Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by ....Ring constructions and algorithms for enhancing performance of BCH codes. BCH codes form a major class of codes used in modern communication systems. The aim of this project is to enhance the efficiency of this class of codes by combining them in constructions enabling correction of deletion and insertion errors, and develop efficient implementations of encoding and decoding algorithms incorporating soft decision methods for enhanced error correction. Significance of the project is explained by the role of fast, secure and reliable communications in modern information and communication technology. Expected outcomes include new efficient algorithms and commercial modules available for symbolic computation systems with applications in telecommunications industry.
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A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for e ....A new generation of fractals: theory, computation, and applications particularly to digital imaging. The project develops the mathematical and algorithmic foundations of superfractals and applies these results to a number of different areas, including in particular, digital imaging. For example, the ``third generation'' of mobile communications (3G), combines wireless mobile technology with high data transmission capacities. Currently the requirement for extensive bandwidth is a problem for efficient use. Superfractals and the associated colouring algorithm could be used to develop a new system to produce synthetic content for wireless devices that would require only low bandwidth.Read moreRead less
ROBUST SOLID OXIDE FUEL CELL TECHNOLOGY FOR SMALL-SCALE APPLICATIONS. The project aims to develop nano-materials for the next generation planar Solid Oxide Fuel Cell (SOFC) that will operate at temperatures between 600 and 800°C. The goal is to identify and demonstrate materials that meet the robust requirements for small scale power generators at the 3-5kW scale. It is expected that these will be used in stationary power generation applications, in remote area power supplies, and for providing ....ROBUST SOLID OXIDE FUEL CELL TECHNOLOGY FOR SMALL-SCALE APPLICATIONS. The project aims to develop nano-materials for the next generation planar Solid Oxide Fuel Cell (SOFC) that will operate at temperatures between 600 and 800°C. The goal is to identify and demonstrate materials that meet the robust requirements for small scale power generators at the 3-5kW scale. It is expected that these will be used in stationary power generation applications, in remote area power supplies, and for providing auxiliary power in vehicles. The work builds on the world-leading position that Ceramic Fuel Cells Ltd. has in planar SOFC technology, utilising micro-analysis and fuel cell expertise at the University of Queensland.Read moreRead less
Topological Optimisation of Fluid Mixing. The proposed research is aimed at improving the efficiency of fluid mixers,
which in the long term has potential to reduce vastly the economic and
environmental costs associated with large-scale mixing processes in Australian
chemical industries. The research will not only impact on practical mixer
design, but will also develop important results in the application of topology
to the the field of chaotic dynamical systems. This project will also prov ....Topological Optimisation of Fluid Mixing. The proposed research is aimed at improving the efficiency of fluid mixers,
which in the long term has potential to reduce vastly the economic and
environmental costs associated with large-scale mixing processes in Australian
chemical industries. The research will not only impact on practical mixer
design, but will also develop important results in the application of topology
to the the field of chaotic dynamical systems. This project will also provide a
graduate student and post-doctoral researcher with training to pursue a career
in fluid dynamics or general applied mathematics research.
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Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended wor ....Mathematics of Elliptic Curve Cryptography. The Australian society and economy requires fast, reliable, and secure digital infrastructure. First-generation security solutions cannot support the efficiency and scalability requirements of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined and analysed. Thus developing a new framework in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Computer Security and E-Commerce.Read moreRead less
Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's meth ....Continued Fractions and Torsion on Hyperelliptic Curves. Scientific advance should not blindly add to our knowledge; a true advance brings insights that collapse different issues into one. Understanding more is to need to remember less. For an important class of examples, this project identifies the study of a fundamental invariant of a quadratic number field, its regulator and hence its class number, with maximum torsion on the Jacobian variety of an hyperelliptic curve. The investigator's methods will surprise some longstanding problems into submission and in particular will lead them to reveal full data on torsion on hyperelliptic curves of low genus.
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Combinatorial structures for computer security and communication. Hadamard matrices in their various guises arise many times in the study of reliable communications and secure communications. The aim of this research project is to use the theory of cyclotomy in both fields and rings to find new number theoretic results which will then be used to obtain new with zero or small autocorrelation functions.
The significance of this research is to propose new construction of Hadamard matrices and bloc ....Combinatorial structures for computer security and communication. Hadamard matrices in their various guises arise many times in the study of reliable communications and secure communications. The aim of this research project is to use the theory of cyclotomy in both fields and rings to find new number theoretic results which will then be used to obtain new with zero or small autocorrelation functions.
The significance of this research is to propose new construction of Hadamard matrices and block designs for computer security and wireless network communication.
We expect some new classes of Hadamard matrices and block designs can be constructed for security and communication applications and several papers would be submitted or published.
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Number Theoretic Methods in Cryptography. It is well known that Number Theory, besides its intrinsic beauty, provides many powerful tools for modern Cryptography. The aim of the project is to formulate and solve new and important mathematical problems, which lie in the background of modern cryptography. They are also of independent value for pure mathematics because they very often stimulate new approaches to and new surprising points of view on classical results and methods. The main outcome w ....Number Theoretic Methods in Cryptography. It is well known that Number Theory, besides its intrinsic beauty, provides many powerful tools for modern Cryptography. The aim of the project is to formulate and solve new and important mathematical problems, which lie in the background of modern cryptography. They are also of independent value for pure mathematics because they very often stimulate new approaches to and new surprising points of view on classical results and methods. The main outcome will be advancing our theoretical knowledge about several major cryptosystems. The project will extend and enrich the area of applications of mathematics to cryptography and related areas.Read moreRead less
Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, ....Mathematics of Cryptography. The Australian society and economy requires fast, reliable, and secure communication. First-generation security solutions are not capable of supporting the efficiency and scalability requirements of mass-market adoption of wireless and embedded consumer applications. New security infrastructures are emerging and must be carefully, but rapidly, defined. Thus developing new mathematically solid tools in this area is one of the most important and urgent tasks. Besides, the intended work advances our knowledge of the theory and the quality of our culture. As such, it will promote the Australian science and will also have many practical applications in Cryptography, Computer Security and E-Commerce.Read moreRead less
Deep Learning for Graph Isomorphism: Theories and Applications. This project aims to investigate graph isomorphism, a fundamental problem in graph theory, using deep learning techniques. Solutions to graph isomorphism are in demand by researchers in many fields of science, such as biology, chemistry, computer science, and quantum computing. The project expects to advance knowledge about graph isomorphism and state-of-the-art methodologies for its applications. The expected outcomes include new t ....Deep Learning for Graph Isomorphism: Theories and Applications. This project aims to investigate graph isomorphism, a fundamental problem in graph theory, using deep learning techniques. Solutions to graph isomorphism are in demand by researchers in many fields of science, such as biology, chemistry, computer science, and quantum computing. The project expects to advance knowledge about graph isomorphism and state-of-the-art methodologies for its applications. The expected outcomes include new theoretical insights on combinatorial structures of graphs, efficient heuristic techniques for (maximum) subgraph isomorphism, and structured representation learning. The project should provide significant benefits to research in a wide range of science fields, as well as many real-world applications.Read moreRead less