Fractional Powers of Almost Non-Negative Operators

Mathematics Subject Classification: Primary 47A60, 47D06.

Numerical and combinatorial applications of generalized Appell polynomials

This thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the construction of new bases for the space of homogeneous holomorphic polynomials whose elements are all isomorphic to the integer powers of the complex variable. For this reason, such polynomials are called pseudo-complex powers (PCP). Different variants of them are subject of a detailed investigation. Special attention is paid to the numerical aspects of PCP. An efficient algorithm based on complex arithmetic is proposed for their implementation. In this context a brief survey on numerical methods for inverting Vandermonde matrices is presented and a modified algorithm is proposed which illustrates advantages of a special type of PCP. Finally, combinatorial applications of generalized Appell polynomials are emphasized. The explicit expression of the coefficients of a particular type of Appell polynomials and their relation to a Pascal simplex with hypercomplex entries are derived. The comparison of two types of 3D Appell polynomials leads to the detection of new trigonometric summation formulas and combinatorial identities of Riordan-Sofo type characterized by their expression in terms of central binomial coefficients.

LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15.

Monogenic polynomials of four variables with binomial expansion

In the recent past one of the main concern of research in the field of Hypercomplex Function Theory in Clifford Algebras was the development of a variety of new tools for a deeper understanding about its true elementary roots in the Function Theory of one Complex Variable. Therefore the study of the space of monogenic (Clifford holomorphic) functions by its stratification via homogeneous monogenic polynomials is a useful tool. In this paper we consider the structure of those polynomials of four real variables with binomial expansion. This allows a complete characterization of sequences of 4D generalized monogenic Appell polynomials by three different types of polynomials. A particularly important case is that of monogenic polynomials which are simply isomorphic to the integer powers of one complex variable and therefore also called pseudo-complex powers.

Emergency powers and pandemics : federalism and the management of public health emergencies in Australia

Under the International Health Regulations 2005 Australia is obliged to develop a domestic framework designed to equip it to respond to public health emergencies. The legislative arrangements for the declaration of a public health emergency in Australia are complex, vary across state jurisdictions and intersect with other emergency powers. The task of harmonising laws and other arrangements within a federal system poses both challenges and opportunities for flexibility and choice. This article argues that Australia's current multi-strand and multi-level response provides a coordinated framework which also accommodates desirable levels of flexibility and choice.

Allocating transmission loss to loads and generators through complex power flow tracing

This paper presents a new method for complex power flow tracing that can be used for allocating the transmission loss to loads or generators. Two algorithms for upstream tracing (UST) and downstream tracing (DST) of the complex power are introduced. UST algorithm traces the complex power extracted by loads back to source nodes and assigns a fraction of the complex power flow through each line to each load. DST algorithm traces the output of the generators down to the sink nodes determining the contributions of each generator to the complex power flow and losses through each line. While doing so, active- and reactive-power flows as well as complex losses are considered simultaneously, not separately as most of the available methods do. Transmission losses are taken into consideration during power flow tracing. Unbundling line losses are carried out using an equation, which has a physical basis, and considers the coupling between active- and reactive-power flows as well as the cross effects of active and reactive powers on active and reactive losses. The tracing algorithms introduced can be considered direct to a good extent, as there is no need for exhaustive search to determine the flow paths as these are determined in a systematic way during the course of tracing. Results of application of the proposed method are also presented.

Evidence for the complex relationship between free amino acid and sugar concentrations and acrylamide-forming potential in potato

Free amino acids and reducing sugars participate in the Maillard reaction during high-temperature cooking and processing. This results not only in the formation of colour, aroma and flavour compounds, but also undesirable contaminants, including acrylamide, which forms when the amino acid that participates in the reaction is asparagine. In this study, tubers of 13 varieties of potato (Solanum tuberosum), which had been produced in a field trial in 2010 and sampled immediately after harvest or after storage for 6 months, were analysed to show the relationship between the concentrations of free asparagine, other free amino acids, sugars and acrylamide-forming potential. The varieties comprised five that are normally used for crisping, seven that are used for French fry production and one that is used for boiling. Acrylamide formation was measured in heated flour, and correlated with glucose and fructose concentration. In French fry varieties, which contain higher concentrations of sugars, acrylamide formation also correlated with free asparagine concentration, demonstrating the complex relationship between precursor concentration and acrylamide-forming potential in potato. Storage of the potatoes for 6 months at 9°C had a significant, variety-dependent impact on sugar and amino acid concentrations and acrylamide-forming potential.

Directors' duty to use their powers for proper or permissable purposes

This article focuses generally on the interaction among several internal company law doctrines such as the supremacy of the articles of association; that other organs cannot interfere with powers exclusively conferred upon a particular organ; that courts will not readily interfere with internal company matters; that directors are under a duty to act in good faith and in the best interest of the company as a whole and under a duty to use their powers for proper or permissible purposes; and that there are some remedies available to shareholders if directors did not perform their powers for a proper or permissible purpose. The specific aim with the article is to establish when and why the courts will be prepared to set aside decisions by directors if they have taken them for an improper or impermissible purpose. The article concludes that the courts will be prepared to set the decisions of directors aside when they have used a particular power substantially or primarily for an improper or impermissible purpose. When the exercise of directors' powers is challenged under circumstances where there were both permissible and impermissible purposes for exercising a particular power, there is no alternative for the court but to inquire into the complex area of the state of mind of those who acted and the motive on which they acted. This is, in fact, second-guessing the decisions of directors.

Synthesis and thermal characterization of luminescent powers of terbium(III) with mixed ligands

This work deals with the synthesis and thermal decomposition of complexes of general formula: Ln(beta-dik)(3)L (where Ln=Tb(+3), beta-dik=4,4,4-trifluoro-1-phenyl-1,3butanedione(btfa) and L=1,10-fenantroline(phen) or 2,2-bipiridine(bipy). The powders were characterized by melting point, FTIR spectroscopy, LTV-visible, elemental analysis, scanning differential calorimeter(DSC) and thermogravimetry(TG). The TG/DSC curves were obtained simultaneously in a system DSC-TGA, under nitrogen atmosphere. The experimental conditions were: 0.83 ml.s(-1) carrier gas flow, 2.0 +/- 0.5 mg samples and 10 degrees C.min(-1) heating rate. The CHN elemental analysis of the Tb(btfa)(3)bipy and Tb(btfa)(3)phen complexes, are in good agreement with the expected values. The IR spectra evinced that the metal ion is coordinated to the ligands via C=O and C-N groups. The TG/DTG/DSC curves of the complexes show that they decompose before melting. The profiles of the thermal decomposition of the Tb(btfa)3phen and Tb(btfa)3bipy showed six and five decomposition stages, respectively. Our data suggests that the thermal stability of the complexes under investigation followed the order: Tb(btfa)(3)phen < Tb(btfa)(3)bipy.

New concepts of the power received by ideal energy storage elements: the instantaneous complex power approach

This paper presents some definitions and concepts of the Instantaneous Complex Power Theory [1] which is a new approach for the Akagi's Instantaneous Reactive Power Theory [2].The powers received by an ideal inductor are interpreted and the knowledge of the actual nature of these powers may lead to changes of the conventional electrical power concepts.

Power analysis applying the instantaneous complex power analytical expressions on a RL symmetrical three-phase system

This paper enhances some concepts of the Instantaneous Complex Power Theory by analyzing the analytical expressions for voltages, currents and powers developed on a symmetrical RL three-phase system, during the transient caused by a sinusoidal voltage excitation. The powers delivered to an ideal inductor will be interpreted, allowing a deep insight in the power phenomenon by analyzing the voltages in each element of the circuit. The results can be applied to the understanding of non-linear systems subject to sinusoidal voltage excitation and distorted currents.

A proposed roadmap to optimise the adjudication of complex payment disputes in Australia

In Australia, statutory construction adjudication has recently received a lot of criticism due to the increasing amount of determinations that have been quashed upon judicial review, and anecdotal evidence from some quarters showing dissatisfaction with the quality of adjudication decisions. Such criticism is particularly aimed at adjudications of large and technically and legally complex payment disputes, where adjudicators are under pressure to consider substantial volumes of submissions in very tight timeframes. More specifically, criticisms have been directed at, inter alia, adjudicator’s regulations, procedural fairness, jurisdictional powers and finality of decisions. This paper reviews the measures to improve the quality of adjudications of complex payment disputes then proposes a roadmap by selecting the Qld model as a benchmark but suggesting further improvements identified and explained via specific steps or pit stops. The pit stops include criteria for timeframes of complex claims, appointment, regulation and powers of adjudicators and a review system on the merits to control the quality of adjudication decisions replicating the Singapore model. The findings remain as blunt instruments and deemed as hypotheses to inform subsequent empirical research which the authors are currently undertaking to further investigate, strengthen and validate the findings of this study in order to propose a reliable and useful guide to any parliament seeking to optimise its statutory adjudication to effectively deal with complex payment disputes.

The big picture: causes of compromised outcome of complex statutory adjudications in Australia

Statutory adjudication has been enacted progressively throughout Australia on a stat-by-state basis over a period of 10 years. The legislation with more emphasis on the Eastern States has come under much criticism recently for failing to facilitate decisions of sufficient quality with respect to complex adjudications. This paper reviews this criticism and discusses the key causes of the unsatisfactory outcome of complex adjudications in Australia. The identified causes are namely flawed appointment, relaxed eligibility and regulation, intimidation of adjudicators, fuzzy jurisdictional boundaries, abbreviated timeframes, limited inquisitorial powers and want of review mechanism. The implication of the research is a better understanding of the nature of the quality of complex adjudication outcome and the relevant worthwhile reform opportunities in Australia, especially with regard to introducing legislative review mechanisms.