-Massenspektrometrie zur Charakterisierung von Makromolekülen einzusetzen, bei denen die konventionellen polymeranalytischen Methoden nur unzureichende Informationen oder gar falsche bzw. gar keine Ergebnisse liefern. Mittels einer methodischen Entwicklung der MALDI-TOF-Massenspektrometrie gelang es, die bisherigen Grenzen der Methode zu erweitern und neue Anwendungsbereiche der Polymeranalytik aufzuzeigen. Anhand der erzielten Ergebnisse wurden darüber hinaus neue Erklärungsansätze formuliert, die zu einem besseren Verständnis des noch immer ungeklärten MALDI-Prozesses beitragen können. Besonders vielversprechend sind zum einen die Ergebnisse der Fragmentionenanalyse synthetischer Polymere und zum anderen die Charakterisierung von unlöslichen PAHs (Polycyclic Aromatic Hydrocarbons). Die Möglichkeiten und Aussagekraft der Fragmentionenanalyse wurde an synthetischen Polymeren getestet. Mit Hilfe dieser neuen Technik konnte die komplizierte Endgruppenverteilung einer Polycarbonat-Probe sowie die Zusammensetzung eines Poly-para-phenylenethynylen-b-Polyethylenoxid-Diblock-Copolymers eindeutig bestimmen werden, während die konventionellen MALDI-Massenspektren nur über einen wesentlich geringeren Informationsgehalt verfügten. Auf dem Gebiet der Analytik von unlöslichen PAHs wurde mit der Entwicklung einer neuen MALDI-Probenvorbereitung eine Methode gefunden, die über die PAH Analytik hinaus von großem Nutzen ist. Diese erstmalig angewendete Probenvorbereitung unterscheidet sich von den üblichen MALDI-Probenpräparationen, indem sie auf die Beteiligung eines Lösungsmittels vollkommen verzichtet. Damit konnte speziell ein unlöslicher, zuvor nicht nachweisbarer PAH von ca. 2700 Da mit MALDI eindeutig charakterisiert werden.

Expressiveness in biologically inspired languages

A very recent and exciting new area of research is the application of Concurrency Theory tools to formalize and analyze biological systems and one of the most promising approach comes from the process algebras (process calculi). A process calculus is a formal language that allows to describe concurrent systems and comes with well-established techniques for quantitative and qualitative analysis. Biological systems can be regarded as concurrent systems and therefore modeled by means of process calculi. In this thesis we focus on the process calculi approach to the modeling of biological systems and investigate, mostly from a theoretical point of view, several promising bio-inspired formalisms: Brane Calculi and k-calculus family. We provide several expressiveness results mostly by means of comparisons between calculi. We provide a lower bound to the computational power of the non Turing complete MDB Brane Calculi by showing an encoding of a simple P-System into MDB. We address the issue of local implementation within the k-calculus family: whether n-way rewrites can be simulated by binary interactions only. A solution introducing divergence is provided and we prove a deterministic solution preserving the termination property is not possible. We use the symmetric leader election problem to test synchronization capabilities within the k-calculus family. Several fragments of the original k-calculus are considered and we prove an impossibility result about encoding n-way synchronization into (n-1)-way synchronization. A similar impossibility result is obtained in a pure computer science context. We introduce CCSn, an extension of CCS with multiple input prefixes and show, using the dining philosophers problem, that there is no reasonable encoding of CCS(n+1) into CCSn.

Ectomycorrhizae of sessile oak (Quercus petraea (Matt.) Liebl.)

Investigations were performed during the years 1999 to 2001 on a limed and unlimed plot within a high-elevated sessile oak forest. The oak forest (with 90 years old European beech at the understorey) was 170 to 197 years old. It is located at forest district Merzalben, location 04/0705, which is situated in the Palatinate Forest in south-west Germany. Liming was performed in December 1988 when 6 tons/ha of powdered Dolomite were brought up by the forestry department. Liming was performed to counteract the effects of soil acidification (pH(H2O) at Horizon A (0-10 cm): 3.9), which is induced by long-term (anthropogenic) acidic cloud cover and precipitation. Potentially toxic Al3+ ions, which become solubilized below pH 5, were suspected to be responsible for forest dieback and sudden death of the mature oaks. The most logical entry point for these toxic ions was suspected to occur in the highly absorptive region of the ectomycorrhizae (fungal covered root tips). However, the diversity and abundance of oak-ectomycorrhizal species and their actual roles in aluminum translocation (or blockage) were unknown. It was hypothesized that the ectomycorrhizae of sessile oaks in a limed forest would exhibit greater seasonal diversity and abundance with less evidence of incorporated aluminum than similar oak ectomycorrhizae from unlimed soils. To test this hypothesis, 12 oaks in the limed plot and 12 in an adjacent unlimed plot were selected. Each spring and fall for 2 years (1999 & 2000), 2 sets of soil cylinders (9.9 cm dia.) were extracted from Horizon A (0-10 cm), Horizon B (30-40 cm) and Horizon C (50-60 cm depth) at a distance of 1 meter from each tree base. Roots were extracted from each probe by gentle sieving and rinsing. Soil samples were retained for pH (H2O, CaCl2, and KCl) and moisture analysis. One set of roots was sorted by size and air-dried for biomass analysis. The finest mycorrhizal roots of this set were used for bound and unbound (cytosolic) mineral [Al, Ca, Mg, K, Na, Mn, S, Zn, Fe, Cd and Pb] analysis (by Landwirtschaftliche Untersuchungs- und Forschungsanstalt Rheinland Palatinate (LUFA)). Within 7 days of collection, the mycorrhizal tips from the second set of probes were excised, sorted, identified (using Agerer’s Color Atlas), counted and weighed. Seasonal diversity and abundance was characterized for 50 of the 93 isolates. The location and relative abundance of Al within the fungal and root cell walls was characterized for 68 species using 0.01% Morin dye and fluorescence microscopy. Morin complexes with Al to produce an intense yellow fluorescence. The 4 most common species (Cenococcum geophilum, Quercirhiza fibulocsytidiata, Lactarius subdulcis, Piceirhiza chordata) were prepared for bound Al, Ca, Fe and K mineral analysis by LUFA. The unlimed and limed plots were then compared. Only 46 of the 93 isolated ectomycorrhizal species had been previously associated with oaks in the literature. Mycorrhizal biomass was most abundant in Horizon A, declining with depth, drought and progressive soil acidification. Mycorrhizae were most diverse (32 species) in the limed plot, but individual species abundance was low (R Selection) in comparison to the unlimed plot, where there were fewer species (24) but each species present was abundant (K Selection). Liming increased diversity and altered dominance hierarchy, seasonal distributions and succession trends of ectomycorrhizae at all depths. Despite an expected reduction in Al content, the limed ectomycorrhizae both qualitatively (fluorescence analysis) and quantitatively (mineral analysis) contained more bound Al, especially so in Horizon A. The Al content qualitatively and quantitatively increased with depth in the unlimed and limed plots. The bound Al content fluctuated between 4000-and 20000 ppm while the unbound component was consistently lower (4 -14 ppm). The relative amount of unbound Al declined upon liming implying less availability for translocation to the crown area of the trees. This correspouds with the findings of good crown appearance and lower tree mortality in the limed zone. Each ectomycorrhizal species was unique in its ability to block, sequester (hold) or translocate Aluminum. In several species, Al uptake varied with changes in moisture, pH, depth and liming. According to the fluorescence study, about 48% of the isolated ectomycorrhizal species blocked and/or sequestered (held) Al in their mantle and/or Hartig net walls, qualitatively lowering bound Al in the adjacent root cell walls. Generally, if Al was more concentrated in the fungal walls, it was less evident in the cortex and xylem and conversely, if Al was low or absent from the fungal walls it was frequently more evident in the cortex and xylem.

Algebraische Beschreibung von Symmetrien: das Modell der Nichtkommutativen Multi-Tori

In der Nichtkommutativen Geometrie werden Räume und Strukturen durch Algebren beschrieben. Insbesondere werden hierbei klassische Symmetrien durch Hopf-Algebren und Quantengruppen ausgedrückt bzw. verallgemeinert. Wir zeigen in dieser Arbeit, daß der bekannte Quantendoppeltorus, der die Summe aus einem kommutativen und einem nichtkommutativen 2-Torus ist, nur den Spezialfall einer allgemeineren Konstruktion darstellt, die der Summe aus einem kommutativen und mehreren nichtkommutativen n-Tori eine Hopf-Algebren-Struktur zuordnet. Diese Konstruktion führt zur Definition der Nichtkommutativen Multi-Tori. Die Duale dieser Multi-Tori ist eine Kreuzproduktalgebra, die als Quantisierung von Gruppenorbits interpretiert werden kann. Für den Fall von Wurzeln der Eins erhält man wichtige Klassen von endlich-dimensionalen Kac-Algebren, insbesondere die 8-dim. Kac-Paljutkin-Algebra. Ebenfalls für Wurzeln der Eins kann man die Nichtkommutativen Multi-Tori als Hopf-Galois-Erweiterungen des kommutativen Torus interpretieren, wobei die Rolle der typischen Faser von einer endlich-dimensionalen Hopf-Algebra gespielt wird. Der Nichtkommutative 2-Torus besitzt bekanntlich eine u(1)xu(1)-Symmetrie. Wir zeigen, daß er eine größere Quantengruppen-Symmetrie besitzt, die allerdings nicht auf die Spektralen Tripel des Nichtkommutativen Torus fortgesetzt werden kann.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Climate signatures in corals of the tropical-temperate transition zone (Late Miocene, Crete/Greece)

The present study describes a Late Miocene (early Tortonian - early Messinian) transitional carbonate system that combines elements of tropical and cool-water carbonate systems (Irakleion Basin, island of Crete, Greece). As documented by stratal geometries, the submarine topography of the basin was controlled by tilting blocks. Coral reefs formed by Porites and Tarbellastrea occurred in a narrow clastic coastal belt along a „central Cretan landmass“, and steep escarpments formed by faulting. Extensive covers of level-bottom communities existed in a low-energy environment on the gentle dip-slope ramps of the blocks that show the widest geographical distribution within the basin. Consistent patterns of landward and basinward shift of coastal onlap in all outcrop studies reveal an overriding control of 3rd and 4th order sea level changes on sediment dynamics and facies distributions over block movements. An increasingly dry climate and the complex submarine topography of the fault block mosaic kept sediment and nutrient discharge at a minimum. The skeletal limestone facies therefore reflects oligotrophic conditions and a sea surface temperature (SST) near the lower threshold temperature of coral reefs in a climatic position transitional between the tropical coral reef belt and the temperate zone. Stable isotope records (δ18O, δ13C) from massiv, exceptionally preserved Late Miocene aragonite coral skeletons reflect seasonal changes in sea surface temperature and symbiont autotrophy. Spectral analysis of a 69 years coral δ18O record reveals significant variance at interannual time scales (5-6 years) that matches the present-day eastern Mediterranean climate variability controlled by the Arctic Oscillation/North Atlantic Oscillation (AO/NAO), the Northern Hemisphere’s dominant mode of atmospheric variability. Supported by simulations with a complex atmospheric general circulation model coupled to a mixed-layer ocean model, it is suggested, that climate dynamics in the eastern Mediterranean and central Europe reflect atmospheric variability related to the Icelandic Low 10 million years ago. Usually, Miocene corals are transformed in calcite spar in geological time and isotope values are reset by diagenetic alteration. It is demonstrated that the relicts of growth bands represent an intriguing source of information for the growth conditions of fossil corals. Recrystallized growth bands were measured systematically in massive Porites from Crete. The Late Miocene corals were growing slowly with 2-4 mm/yr, compatible with present-day Porites from high latitude reefs, a relationship that fits the position of Crete at the margin of the Miocene tropical reef belt. Over Late Miocene time (Tortonian - early Messinian) growth rates remained remarkably constant, and if the modern growth temperature relationship for massive Porites applies to the Neogene, minimum (winter) SST did not exceed 19-21°C.