A pseudo-Anosov surface automorphism φ has associated to it an algebraic unit λφ called the dilatation of φ. It is known that in many cases λφ appears as the spectral radius of a Perron–Frobenius matrix preserving a symplectic form L. We investigate what algebraic units could potentially appear as dilatations by first showing that every algebraic unit λ appears as an eigenvalue for some integra...

We propose a newmethod to analyze and represent data recorded on a domain of general shape in R by computing the eigenfunctions of Laplacian defined over there and expanding the data into these eigenfunctions. Instead of directly solving the eigenvalue problemon such a domain via theHelmholtz equation (which can be quite complicated and costly), we find the integral operator commuting with the ...

Abstract. Both analytic and geometric forms of an optimal monotone principle for Lp-integral of the Green function of a simply-connected planar domain Ω with rectifiable simple curve as boundary are established through a sharp one-dimensional power integral estimate of Riemann-Stieltjes type and the Huber analytic and geometric isoperimetric inequalities under finiteness of the positive part of...

The pinch-off of a two-dimensional region of inviscid fluid is investigated using numerical and analytical techniques. We find that pinch-off occurs when a sufficiently deformed 2D drop is released from rest. The asymptotic collapse of the pinching region is characterized by an anomalous, nonrational similarity exponent , indicating the existence of self-similarity of the second kind. Numerical...

We study the maximization problem, among all subsets X of a given domain Ω, of the quotient of the integral in X of a given function f by the integral on the boundary ofX of another function g. This is a generalization of the well-known Cheeger problem corresponding to constant functions f, g. The non-constant case is motivated by applications to landslides modeling where the the supremum given...

We propose and prove a set of identities for ${\rm GL}_M$ elliptic $R$-matrix (in the fundamental representation). In scalar case ($M=1$) these are function derived by S.N.M. Ruijsenaars as necessary sufficient conditions his kernel identity underlying construction integral solutions to quantum spinless Ruijsenaars-Schneider model. this respect result present paper can be considered first step ...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

The previously developed eigenvalue method for computing the size effect of cohesive crack model is extended to the cohesive crack model with a finite residual stress. In this model, the structure size for which a specified relative length of kink-band corresponds to the maximum load is obtained as an eigenvalue of a homogeneous Fredholm integral equation. This new method is direct and much mor...

Past work on stability analysis of traveling waves in neuronal media has mostly focused on linearization around perturbations of spike times and has been done in the context of a restricted class of models. In theory, stability of such solutions could be affected by more general forms of perturbations. In the main result of this paper, linearization about more general perturbations is used to d...