18,503 research outputs found
On the determination of the earthquake slip distribution via linear programming techniques
The description that one can have of the seismic source is the mani-
festation of an imagined model, obviously outlined from Physic Theories
and supported by mathematical methods. In that context, the modelling
of earthquake rupture consists in finding values of the parameters of the
selected physics-mathematical model, through which it becomes possible
to reproduce numerically the records of earthquake effects on the Earths
surface. We present and test a Linear Programming (LP) inversion in dual
form, for reconstructing the kinematics of the rupture of large earthquakes
through space-time seismic slip distribution on finite faults planes
On orthogonal expansions of the space of vector functions which are square-summable over a given domain and the vector analysis operators
The Hilbert space L2(omega) of vector functions is studied. A breakdown of L2(omega) into orthogonal subspaces is discussed and the properties of the operators for projection onto these subspaces are investigated from the standpoint of preserving the differential properties of the vectors being projected. Finally, the properties of the operators are examined
Quasi-exactly solvable problems and the dual (q-)Hahn polynomials
A second-order differential (q-difference) eigenvalue equation is constructed
whose solutions are generating functions of the dual (q-)Hahn polynomials. The
fact is noticed that these generating functions are reduced to the (little
q-)Jacobi polynomials, and implications of this for quasi-exactly solvable
problems are studied. A connection with the Azbel-Hofstadter problem is
indicated.Comment: 15 pages, LaTex; final version, presentation improved, title changed,
to appear in J.Math.Phy
An Algorithm to Construct Groebner Bases for Solving Integration by Parts Relations
This paper is a detailed description of an algorithm based on a generalized
Buchberger algorithm for constructing Groebner-type bases associated with
polynomials of shift operators. The algorithm is used for calculating Feynman
integrals and has proven itself efficient in several complicated cases.Comment: LaTeX, 9 page
Extended Seismic Source Characterisation using Linear Programming Inversion in a Dual Formulation
A linear programming (LP) inversion method in a dual formulation was applied to reconstruct the kinematics of
finite seismic ruptures. In a general setting, this approach can yield results from several data sets: strong ground
motion, teleseismic waveforms or/and geodesic data (static deformation). The dual formulation involves the
transformation of a normal solution space into an equivalent but reduced space: the dual space. The practical
result of this transformation is a simpler inversion problem that is therefore faster to resolve, more stable and
more robust. The developed algorithm includes a forward problem that calculates Green’s functions using a
finite differences method with a 3D structure model. To evaluate the performance of this algorithm, we applied it
to the reconstitution of a realistic slip distribution model from a data set synthesised using this model, i.e., the
solution of the forward problem. Several other standard inversion approaches were applied to the same synthetic
data for comparison
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