Pseudo-Newtonian potentials and the radiation emitted by a source swirling around a stellar object

We use pseudo-Newtonian potentials to compute the scalar radiation emitted by a source orbiting a stellar object. We compare the results obtained in this approach with the ones obtained via quantum field theory in Schwarzschild spacetime. We find that, up to the marginally stable circular orbit, the potential that better reproduces the Schwarzschild results is the Nowak–Wagoner one. For unstable circular orbits, none of the pseudo-Newtonian potentials considered in our analysis produces satisfactory results. We show that the Paczyński–Wiita potential, the most used in the literature to analyze accretion disks, generates the least satisfactory results for the scalar radiation emitted by the source in circular orbit around a Schwarzschild black hole.     

Monadic MV-algebras I: a study of subvarieties

In this paper, we study and classify some important subvarieties of the variety of monadic MV-algebras. We introduce the notion of width of a monadic MV-algebra and we prove that the equational class of monadic MV-algebras of finite width k is generated by the monadic MV-algebra [0, 1] ^k . We describe completely the lattice of subvarieties of the subvariety ${\mathcal{V}([{\bf 0}, {\bf 1}]^k)}$ generated by [0, 1] ^k . We prove that the subvariety generated by a subdirectly irreducible monadic MV-algebra of finite width depends on the order and rank of ?A, the partition associated to A of the set of coatoms of the boolean subalgebra B(A) of its complemented elements, and the width of the algebra. We also give an equational basis for each proper subvariety in ${\mathcal{V}([{\bf 0}, {\bf 1}]^k)}$ . Finally, we give some results about subvarieties of infinite width.     

Monadic MV-algebras II: Monadic implicational subreducts

In this paper, we study the class of all monadic implicational subreducts, that is, the ${\{\rightarrow, \forall,1\}}$ -subreducts of the class of monadic MV-algebras. We prove that this class is an equational class, which we denote by ${\mathcal{ML}}$ , and we give an equational basis for this variety. An algebra in ${\mathcal{ML}}$ is called a monadic ?ukasiewicz implication algebra. We characterize the subdirectly irreducible members of ${\mathcal{ML}}$ and the congruences of every monadic ?ukasiewicz implication algebra by monadic filters. We prove that ${\mathcal{ML}}$ is generated by its finite members. Finally, we completely describe the lattice of subvarieties, and we give an equational basis for each proper subvariety.     

Block preconditioners for linear systems arising from multiscale collocation with compactly supported RBFs

Symmetric collocation methods with RBFs allow approximation of the solution of a partial differential equation, even if the right‐hand side is only known at scattered data points, without needing to generate a grid. However, the benefit of a guaranteed symmetric positive definite block system comes at a high computational cost. This cost can be alleviated somewhat by considering compactly supported RBFs and a multiscale technique. But the condition number and sparsity will still deteriorate with the number of data points. Therefore, we study certain block diagonal and triangular preconditioners. We investigate ideal preconditioners and determine the spectra of the preconditioned matrices before proposing more practical preconditioners based on a restricted additive Schwarz method with coarse grid correction. Numerical results verify the effectiveness of the preconditioners. Copyright © 2015 John Wiley & Sons, Ltd.     

Riemann-Christoffel Flows

A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For n dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a “detonant” sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel flows. Possible generalizations are mentioned.     

Analysis of the interactions in FCCF:(H2O) and FCCF:(H2O)2 complexes through the study of their indirect spin–spin coupling constants

A theoretical study of FCCF:(H₂O)_n complexes, with n?=?1 and 2, has been carried out by means of ab initio computational methods. Three kinds of interactions are observed in the complexes: H···π and H···F hydrogen bonds and O···FC tetrel bonds. The indirect spin–spin coupling constants have been calculated at the CCSD/aug-cc-pVTZ-J computational level. Special attention has been paid to the dependence of the different intramolecular coupling constants in FCCF on the distance between the coupled nuclei and the presence or absence of water molecules. The exceptional sensitivity shown by these coupling constants to the presence of water molecules is quite notorious and can provide information on the bonding structure of the molecule.