Hyperbolic cross approximations by some classical orthogonal polynomials/functions in both bounded and unbounded domains are considered in this paper. Optimal error estimates in proper anisotropic weighted Korobov spaces for both regular hyperbolic cross approximations and optimized hyperbolic cross approximations are established. These fundamental approximation results indicate that spectral m...

We show in this paper that thirdand fourth-order low storage Runge-Kutta algorithms can be built specifically for quadratic nonlinear operators, at the expense of roughly doubling the time needed for evaluating the temporal derivatives. The resulting algorithms are especially well suited for computational fluid dynamics. Examples are given for the Hénon-Heiles Hamiltonian system and, in one and...

The autocorrelation function of spectral determinants is proposed as a convenient tool for the characterization of spectral statistics in general, and for the study of the intimate link between quantum chaos and random matrix theory, in particular. For this purpose, the correlation functions of spectral determinants are evaluated for various random matrix ensembles, and are compared with the co...

Intelligent tutoring systems need to know a mapping between particular problems and general domain concepts. Such mapping can be constructed manually by an expert, but that is time consuming and error prone. Our aim is to detect concepts automatically from problem solving times. We propose and evaluate two approaches: a model of problem solving times with multidimensional skill and an applicati...

We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant. e-mail [email protected]

Spectral morphisms between Banach algebras are useful for comparing their K-theory and their “noncommutative dimensions” as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral information is only known over a dense subalgebra. We investigate such relatively spectral morphisms. We prove a relative version of the Density Theorem regarding ...

In this article we show how to compute the semi-classical spectral measure associated with the Schrödinger operator on Rn, and, by examining the first few terms in the asymptotic expansion of this measure, obtain inverse spectral results in one and two dimensions. (In particular we show that for the Schrödinger operator on R2 with a radially symmetric electric potential, V , and magnetic potent...

We prove that, for any quantum evolution in`2 (Z D), there exist arbitrarily long time scales on which the qth moment of the position operator increases at least as fast as a power of time given by q=D times the packing dimension of the spectral measure. Packing dimensions of measures and their connections to scaling exponents and box-counting dimensions are also discussed.

We consider a scenario of cosmological inflation coming from a grand unified theory in higher dimensional orbifold. Flatness of the potential is automatically guaranteed in this orbifold setup thanks to the nonlocality of the Wilson line on higher dimensions and the local quantum gravitational corrections are exponentially suppressed. The spectral index of scalar perturbation (ns ≃ 0.92−0.97) a...

We consider the production of gravitational KK modes via cosmological photon-photon and electron-positron annihilation in models with large factorisable extra dimensions. We place constraints on this production using recent results from a joint analysis of the power spectra of the 2dF Galaxy Redshift Survey (2dFGS) and the cosmic microwave background (CMB) anisotropies. We obtain a more accurat...