Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

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.

On Orlicz-Sobolev capacities

This thesis consists of three articles on Orlicz-Sobolev capacities. Capacity is a set function which gives information of the size of sets. Capacity is useful concept in the study of partial differential equations, and generalizations of exponential-type inequalities and Lebesgue point theory, and other topics related to weakly differentiable functions such as functions belonging to some Sobolev space or Orlicz-Sobolev space. In this thesis it is assumed that the defining function of the Orlicz-Sobolev space, the Young function, satisfies certain growth conditions. In the first article, the null sets of two different versions of Orlicz-Sobolev capacity are studied. Sufficient conditions are given so that these two versions of capacity have the same null sets. The importance of having information about null sets lies in the fact that the sets of capacity zero play similar role in the Orlicz-Sobolev space setting as the sets of measure zero do in the Lebesgue space and Orlicz space setting. The second article continues the work of the first article. In this article, it is shown that if a Young function satisfies certain conditions, then two versions of Orlicz-Sobolev capacity have the same null sets for its complementary Young function. In the third article the metric properties of Orlicz-Sobolev capacities are studied. It is usually difficult or impossible to calculate a capacity of a set. In applications it is often useful to have estimates for the Orlicz-Sobolev capacities of balls. Such estimates are obtained in this paper, when the Young function satisfies some growth conditions.

Dynamic Instabilities in Slender Space Launch Vehicles under Propulsive Thrust and Aerodynamic Forces

A mechanics based linear analysis of the problem of dynamic instabilities in slender space launch vehicles is undertaken. The flexible body dynamics of the moving vehicle is studied in an inertial frame of reference, including velocity induced curvature effects, which have not been considered so far in the published literature. Coupling among the rigid-body modes, the longitudinal vibrational modes and the transverse vibrational modes due to asymmetric lifting-body cross-section are considered. The model also incorporates the effects of aerodynamic forces and the propulsive thrust of the vehicle. The effects of the coupling between the combustion process (mass variation, developed thrust etc.) and the variables involved in the flexible body dynamics (displacements and velocities) are clearly brought out. The model is one-dimensional, and it can be employed to idealised slender vehicles with complex shapes. Computer simulations are carried out using a standard eigenvalue problem within h-p finite element modelling framework. Stability regimes for a vehicle subjected to propulsive thrust are validated by comparing the results from published literature. Numerical simulations are carried out for a representative vehicle to determine the instability regimes with vehicle speed and propulsive thrust as the parameters. The phenomena of static instability (divergence) and dynamic instability (flutter) are observed. The results at low Mach number match closely with the results obtained from previous models published in the literature.

Hazard Function Models to Estimate Mortality Rates Affecting Fish Populations with Application to the Sea Mullet (Mugil cephalus) Fishery on the Queensland Coast (Australia)

Fisheries management agencies around the world collect age data for the purpose of assessing the status of natural resources in their jurisdiction. Estimates of mortality rates represent a key information to assess the sustainability of fish stocks exploitation. Contrary to medical research or manufacturing where survival analysis is routinely applied to estimate failure rates, survival analysis has seldom been applied in fisheries stock assessment despite similar purposes between these fields of applied statistics. In this paper, we developed hazard functions to model the dynamic of an exploited fish population. These functions were used to estimate all parameters necessary for stock assessment (including natural and fishing mortality rates as well as gear selectivity) by maximum likelihood using age data from a sample of catch. This novel application of survival analysis to fisheries stock assessment was tested by Monte Carlo simulations to assert that it provided unbiased estimations of relevant quantities. The method was applied to the data from the Queensland (Australia) sea mullet (Mugil cephalus) commercial fishery collected between 2007 and 2014. It provided, for the first time, an estimate of natural mortality affecting this stock: 0.22±0.08 year −1 .

Effective earth and space science analogies

There are several good reasons why Earth and Space Science should be a part of any science curriculum. Nearly everything we do each day is connected in some way to the Earth: to its land, oceans, atmosphere, plants and animals. By 2025, eight billion people will live on Earth. If we are to continue extracting resources to maintain a high quality of life, then it is important that our children are scientifically literate in a way that allows them to exploit the Earth’s resources in a sustainable way. People who understand how earth systems work can make informed decisions and may be able to help resolve issues surrounding clean water, urban planning and development, global climate change and the use and management of natural resources.

Soil N availability, rather than N deposition, controls indirect N2O emissions

Ammonia volatilised and re-deposited to the landscape is an indirect N2O emission source. This study established a relationship between N2O emissions, low magnitude NH4 deposition (0–30  kg N ha − 1 ), and soil moisture content in two soils using in-vessel incubations. Emissions from the clay soil peaked ( < 0.002 g N [ g soil ] − 1 min − 1 ) from 85 to 93% WFPS (water filled pore space), increasing to a plateau as remaining mineral-N increased. Peak N2O emissions for the sandy soil were much lower ( < 5 × 10 − 5 μg N [ g soil ] − 1 min − 1 ) and occurred at about 60% WFPS, with an indistinct relationship with increasing resident mineral N due to the low rate of nitrification in that soil. Microbial community and respiration data indicated that the clay soil was dominated by denitrifiers and was more biologically active than the sandy soil. However, the clay soil also had substantial nitrifier communities even under peak emission conditions. A process-based mathematical denitrification model was well suited to the clay soil data where all mineral-N was assumed to be nitrified ( R 2 = 90 % ), providing a substrate for denitrification. This function was not well suited to the sandy soil where nitrification was much less complete. A prototype relationship representing mineral-N pool conversions (NO3− and NH4+) was proposed based on time, pool concentrations, moisture relationships, and soil rate constants (preliminary testing only). A threshold for mineral-N was observed: emission of N2O did not occur from the clay soil for mineral-N <70 mg ( kg of soil ) − 1 , suggesting that soil N availability controls indirect N2O emissions. This laboratory process investigation challenges the IPCC approach which predicts indirect emissions from atmospheric N deposition alone.

Cointegration and causal relationships between energy consumption and output: Assessing the evidence from Australia

In this paper, we describe our investigation of the cointegration and causal relationships between energy consumption and economic output in Australia over a period of five decades. The framework used in this paper is the single-sector aggregate production function, which is the first comprehensive approach used in an Australian study of this type to include energy, capital and labour as separate inputs of production. The empirical evidence points to a cointegration relationship between energy and output and implies that energy is an important variable in the cointegration space, as are conventional inputs capital and labour. We also find some evidence of bidirectional causality between GDP and energy use. Although the evidence of causality from energy use to GDP was relatively weak when using the thermal aggregate of energy use, once energy consumption was adjusted for energy quality, we found strong evidence of Granger causality from energy use to GDP in Australia over the investigated period. The results are robust, irrespective of the assumptions of linear trends in the cointegration models, and are applicable for different econometric approaches.

Cognitive function in schizophrenia: Conflicting findings and future directions

Introduction Schizophrenia is a severe mental disorder with multiple psychopathological domains being affected. Several lines of evidence indicate that cognitive impairment serves as the key component of schizophrenia psychopathology. Although there have been a multitude of cognitive studies in schizophrenia, there are many conflicting results. We reasoned that this could be due to individual differences among the patients (i.e. variation in the severity of positive vs. negative symptoms), different task designs, and/or the administration of different antipsychotics. Methods We thus review existing data concentrating on these dimensions, specifically in relation to dopamine function. We focus on most commonly used cognitive domains: learning, working memory, and attention. Results We found that the type of cognitive domain under investigation, medication state and type, and severity of positive and negative symptoms can explain the conflicting results in the literature. Conclusions This review points to future studies investigating individual differences among schizophrenia patients in order to reveal the exact relationship between cognitive function, clinical features, and antipsychotic treatment.

Excel’s Sumif and Sumifs function

As accountants, we are all familiar with the SUM function, which calculates the sum in a range of numbers. However, there are instances where we might want to sum numbers in a given range based on a specified criteria. In this instance the SUM IF function can achieve this objective.

Ternary function and circuit design using ternary multiplexers

The recent trend towards minimizing the interconnections in large scale integration (LSI) circuits has led to intensive investigation in the development of ternary circuits and the improvement of their design. The ternary multiplexer is a convenient and useful logic module which can be used as a basic building block in the design of a ternary system. This paper discusses a systematic procedure for the simplification and realization of ternary functions using ternary multiplexers as building blocks. Both single level and multilevel multiplexing techniques are considered. The importance of the design procedure is highlighted by considering two specific applications, namely, the development of ternary adder/subtractor and TCD to ternary converter.

The effect of internal audit function quality and internal audit contribution to external audit on audit fees

Corporate governance mandates and listing rules identify internal audit functions (IAF) as a central internal control mechanism. External audits are expected to assess the quality of IAF before placing reliance on its work. We provide evidence on the effect of IAF quality and IAF contribution to external audit on audit fees. Using data from a matched survey of both external and internal audits, we extend prior research which is based mainly on internal audits' assessment and conducted predominantly in highly developed markets. We find a positive relationship between IAF quality and audit fees as well as a reduction in audit fees as a result of external auditors' reliance on IAF. The interaction between IAF quality and IAF contribution to external audit suggests that high quality IAF induces greater external auditor reliance on internal auditors' work and thus result in lower external audit fees.

Characterization of the molecular components and function of BARE-1, Hin-Mu and Mu transposition machineries

Transposable elements, transposons, are discrete DNA segments that are able to move or copy themselves from one locus to another within or between their host genome(s) without a requirement for DNA homology. They are abundant residents in virtually all the genomes studied, for instance, the genomic portion of TEs is approximately 3% in Saccharomyces cerevisiae, 45% in humans, and apparently more than 70% in some plant genomes such as maize and barley. Transposons plays essential role in genome evolution, in lateral transfer of antibiotic resistance genes among bacteria and in life cycle of certain viruses such as HIV-1 and bacteriophage Mu. Despite the diversity of transposable elements they all use a fundamentally similar mechanism called transpositional DNA recombination (transposition) for the movement within and between the genomes of their host organisms. The DNA breakage and joining reactions that underlie their transposition are chemically similar in virtually all known transposition systems. The similarity of the reactions is also reflected in the structure and function of the catalyzing enzymes, transposases and integrases. The transposition reactions take place within the context of a transposition machinery, which can be particularly complex, as in the case of the VLP (virus like particle) machinery of retroelements, which in vivo contains RNA or cDNA and a number of element encoded structural and catalytic proteins. Yet, the minimal core machinery required for transposition comprises a multimer of transposase or integrase proteins and their binding sites at the element DNA ends only. Although the chemistry of DNA transposition is fairly well characterized, the components and function of the transposition machinery have been investigated in detail for only a small group of elements. This work focuses on the identification, characterization, and functional studies of the molecular components of the transposition machineries of BARE-1, Hin-Mu and Mu. For BARE-1 and Hin-Mu transpositional activity has not been shown previously, whereas bacteriophage Mu is a general model of transposition. For BARE-1, which is a retroelement of barley (Hordeum vulgare), the protein and DNA components of the functional VLP machinery were identified from cell extracts. In the case of Hin-Mu, which is a Mu-like prophage in Haemophilus influenzae Rd genome, the components of the core machinery (transposase and its binding sites) were characterized and their functionality was studied by using an in vitro methodology developed for Mu. The function of Mu core machinery was studied for its ability to use various DNA substrates: Hin-Mu end specific DNA substrates and Mu end specific hairpin substrates. The hairpin processing reaction by MuA was characterized in detail. New information was gained of all three machineries. The components or their activity required for functional BARE-1 VLP machinery and retrotransposon life cycle were present in vivo and VLP-like structures could be detected. The Hin-Mu core machinery components were identified and shown to be functional. The components of the Mu and Hin-Mu core machineries were partially interchangeable, reflecting both evolutionary conservation and flexibility within the core machineries. The Mu core machinery displayed surprising flexibility in substrate usage, as it was able to utilize Hin-Mu end specific DNA substrates and to process Mu end DNA hairpin substrates. This flexibility may be evolutionarily and mechanistically important.

Find my office: Navigating real space from semantic descriptions

This paper shows that by using only symbolic language phrases, a mobile robot can purposefully navigate to specified rooms in previously unexplored environments. The robot intelligently organises a symbolic language description of the unseen environment and “imagines” a representative map, called the abstract map. The abstract map is an internal representation of the topological structure and spatial layout of symbolically defined locations. To perform goal-directed exploration, the abstract map creates a high-level semantic plan to reason about spaces beyond the robot’s known world. While completing the plan, the robot uses the metric guidance provided by a spatial layout, and grounded observations of door labels, to efficiently guide its navigation. The system is shown to complete exploration in unexplored spaces by travelling only 13.3% further than the optimal path.