– We present an analogue of the Harer-Zagier recursion formula for the moments of the Gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple Gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the Gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as ...

In this paper we consider the so-called procedure of Continuous Steiner Symmetrization , introduced by Brock in [F. Brock, Math. Nachr. 172 (1995) 25–48 and F. Proc. Indian Acad. Sci. 110 (2000) 157–204]. It transforms every open set Ω ⊂⊂ ℝ d into ball keeping volume fixed letting first eigenvalue torsional rigidity respectively decrease increase. While does not provide, general, a γ -continuou...

and Applied Analysis 3 by Fujimoto 3 and Liu and Chen 4, 5 with the functional analysis approach. As for b , in case X is convex compact, and S is convex compact-valued with and without the upper hemicontinuous condition, it has also been studied by Liu and Zhang 6, 7 with the nonlinear analysis methods attributed to 8–10 , in particular, using the classical RogalskiCornet Theorem see 8, Theore...

We obtain and solve algebraic eigenvalue equations that predict the dependence of the pulse energy of a dispersion-managed soliton on pulse duration, chirp, and dispersion-map parameters. We demonstrate that a variational ansatz based on a Gaussian pulse shape remains useful even when the actual pulse shape is not Gaussian, and we show that the enhancement factor saturates as the pulse duration...

The real-analytic Jacobi forms of Zwegers’ PhD thesis play an important role in the study of mock theta functions and related topics, but have not been part of a rigorous theory yet. In this paper, we introduce harmonic Maass–Jacobi forms, which include the classical Jacobi forms as well as Zwegers’ functions as examples. Maass–Jacobi–Poincaré series also provide prime examples. We compute thei...

This paper presents an eigenvalue algorithm for accurately computing the Hausdorff dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials and Blaschke products, yielding both numerical and theoretical results. Dimension graphs are presented for (a) the family of Fuchsian groups generated by reflections in 3 ...

This paper presents an eigenvalue algorithm for accurately computing the Hausdorr dimension of limit sets of Kleinian groups and Julia sets of rational maps. The algorithm is applied to Schottky groups, quadratic polynomials and Blaschke products, yielding both numerical and theoretical results. Dimension graphs are presented for (a) the family of Fuchsian groups generated by reeections in 3 sy...

We study the nonlinear eigenvalue problem f(x) = λx for a class of maps f : K → K which are homogeneous of degree one and order-preserving, where K ⊆ X is a closed convex cone in a Banach space X. Solutions are obtained, in part, using a theory of the “cone spectral radius” which we develop. Principal technical tools are the generalized measure of noncompactness and related degree-theoretic tec...

A continuous wavelet transform, with Morlet wavelets as the basis functions, is used to map speech into the time-frequency domain. Forward and inverse FFT routines are used to implement the wavelet transforms. A coefficient covariance matrix is defined and an Eigenvalue decomposition is used to optimally determine significant wavelet based filters that accurately represent speech and potentiall...

We consider a Dirichlet problem, which is perturbation of the eigenvalue problem for anisotropic p-Laplacian. assume that (p(z)−1)-sublinear, and we prove an existence nonexistence theorem positive solutions as parameter λ moves on semiaxis. also show smallest solution determine monotonicity continuity properties minimal map.