نتایج جستجو برای: eigenfunction

تعداد نتایج: 1523  

2000
SUHEIL A. KHURI

The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

Journal: :Journal of Nonlinear Mathematical Physics 2021

With the help of squared eigenfunction potential, action Virasoro symmetry on tau function constrained discrete KP hierarchy is derived.

2009
Jane B. Lawrie

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 significantl...

2011
Simon RUIJSENAARS

In previous work we introduced and studied a function R(a+, a−, c; v, v̂) that is a generalization of the hypergeometric function 2F1 and the Askey–Wilson polynomials. When the coupling vector c ∈ C is specialized to (b, 0, 0, 0), b ∈ C, we obtain a function R(a+, a−, b; v, 2v̂) that generalizes the conical function specialization of 2F1 and the q-Gegenbauer polynomials. The function R is the joi...

Journal: :Int. J. Math. Mathematical Sciences 2009
Peter Zhidkov

We consider the following eigenvalue problem: −Δu f u λu, u u x , x ∈ B {x ∈ R3 : |x| < 1}, u 0 p > 0, u||x| 1 0, where p is an arbitrary fixed parameter and f is an odd smooth function. First, we prove that for each integer n ≥ 0 there exists a radially symmetric eigenfunction un which possesses precisely n zeros being regarded as a function of r |x| ∈ 0, 1 . For p > 0 sufficiently small, such...

Journal: :Machine learning in medical imaging. MLMI 2011
Moo K. Chung Seongho Seo Nagesh Adluru Houri K. Vorperian

The second eigenfunction of the Laplace-Beltrami operator follows the pattern of the overall shape of an object. This geometric property is well known and used for various applications including mesh processing, feature extraction, manifold learning, data embedding and the minimum linear arrangement problem. Surprisingly, this geometric property has not been mathematically formulated yet. This ...

2011
Grégoire Allaire Yves Capdeboscq Marjolaine Puel GRÉGOIRE ALLAIRE YVES CAPDEBOSCQ

We study the asymptotic behavior of the rst eigenvalue and eigenfunction of a one-dimensional periodic elliptic operator with Neumann boundary conditions. The second order elliptic equation is not self-adjoint and is singularly perturbed since, denoting by ε the period, each derivative is scaled by an ε factor. The main di culty is that the domain size is not an integer multiple of the period. ...

2002
NORBERT RIEDEL

For almost Mathieu operators, it is shown that the occurrence of Cantor spectrum and the existence, for every point in the spectrum and suitable phase parameters, of at least one localized eigenfunction which decays exponentially are inconsistent properties.

Journal: :JAMDS 2001
Alfred D. Sneyd

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion,

2007
Antônio Luiz Pereira Marcone Corrêa Pereira M. C. Pereira

In this work we show that, generically in the set of C2 bounded regions of Rn, n ≥ 2, the inequality R Ω φ 3 6= 0 holds for any eigenfunction of the Laplacian with either Dirichlet or Neumann boundary conditions.

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