In this paper, we consider the problem: what kinds of Riemann surfaces S will have rst eigenvalue 1 (S) large? Bye large, we mean that there is some positive lower bound for S independent of the genus. There are a number of constructions of surfaces with 1 large, the main example being the quotients of the hyperbolic plane by the congruence subgroups of PSL(2; Z). Most of the known examples rel...

We provide a review of different approaches to linking model structure to observed behavior with a particular view towards using models for theory building. We identify four such approaches, namely the " classical " approach, the " pathway participation " approach, the " eigenvalue elasticity " approach, and the " eigenvector " approach, respectively. We outline our assessment of the strengths ...

The eigenvalues of a matrix A are the zeros of its characteristic polynomial fiX) = dtt[A XI]. With Hyman's method of determinant evaluation, a new homotopy continuation method, homotopy-determinant method, is developed in this paper for finding all eigenvalues of a real upper Hessenberg matrix. In contrast to other homotopy continuation methods, the homotopy-determinant method calculates eigen...

We establish universality of local eigenvalue correlations in unitary random matrix ensembles 1 Zn | det M | 2α e −ntr V (M) dM near the origin of the spectrum. If V is even, and if the recurrence coefficients of the orthogonal polynomials associated with |x| 2α e −nV (x) have a regular limiting behavior, then it is known from work of Akemann et al., and Kanzieper and Freilikher that the local ...

We consider eigenvalue problems for self-adjoint Sturm-Liouville difference equations of any even order. It is well known that such problems with Dirichlet boundary conditions can be transformed into an algebraic eigenvalue problem for a banded, real-symmetric matrix, and vice versa. In this article it is shown that such a transform exists for general separated, self-adjoint boundary conditions...

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here “eigenvalue” means eigenvalue of the corresponding Perron-Frobenius operator acting on the space of functions of bounded variation.) This result applies e.g. to the approxi...

The paper concerns the pairwise comparison method used to rank a finite, usually small number of alternatives, in the Analytic Hierarchy Process (AHP), which belongs to a certain class of multiple attribute decision making methods. Ranking of alternatives is calculated based on expert judgments expressing relative importance for each pair of alternatives. From mathematical point of view calcula...

In this work we calculate the eigenvalues obtained by preconditioning the discrete Helmholtz operator with Sommerfeld-like boundary conditions on a rectilinear domain, by a related operator with boundary conditions that permit the use of fast solvers. The main innovation is that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional e...

The paper concerns worst-case compliance optimization by finding the structural topology with minimum compliance for the loading due to the worst possible acceleration of the structure and attached non-structural masses. A main novelty of the paper is that it is shown how this min-max problem can be formulated as a non-linear semi-definite programming (SDP) problem involving a small-size constr...