Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expe ....Operator Integrals and Derivatives. The project is a contribution to the study of non-commutative differential and integral calculus. The novelty of the present project lies in the study of smoothness properties of functions whose domains and ranges are spaces of unbounded, non-commuting operators on some Hilbert space. Our general approach will be based on a detailed investigation of properties of double operator integrals, which permit smoothness estimates of operator-functions. It can be expected that the new techniques generated will find further application in areas of mathematical physics and non-commutative geometry related to quantized calculus.
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Non-commutative analysis and differential calculus. This project is in an area of central mathematical importance and will lead to important scientific advances that will keep Australia at the forefront internationally in this field of research. There is an emphasis on international networking and we will collaborate with leading researchers in USA and France.
Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be ....Option pricing via path integrals: a new perspective. The risk management of derivative securities is a very exciting challenge for financial market researchers. The knowledge base resulting from this proposal will benefit both large financial institutions and Australia's financial system by creating a more competitive and efficient economic environment, which will inevitably lead to more gross domestic product (GDP) gains.Furthermore a large amount of software and numerical analysis work to be developed during the project can be turned into IP for Australia. This will contribute to catalysing development of internationally competitive financial risk management software industry.Read moreRead less
Three-dimensional magnetotelluric imaging of lithospheric-scale mineral systems from source to deposit. Geochemical studies indicate that world-class mineral deposits are partly sourced from fluids emerging from Earth's mantle and lower crust. Finding major mineral deposits in the future will therefore require knowledge of which parts of the crust and mantle yield the most prospective locations. However, there are few methods that can image deep Earth resources, and these can be very expensive ....Three-dimensional magnetotelluric imaging of lithospheric-scale mineral systems from source to deposit. Geochemical studies indicate that world-class mineral deposits are partly sourced from fluids emerging from Earth's mantle and lower crust. Finding major mineral deposits in the future will therefore require knowledge of which parts of the crust and mantle yield the most prospective locations. However, there are few methods that can image deep Earth resources, and these can be very expensive. We propose to develop the magnetotelluric method as a low-cost and rapid approach for delineating 3D information on deep mineral systems beneath existing major deposits, and adapting this to explore in greenfield locations.Read moreRead less
Linkage Infrastructure, Equipment And Facilities - Grant ID: LE0668155
Funder
Australian Research Council
Funding Amount
$350,000.00
Summary
Instrumentation for combined seismic and electromagnetic Earth sounding. The set of geophysical recorders will provide the means to enhance understanding of the structure of the Australian continent in 3-D. The interpretation of multiple images of Earth structure will help to link features in the crust and mantle beneath, and provide controls on the evolution and assembly of the present continent, with a major contribution to possible geotransects as recommended in the 2003 National Strategic Pl ....Instrumentation for combined seismic and electromagnetic Earth sounding. The set of geophysical recorders will provide the means to enhance understanding of the structure of the Australian continent in 3-D. The interpretation of multiple images of Earth structure will help to link features in the crust and mantle beneath, and provide controls on the evolution and assembly of the present continent, with a major contribution to possible geotransects as recommended in the 2003 National Strategic Plan for the Geosciences. Combining seismic and electromagnetic methods will provide both geochemeical and geophysical constaints, e.g., on zones of alteration and shear with the potential for deep mineralisation. Read moreRead less
Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate eco ....Nonlinear spatial and spatiotemporal econometrics: theory with applications. Modern societies like Australia have major challenges in the forecasting, measuring and managing of risks associated with global economic and environmental/climate changes. These tasks require advanced econometric techniques in modelling and forecasting of complex nonlinear spatiotemporal variability in economic and social systems. This project will develop frontier econometric technologies that enable more accurate economic and climate forecasts. The tools produced will provide Australia's scientists and policy-makers with a greater capacity to manage the risks associated with these challenges. A side-benefit of the research will be high-quality publications that enhance the nation's reputation in this cutting edge research.Read moreRead less
Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms tha ....Operator-Analytic Methods in Telecommunication Systems. Many systems in information technology and telecommunications evolve under conditions of uncertainty. In this context, mathematical modelling is an essential component of the design process. We shall provide techniques for analysing a class of mathematical models, called operator-analytic models, which can be used to study many of the above-mentioned systems, such as the Internet. This project will deliver efficient numerical algorithms that will make possible practical analysis of operator-analytic models.Read moreRead less
Nonlinear Panel Data Econometrics: Theory and Practice. This research addresses the ARC National Research Priorities Goal of 'An Environmentally Sustainable Australia', specifically 'Reducing and capturing emissions in transport and energy generation'. Avoiding, managing, and/or adapting to the climate change impacts is now the most pressing global environmental problem. This project will produce tangible and original insights into policy options for institutional adjustment to future climate ....Nonlinear Panel Data Econometrics: Theory and Practice. This research addresses the ARC National Research Priorities Goal of 'An Environmentally Sustainable Australia', specifically 'Reducing and capturing emissions in transport and energy generation'. Avoiding, managing, and/or adapting to the climate change impacts is now the most pressing global environmental problem. This project will produce tangible and original insights into policy options for institutional adjustment to future climate change in Australia; will provide insight into the scope for positive community behavioural change; and possible transformations in Australian social debate to maximise adaptive capacity. It will also strengthen and produce original conceptual approaches and research methods.Read moreRead less
Physical and Chemical Constraints of Fluid Activated Processes During the Polyphase Tectonic Evolution of the Olary Domain, S.A. The Olary Domain, eastern South Australia, underwent several phases of deformation and metamorphism. These events mobilised fluids leading, amongst other features, to the formation of breccia bodies and mineral deposits. The complex nature of the geological evolution of the region obscures relationships of fluid migration to the structural history. Fluid inclusion stud ....Physical and Chemical Constraints of Fluid Activated Processes During the Polyphase Tectonic Evolution of the Olary Domain, S.A. The Olary Domain, eastern South Australia, underwent several phases of deformation and metamorphism. These events mobilised fluids leading, amongst other features, to the formation of breccia bodies and mineral deposits. The complex nature of the geological evolution of the region obscures relationships of fluid migration to the structural history. Fluid inclusion studies and stable isotope analyses combined with structural analyses on micro to macro scales shall establish links between the thermal and structural evolution of the area. This will provide insigth into the scale and physico-chemical characteristics of fluids and mineralising processes an relate these to the tectono-thermal history.Read moreRead less