We study the effect of a finite topology on the temperature correlations of the cosmic microwave background in a flat universe. Analytic expressions for the angular power spectrum are given for all possible finite flat models. We examine the angular correlation function itself, pointing out visible and discrete features that arise from topology. While observations of the power spectrum on large...

In this study, the authors consider the problem of multiple antenna spectrum sensing by exploiting the prior information about unknown parameters. Under assumption that additional statistical side information is available about unknown parameters, a novel framework and some detectors are proposed, which are optimal for finite number of received samples. locally most powerful, average likelihood...

Abstract In this chapter, we prove a version of the main result using length spectrum instead Laplace spectrum, in case manifold is negatively curved. We introduce L -series corresponding to unitary representation fundamental group, recall its convergence properties relation volume entropy, and behaviour finite covers.

We prove for a large class of operators J, including block Jacobi matrices, that if .J / n Œ ̨; ˇ is a finite set, each point of which is an eigenvalue of finite multiplicity, then a finite coefficient stripped, JN , has .JN / Œ ̨; ˇ . We use an abstract Dirichlet decoupling. Mathematics Subject Classification (2010). 47B26, 34L15, 81Q10.

For any even positive integer 2n and any positive integermwe construct a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at most (2n − 1)m + 1 eigenvalues. Our main result reduces to previously known results for the cases n = 1 and n = 2. In the self-adjoint case with separated boundary conditions this upper bound can be improved to n(m + 1)...

We construct a natural continuous map from the triangular spectrum of a tensor triangulated category to the algebraic Zariski spectrum of the endomorphism ring of its unit object. We also consider graded and twisted versions of this construction. We prove that these maps are quite often surjective but far from injective in general. For instance, the stable homotopy category of finite spectra ha...

In this paper we consider constraints on the cosmological density parameters from the spatial power spectrum of QSOs. We first review an analytic approach to the spatial power spectrum of QSOs, then we compare the result of the analytic approach with a preliminary result of the power spectrum from the two-degree Field QSO redshift (2QZ) survey. From a simple χ test, we show that a finite baryon...

We derive the glueball masses in noncommutative super Yang–Mills theories in four dimensions via the dual supergravity description. The spectrum of glueball masses is discrete due to the noncommutativity and the glueball masses are proportional to the noncommutativity parameter with dimension of length. The mass spectrum in the WKB approximation closely agrees with the mass spectrum in finite t...

The dynamical mean-field concept of approximating an unsolvable many-body problem in terms of the solution of an auxiliary quantum impurity problem, introduced to study bulk materials with a continuous energy spectrum, is here extended to molecules, i.e., finite systems with a discrete energy spectrum. The application to small clusters of hydrogen atoms yields ground state energies which are co...

We present experimental results for water wave turbulence excited by piston-like programmed wavemakers in a water flume with dimensions 6 × 12 × 1.5 meters. Our main finding is that for a wide range of excitation amplitudes the energy spectrum has a power-law scaling, Eω ∼ ω−ν . These scalings were achieved in up to one-decade wide frequency range, which is significantly wider than the range av...