The method of spectral analysis is employed to research the spatial dynamics of urban population distribution. First of all, the negative exponential model is derived in a new way by using an entropy-maximizing idea. Then an approximate scaling relation between wave number and spectral density is derived by Fourier transform of the negative exponential model. The theoretical results suggest the...

We consider the basilica Julia set of the polynomial P (z) = z − 1 and construct all possible resistance (Dirichlet) forms, and the corresponding Laplacians, for which the topology in the effective resistance metric coincides with the usual topology. Then we concentrate on two particular cases. One is a self-similar harmonic structure, for which the energy renormalization factor is 2, the spect...

Introduction Proton MR chemical shift imaging (CSI) of brain metabolites can identify biomarkers relevant to healthy or metabolic cerebral metabolism. At short TE, strongly J-coupled and short T2 metabolites can be detected. High field offers higher SNR and improved spectral resolution with the disadvantage of increased B1 and B0 heterogeneities as well as chemical shift displacement error (CSD...

We construct a family of self-adjoint operators DN , N ∈ Z, which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space CPq, for any ` ≥ 2 and 0 < q < 1. They provide 0-dimensional equivariant even spectral triples. If ` is odd and N = 1 2 (` + 1), the spectral triple is real with KO-dimension 2` mod 8.

We look at invariance of a.e. boundary condition spectral behavior under perturbations, W ; of half-line, continuum or discrete Schrödinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported W ’s to suitable short-range W : We also discuss invariance of the local Hausdorff dimension of spectral measures under such perturbations. r 2002 Elsevier Science (USA). All...

Using spectral function of photon we find the reliable results for the effects of vacuum polarization for the dressed fermion propagator in three-dimensional QED.The lowest order spectral function has logarithmically divergent Coulomb energy as well as self-energy which is absent in four-dimension.

The experimental progress in controlling quantum optical and atomic systems, which has been achieved over the last few years, prompted ideas for new realizations of strongly-correlated many body systems, such as ultracold gases of atoms trapped in optical lattices [1–3] or light-matter systems [4–6]. The latter consist of photons, which interact with atoms or atomic-like structures. Normally, t...

A genericity condition is removed from a result of Agler and Young which reduces the spectral Nevanlinna-Pick problem in two dimensions to a family of classical Nevanlinna-Pick problems. Unlike the original approach, the argument presented here does not involve state-space methods.

The return-to-origin probability and the first-passage-time distribution are essential quantities for understanding transport phenomena in diverse systems. The behaviors of these quantities typically depend on the spectral dimension d(s). However, it was recently revealed that in scale-free networks these quantities show a crossover between two power-law regimes characterized by d(s) and the so...