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  • Electronic Resource  (2)
  • 2020-2024
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  • 1860-1869
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  • 2002  (2)
  • PACS. 01.75.+m Science and society  (1)
  • PACS. 02.20.Tw Infinite-dimensional Lie groups – 02.30.Jr Partial differential equations – 04.20.Jb Exact solutions – 03.65.Fd Algebraic methods  (1)
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  • Electronic Resource  (2)
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  • 2020-2024
  • 2000-2004  (2)
  • 1995-1999
  • 1860-1869
Year
  • 2022
  • 2002  (2)
Keywords
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The European physical journal 29 (2002), S. 203-206 
    ISSN: 1434-6036
    Keywords: PACS. 02.20.Tw Infinite-dimensional Lie groups – 02.30.Jr Partial differential equations – 04.20.Jb Exact solutions – 03.65.Fd Algebraic methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By studying the integrability conditions of this automorphic system, i.e. the resolving equations, one can provide an explicit foliation of the entire solution manifold into separate orbits. The new important feature of the method is the extensive use of the operators of invariant differentiation for the derivation of the resolving equations and for obtaining their particular solutions. Applying this method we obtain exact analytical solutions of the heavenly equation, non-invariant under any subgroup of the symmetry group of the equation.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1434-6036
    Keywords: PACS. 01.75.+m Science and society
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract: Property is an asset which forms part of the portfolios of many investors, particularly institutional ones, along with equities and bonds. Techniques from physics, particularly that of random matrix theory, have provided powerful insights into the behaviour of financial assets. A large database providing time series data for over 10,000 individual properties is available for the UK. Some of the data is available at an annual and some at a monthly frequency. However, even at the monthly frequency, only a relatively small number of observations is available, certainly in comparison with that available with financial assets. A key issue in translating methods of analysis in financial markets to property data is whether they are applicable given the small number of data points available. This paper addresses this issue. Using the tools of random matrix theory, we find that a great deal of information is contained within property data. The correlations between different types and geographical locations of property tend to have far more true information and be more stable over time than is the case with financial data, despite the large number of observations available with the latter.
    Type of Medium: Electronic Resource
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