Dirichlet problem at infinity for p-harmonic functions on negatively curved spaces

The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.

Jumping numbers of a simple complete ideal in a two-dimensional regular local ring

The multiplier ideals of an ideal in a regular local ring form a family of ideals parametrized by non-negative rational numbers. As the rational number increases the corresponding multiplier ideal remains unchanged until at some point it gets strictly smaller. A rational number where this kind of diminishing occurs is called a jumping number of the ideal. In this manuscript we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.

1-D hydrogen-bonded organization of hexanuclear {3d-4f-5d} complexes: evidence for slow relaxation of the magnetization for [{LMe2Ni(H2O)Ln(H2O)4.5}2{W(CN)8}2] with Ln = Tb and Dy

Heterometallic {3d-4f-5d} aggregates with formula [{LMe2Ni(H2O)Ln(H2O)4.5}2{W(CN)8}2]·15H2O, (LMe2 stands for N,N-2,2-dimethylpropylenedi(3-methoxysalicylideneiminato) Schiff-base ligand) with Ln = Gd, Tb, Dy, have been obtained by reacting bimetallic [LMe2Ni(H2O)2Ln(NO3)3] and Cs3{W(CN)8} in H2O. The hexanuclear complexes are organized in 1-D arrays by means of hydrogen bonds established between the solvent molecules coordinated to Ln and the CN ligands of an octacyanometallate moiety. The X-ray structure was solved for the Tb derivative. Magnetic behavior indicates ferromagnetic {W–Ni} and {Ni–Ln} interactions (JNiW = 18.5 cm-1, JNiGd = 1.85 cm-1) as well as ferromagnetic intermolecular interactions mediated by the H-bonds. Dynamic magnetic susceptibility studies reveal slow magnetic relaxation processes for the Tb and Dy derivatives, suggesting SMM type behavior for these compounds.

Isotope shifts and hyperfine structure in the 555.8-nm S-1(0) -> P-3(1) line of Yb

We apply our technique of using a Rb-stabilized ring-cavity resonator to measure the frequencies of various spectral components in the 555.8-nm 1S0-->3P1 line of Yb. We determine the isotope shifts with 60 kHz precision, which is an order-of-magnitude improvement over the best previous measurement on this line. There are two overlapping transitions, 171Yb(1/2-->3/2) and 173Yb(5/2-->3/2), which we resolve by applying a magnetic field. We thus obtain the hyperfine constants in the 3P1 state of the odd isotopes with a significantly improved precision. Knowledge of isotope shifts and hyperfine structure should prove useful for high-precision calculations in Yb necessary to interpret ongoing experiments testing parity and time-reversal symmetry violation in the laws of physics.

Data mining for telecommunications network log analysis

Telecommunications network management is based on huge amounts of data that are continuously collected from elements and devices from all around the network. The data is monitored and analysed to provide information for decision making in all operation functions. Knowledge discovery and data mining methods can support fast-pace decision making in network operations. In this thesis, I analyse decision making on different levels of network operations. I identify the requirements decision-making sets for knowledge discovery and data mining tools and methods, and I study resources that are available to them. I then propose two methods for augmenting and applying frequent sets to support everyday decision making. The proposed methods are Comprehensive Log Compression for log data summarisation and Queryable Log Compression for semantic compression of log data. Finally I suggest a model for a continuous knowledge discovery process and outline how it can be implemented and integrated to the existing network operations infrastructure.

IP Mobility in Wireless Operator Networks

Wireless network access is gaining increased heterogeneity in terms of the types of IP capable access technologies. The access network heterogeneity is an outcome of incremental and evolutionary approach of building new infrastructure. The recent success of multi-radio terminals drives both building a new infrastructure and implicit deployment of heterogeneous access networks. Typically there is no economical reason to replace the existing infrastructure when building a new one. The gradual migration phase usually takes several years. IP-based mobility across different access networks may involve both horizontal and vertical handovers. Depending on the networking environment, the mobile terminal may be attached to the network through multiple access technologies. Consequently, the terminal may send and receive packets through multiple networks simultaneously. This dissertation addresses the introduction of IP Mobility paradigm into the existing mobile operator network infrastructure that have not originally been designed for multi-access and IP Mobility. We propose a model for the future wireless networking and roaming architecture that does not require revolutionary technology changes and can be deployed without unnecessary complexity. The model proposes a clear separation of operator roles: (i) access operator, (ii) service operator, and (iii) inter-connection and roaming provider. The separation allows each type of an operator to have their own development path and business models without artificial bindings with each other. We also propose minimum requirements for the new model. We present the state of the art of IP Mobility. We also present results of standardization efforts in IP-based wireless architectures. Finally, we present experimentation results of IP-level mobility in various wireless operator deployments.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Construction of a global map of human gene expression : the process, tools and analysis

This thesis studies human gene expression space using high throughput gene expression data from DNA microarrays. In molecular biology, high throughput techniques allow numerical measurements of expression of tens of thousands of genes simultaneously. In a single study, this data is traditionally obtained from a limited number of sample types with a small number of replicates. For organism-wide analysis, this data has been largely unavailable and the global structure of human transcriptome has remained unknown. This thesis introduces a human transcriptome map of different biological entities and analysis of its general structure. The map is constructed from gene expression data from the two largest public microarray data repositories, GEO and ArrayExpress. The creation of this map contributed to the development of ArrayExpress by identifying and retrofitting the previously unusable and missing data and by improving the access to its data. It also contributed to creation of several new tools for microarray data manipulation and establishment of data exchange between GEO and ArrayExpress. The data integration for the global map required creation of a new large ontology of human cell types, disease states, organism parts and cell lines. The ontology was used in a new text mining and decision tree based method for automatic conversion of human readable free text microarray data annotations into categorised format. The data comparability and minimisation of the systematic measurement errors that are characteristic to each lab- oratory in this large cross-laboratories integrated dataset, was ensured by computation of a range of microarray data quality metrics and exclusion of incomparable data. The structure of a global map of human gene expression was then explored by principal component analysis and hierarchical clustering using heuristics and help from another purpose built sample ontology. A preface and motivation to the construction and analysis of a global map of human gene expression is given by analysis of two microarray datasets of human malignant melanoma. The analysis of these sets incorporate indirect comparison of statistical methods for finding differentially expressed genes and point to the need to study gene expression on a global level.

Ni(II)chelates of 4,9-dimethyl-5,8-dizadodeca-4,8-diene-2,11-dione-3,10-diphenyl hydrazone and related molecules

Syntheses and structural characterization of Ni(II) chelates of a new series of symmetric and unsymmetric tetradentate linear ligands are described. Preparative routes involve either the direct reaction between a metal complex and arene diazonium diazonium salts or a simple metal incorporation into the independently synthesized ligands. Recent X-ray structure determination of 4,9-dimethyl-5,8-diazadodeca-4,8-diene-2,11-dione-3,10-di(4′-methyl phenyl) hydrazonatonickel(II) complex reveals the geometry around the Ni(II) to be very close to square planar. The expected distortion because of the disposition of bulky aromatic groups on the neighbouring nitrogens is minimized by their projection in the opposite directions from the plane. PMP, IR and electronic spectral data for the complexes are quite in agreement with this structure.

Names of boys and girls in the K.K.S.I school, March 8, 1795. Report of the School Committee, February 2, 1794

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Editorial of "International Journal of Critical Indigenous Studies, Volume 8, Number 1, 2015"

This edition includes a diverse range of contributions that collectively illustrate two elevated concerns of critical Indigenous studies: First, an interest in establishing ways and means of conducting ethical research with Indigenous communities; and second, critically engaging with constructions of Indigeneity. The first article, by Craig Sinclair, Peter Keelan, Samuel Stokes, Annette Stokes and Christine Jefferies-Stokes, examines the increasingly popular use of participatory video (PV) as a means of engagement, in this case with children in remote Aboriginal communities as participants in health research. The authors note that, whilst not without methodological disadvantages, the PV method, with its flexibility to respond to community priorities is particularly well suited to research with remote Aboriginal communities.

Editorial of "International Journal of Critical Indigenous Studies, Volume 8, Number 2, 2015"

The articles in this edition address two critical concerns that can be broadly characterised as Indigeneity as a spectacle and the elision of Indigenous sovereignty by multiculturalism and diversity. The first article, by Maryrose Casey, examines nineteenth and early twentieth century Indigenous performances that drew on cultural practices for entertainment. She highlights how these commercially driven performances were, in fact, demonstrations of sovereignty that white colonisers paid to observe. A measure of the success of these demonstrations can be found in the reactions of audiences, which often involved disrupting the spectacle by physically occupying the performance space.

Plan zemelʻnogo uchastka poselka Ratendorf N 8

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Scheme of the land section colony "Ratendorf" N 8, Kherson district

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