Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

No evidence of UV cone input to mono- and biphasic horizontal cells in the goldfish retina

Many animal species make use of ultraviolet (UV) light in a number of behaviors, such as feeding and mating. The goldfish (Carassius auratus) is among those with a UV photoreceptor and pronounced UV sensitivity. Little is known, however, about the retinal processing of this input. We addressed this issue by recording intracellularly from second-order neurons in the adult goldfish retina. In order to test whether cone-driven horizontal cells (HCs) receive UV cone inputs, we performed chromatic adaptation experiments with mono- and biphasic HCs. We found no functional evidence of a projection from the UV-sensitive cones to these neurons in adult animals. This suggests that goldfish UV receptors may contact preferentially triphasic HCs, which is at odds with the hypothesis that all cones contact all cone-driven HC types. However, we did find evidence of direct M-cone input to monophasic HCs, favoring the idea that cone-HC contacts are more promiscuous than originally proposed. Together, our results suggest that either UV cones have a more restricted set of post-synaptic partners than the other three cone types, or that the UV input to mono- and biphasic HCs is not very pronounced in adult animals.

A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

Kinetic and Thermodynamic Studies on the Adsorption of Reactive Red 239 by Carra Sawdust Treated with Formaldehyde

In this study, carra sawdust pre-treated with formaldehyde was used to adsorb reactive red 239 (RR239). The effects of several experimental conditions, including the concentration of dye, sorbent dosage, temperature, ionic strength, stirring speed and solution pH, on the kinetics of the adsorption process have been studied, and the experimental data were fitted to pseudo-second-order model. A study of the intra-particle diffusion model indicates that the mechanism of dye adsorption using carra sawdust is rather complex and is most likely a combination of external mass transfer and intra-particle diffusion. The experimental data obtained at equilibrium were analyzed using the Langmuir and Freundlich isotherm models, and the results indicated that at this concentration range, both models can be applied for obtaining the equilibrium parameters. The maximum dye uptake obtained at 298 K was found to be 15.1 mg g(-1). In contrast to the usual systems, the reactive dye studied in the present work is strongly attached to the sawdust even after several washes with water, allowing it to be discarded as a solid waste.