95 research outputs found
Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general
investigations on transformational properties of classes of differential
equations is proposed. It is based on mappings between classes of differential
equations, generated by families of point transformations. A class of variable
coefficient (1+1)-dimensional semilinear reaction-diffusion equations of the
general form () is studied from the
symmetry point of view in the framework of the approach proposed. The singular
subclass of the equations with is singled out. The group classifications
of the entire class, the singular subclass and their images are performed with
respect to both the corresponding (generalized extended) equivalence groups and
all point transformations. The set of admissible transformations of the imaged
class is exhaustively described in the general case . The procedure of
classification of nonclassical symmetries, which involves mappings between
classes of differential equations, is discussed. Wide families of new exact
solutions are also constructed for equations from the classes under
consideration by the classical method of Lie reductions and by generation of
new solutions from known ones for other equations with point transformations of
different kinds (such as additional equivalence transformations and mappings
between classes of equations).Comment: 40 pages, this is version published in Acta Applicanda Mathematica
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On the distribution of bids for construction contract auctions
The statistical distribution representing bid values constitutes an essential part of many auction models and has involved a wide range of assumptions, including the Uniform, Normal, Lognormal and Weibull densities. From a modelling point of view, its goodness is defined by how well it enables the probability of a particular bid value to be estimated – a past bid for ex-post analysis and a future bid for ex-ante (forecasting) analysis. However, there is no agreement to date of what is the most appropriate form and empirical work is sparse.
Twelve extant construction datasets from four continents over different time periods are analysed in this paper for their fit to a variety of candidate statistical distributions assuming homogeneity of bidders (ID not known). The results show there is no one single fit-all distribution, but that the 3p Log-Normal, Fréchet/2p Log-Normal, Normal, Gamma and Gumbel generally rank the best ex-post, and the 2p Log-Normal, Normal, Gamma and Gumbel the best ex-ante – with ex-ante having around three to four times worse fit than ex-post. Final comments focus on the results relating to the third and fourth standardised moments of the bids and a post-hoc rationalisation of the empirical outcome of the analysis
Mass equidistribution of Hilbert modular eigenforms
Let F be a totally real number field, and let f traverse a sequence of
non-dihedral holomorphic eigencuspforms on GL(2)/F of weight (k_1,...,k_n),
trivial central character and full level. We show that the mass of f
equidistributes on the Hilbert modular variety as max(k_1,...,k_n) tends to
infinity.
Our result answers affirmatively a natural analogue of a conjecture of
Rudnick and Sarnak (1994). Our proof generalizes the argument of
Holowinsky-Soundararajan (2008) who established the case F = Q. The essential
difficulty in doing so is to adapt Holowinsky's bounds for the Weyl periods of
the equidistribution problem in terms of manageable shifted convolution sums of
Fourier coefficients to the case of a number field with nontrivial unit group.Comment: 40 pages; typos corrected, nearly accepted for
Negatively Charged Excitons and Photoluminescence in Asymmetric Quantum Well
We study photoluminescence (PL) of charged excitons () in narrow
asymmetric quantum wells in high magnetic fields B. The binding of all
states strongly depends on the separation of electron and hole layers.
The most sensitive is the ``bright'' singlet, whose binding energy decreases
quickly with increasing even at relatively small B. As a result, the
value of B at which the singlet--triplet crossing occurs in the spectrum
also depends on and decreases from 35 T in a symmetric 10 nm GaAs well
to 16 T for nm. Since the critical values of at which
different states unbind are surprisingly small compared to the well
width, the observation of strongly bound states in an experimental PL
spectrum implies virtually no layer displacement in the sample. This casts
doubt on the interpretation of PL spectra of heterojunctions in terms of
recombination
Phenomenology of the Lense-Thirring effect in the Solar System
Recent years have seen increasing efforts to directly measure some aspects of
the general relativistic gravitomagnetic interaction in several astronomical
scenarios in the solar system. After briefly overviewing the concept of
gravitomagnetism from a theoretical point of view, we review the performed or
proposed attempts to detect the Lense-Thirring effect affecting the orbital
motions of natural and artificial bodies in the gravitational fields of the
Sun, Earth, Mars and Jupiter. In particular, we will focus on the evaluation of
the impact of several sources of systematic uncertainties of dynamical origin
to realistically elucidate the present and future perspectives in directly
measuring such an elusive relativistic effect.Comment: LaTex, 51 pages, 14 figures, 22 tables. Invited review, to appear in
Astrophysics and Space Science (ApSS). Some uncited references in the text
now correctly quoted. One reference added. A footnote adde
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