The Experts below are selected from a list of 15093 Experts worldwide ranked by ideXlab platform
J B Lawrie - One of the best experts on this subject based on the ideXlab platform.
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orthogonality relations for fluid structural waves in a three dimensional rectangular duct with flexible walls
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2009Co-Authors: J B LawrieAbstract:An exact expression for the fluid-coupled structural waves that propagate in a three-dimensional, rectangular waveguide with elastic walls is presented in terms of the non-separable Eigenfunctions ψ n ( y , z ). It is proved that these Eigenfunctions are linearly dependent and that an Eigenfunction expansion representation of a suitably smooth function f ( y , z ) converges point-wise to that function. Orthogonality results for the derivatives ψ n y ( a , z ) are derived which, together with a partial orthogonality relation for ψ n ( y , z ), enable the solution of a wide range of acoustic scattering problems. Two prototype problems, of the type typically encountered in two-part scattering problems, are solved, and numerical results showing the displacement of the elastic walls are presented.
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on Eigenfunction expansions associated with wave propagation along ducts with wave bearing boundaries
Ima Journal of Applied Mathematics, 2007Co-Authors: J B LawrieAbstract:A class of boundary value problems, that has application in the propagation of waves along ducts in which the boundaries are wave-bearing, is considered. This class of problems is characterised by the presence of high order derivatives of the dependent variable(s) in the duct boundary conditions. It is demonstrated that the underlying Eigenfunctions are linearly dependent and, most signiflcantly, that an Eigenfunction expansion representation of a suitably smooth function, say f(y), converges point-wise to that function. Two physical examples are presented. It is demonstrated that, in both cases, the Eigenfunction representation of the solution is rendered unique via the application of suitable edge conditions. Within the context of these two examples, a detailed discussion of the issue of completeness is presented.
Sergei Levendorskii - One of the best experts on this subject based on the ideXlab platform.
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the Eigenfunction expansion method in multi factor quadratic termstructure models
Social Science Research Network, 2006Co-Authors: Nina Boyarchenko, Sergei LevendorskiiAbstract:We propose the Eigenfunction expansion method for pricing options in linear-quadratic terms structure models. The eigenvalues, Eigenfunctions and adjoint functions are calculated using elements of the representation theory of Lie algebras not only in the self-adjoint case but in non-selfadjoint case as well; the Eigenfunctions and adjoint functions are expressed in terms of the Hermite polynomials. We demonstrate that the method is efficient for pricing caps, floors and swaptions, if time to maturity is 1 year or more. We also consider the subordination of the same class of models, and show that in the framework of the Eigenfunction expansion approach, the subordinated models are (almost) as simple as pure Gaussian models. We study the dependence of option prices on the type of non-Gaussian innovations, and suggest parameters' fitting procedures based on the properties of the asymptotic expansions.
Schulz O. - One of the best experts on this subject based on the ideXlab platform.
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Decoupling of the leading contribution in the discrete BFKL Analysis of High-Precision HERA Data
Springer, 2017Co-Authors: Kowalski Henri, Lipatov L. N., Ross D. A., Schulz O.Abstract:We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of Eigenfunctions with positive eigenvalues, $ \omega $ , together with a small contribution from a continuum of Eigenfunctions with negative $ \omega $ , provide an excellent description of high-precision HERA $F_2$ data in the region, $x 6 $ $\hbox {GeV}^2$ . The phases of the Eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first Eigenfunction decouples completely or almost completely from the proton. This suggests that there exists an additional ground state, which is naturally saturated and may have the properties of the soft pomeron
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Decoupling of the leading contribution in the discrete BFKL Analysis of High-Precision HERA Data
'Springer Science and Business Media LLC', 2017Co-Authors: Kowalski H., Lipatov L. N., Ross D. A., Schulz O.Abstract:We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of Eigenfunctions with positive eigenvalues, \omega, together with a small contribution from a continuum of Eigenfunctions with negative \omega, provide an excellent description of high-precision HERA F_2 data in the region, x 6 GeV^2. The phases of the Eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first Eigenfunction decouples completely or almost completely from the proton. This suggests that there exist an additional ground state, which is naturally saturated and may have the properties of the soft pomeron.Comment: 35 pages, 16 figures, the new version gives more explanations of the method and of the result
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Decoupling of the leading contribution in the discrete BFKL Analysis of High-Precision HERA Data
2017Co-Authors: Kowalski H., Lipatov L. N., Ross D. A., Schulz O.Abstract:We analyse here in NLO the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of positive Eigenfunctions, $\omega$, together with a small contribution from a continuum of negative $\omega$, provide an excellent description of high-precision HERA $F_2$ data in the region, $x < 0.001, Q^{2} > 6 GeV^2$. The phases of the Eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first Eigenfunction decouples or nearly decouples from the proton. This suggests that there exist an additional ground state, which has no nodes
Uzy Smilansky - One of the best experts on this subject based on the ideXlab platform.
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the number of nodal domains on quantum graphs as a stability index of graph partitions
Communications in Mathematical Physics, 2012Co-Authors: Rami Band, Gregory Berkolaiko, Hillel Moshe Raz, Uzy SmilanskyAbstract:The Courant theorem provides an upper bound for the number of nodal domains of Eigenfunctions of a wide class of Laplacian-type operators. In particular, it holds for generic Eigenfunctions of a quantum graph. The theorem stipulates that, after ordering the eigenvalues as a non decreasing sequence, the number of nodal domains ν n of the n th Eigenfunction satisfies n ≥ ν n . Here, we provide a new interpretation for the Courant nodal deficiency d n = n − ν n in the case of quantum graphs. It equals the Morse index — at a critical point — of an energy functional on a suitably defined space of graph partitions. Thus, the nodal deficiency assumes a previously unknown and profound meaning — it is the number of unstable directions in the vicinity of the critical point corresponding to the n th Eigenfunction. To demonstrate this connection, the space of graph partitions and the energy functional are defined and the corresponding critical partitions are studied in detail.
S A Khuri - One of the best experts on this subject based on the ideXlab platform.
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biorthogonality condition for creeping flow in wedge shaped trenches
Applied Mathematics and Computation, 2003Co-Authors: S A KhuriAbstract:In the present paper, we derive the biorthogonality condition for Stokes flow in wedge-shaped trenches bounded by radial lines and concentric circles centered at the vertex of the wedge. This condition, is a property satisfied by the Eigenfunctions and adjoint Eigenfunctions needed to compute the coefficients of the Eigenfunction expansion solution of the corresponding Stokes flow problem.
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biorthogonality condition for axisymmetric stokes flow in spherical geometries
International Journal of Mathematics and Mathematical Sciences, 2000Co-Authors: S A KhuriAbstract:We derive the biorthogonality condition for axisymmetric Stokes flow in a re- gion between two concentric spheres. This biorthogonality condition is a property satis- fied by the Eigenfunctions and adjoint Eigenfunctions, which is needed to compute the coefficients of the Eigenfunction expansion solution of the corresponding creeping flow problem.
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biorthogonality condition for stokes flow in rectangular regions
International Journal of Computer Mathematics, 1999Co-Authors: S A KhuriAbstract:In this paper, the biorthogonality condition for Stokes flow in a rectangular region is derived. The biorthogonality conditions are properties satisfied by the Eigenfunctions and adjoint eigen-functions, which are needed to compute the coefficients of the Eigenfunction expansion solution of the corresponding Stokes flow problem.
