Modified gravity on the brane and dark energy

We analyze the dynamics of an AdS₅ braneworld with matter fields when gravity is allowed to deviate from the Einstein form on the brane. We consider exact five-dimensional warped solutions which are associated with conformal bulk fields of weight –4 and describe on the brane the following three dynamics: those of inhomogeneous dust, of generalized dark radiation, and of homogeneous polytropic dark energy. We show that, with modified gravity on the brane, the existence of such dynamical geometries requires the presence of non-conformal matter fields confined to the brane.     

Current theories in the calculation of activity coefficients-II. Specific interaction theories applied to some equilibria studies in solution chemistry

The adequation of the current theories for calculating activity coefficients has been studied for a series of ionic equilibria in analytical chemistry: the water ionic product as well as two reactions of complex formation and oxidation-reduction. In all the cases, the specific interaction theory (SIT) has proved to be adequate and simple to apply in a restricted interval (0.5-3M), whereas Pitzer's theory is outstanding for its high precision in reproducing experimental behaviour and to correlate values of equilibrium constants for different conditions and media.     

The X-Class and Almost-Increasing Permutations

In this paper we give a bijection between the class of permutations that can be drawn on an X-shape and a certain set of permutations that appears in Knuth [4] in connection to sorting algorithms. A natural generalization of this set leads us to the definition of almost-increasing permutations, which is a one-parameter family of permutations that can be characterized in terms of forbidden patterns. We find generating functions for almost-increasing permutations by using their cycle structure to map them to colored Motzkin paths. We also give refined enumerations with respect to the number of cycles, fixed points, excedances, and inversions.     

A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

Cosmological models with Yang-Mills fields

Cosmological models with an SU(2) Yang-Mills field are studied. For a specific model with a minimally coupled Yang-Mills Lagrangian, which includes an arbitrary function of the second-order term and a fourth-order term, a corresponding reconstruction program is proposed. It is shown that the model with minimal coupling has no de Sitter solutions, for any nontrivial function of the second-order term. To get de Sitter solutions, a gravitational model with nonminimally coupled Yang-Mills fields is then investigated. It is shown that the model with non-minimal coupling has in fact a de Sitter solution, even in absence of the cosmological constant term.     

From the Galilei to the Lorentz group in a general light-cone frame

The most general coordinate system in which the Galilean symmetries of the ordinary and the Bell and Ruegg light-cone frames appear is found. With a modification of this general coordinate system it is possible to go from the Galilei group in two space dimensions to the Lorentz group, a process inverse to the contraction of the Lorentz group with respect to the subgroup of rotations. As an example of the applicability of this modified general light-cone frame, the two-dimensional Schrödinger-Pauli equation is obtained to all orders.     

One-loop counterterms in 2d dilaton-Maxwell quantum gravity

The renormalization structure of two-dimensional quantum gravity is investigated in a covariant gauge. One-loop divergences of the effective action are calculated. All the surface divergent terms are taken into account thus completing previous one-loop calculations of the theory. It is shown that the on-shell effective action contains only surface divergences. The off-shell renormalizability of the theory is discussed and classes of renormalizable dilaton and Maxwell potentials are found.     

Schur-positive sets of permutations via products and grid classes

Characterizing sets of permutations whose associated quasisymmetric function is symmetric and Schur-positive is a long-standing problem in algebraic combinatorics. In this paper, we present a general method to construct Schur-positive sets and multisets, based on geometric grid classes and the product operation. Our approach produces many new instances of Schur-positive sets and provides a broad framework that explains the existence of known such sets that until now were sporadic cases.     

Synergic extraction of cobalt(II) with mixtures of 4-methyl-N-8-quinolinylbenzene sulphonamide and neutral organophosphorus compounds

The distribution equilibria of cobalt(II) with 4-methyl-N-8-quinolinylbenzene sulphonamide in the presence of tributylphosphate or trioctylphosphine oxide dissolved in toluene were studied as a function of hydrogen ion concentration and the concentration of the organophosphorus compounds. Evaluation of the extraction data made it possible to deduce the stoichiometry of the extracted species, determine their corresponding extraction constants and quantify the synergic effect.