We show that the property of a spectral space, to be a spectral subspace of the real spectrum of a commutative ring, is not expressible in the infinitary first order language L∞λ of its defining lattice. This generalises a result of Delzell and Madden which says that not every completely normal spectral space is a real spectrum.

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral ...

It is well known [Hoc69, Joy71] that profinite T0-spaces are exactly the spectral spaces. We generalize this result to the category of all topological spaces by showing that the following conditions are equivalent: (1) (X,τ) is a profinite topological space. (2) The T0-reflection of (X,τ) is a profinite T0-space. (3) (X,τ) is a quasi spectral space (in the sense of [BMM08]). (4) (X,τ) admits a ...

In this work we propose a roadmap towards the analytical understanding of Device-to-Device (D2D) communications in LTE-A networks. Various D2D solutions have been proposed, which include inband and outband D2D transmission modes, each of which exhibits different pros and cons in terms of complexity, interference, and spectral efficiency achieved. We go beyond traditional mode optimization and m...

It is well known that the sum of negative (positive) eigenvalues of some finite Hermitian matrix V is concave (convex) with respect to V . Using the theory of the spectral shift function we generalize this property to self-adjoint operators on a separable Hilbert space with an arbitrary spectrum. More precisely, we prove that the spectral shift function integrated with respect to the spectral p...