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In this work we construct and analyse some finite difference schemes used to solve a class of timedependent one-dimensional convection-diffusion problems, which present only regular layers in their solution. We use the implicit Euler or the Crank-Nicolson method to discretize the time variable and a HODIE finite difference scheme, defined on a piecewise uniform Shishkin mesh, to discretize the spatial variable. In both cases we prove that the numerical method is uniformly convergent with respect to the diffusion parameter, having order near two in space and order one or 3/2, depending on the method used, in time. We show some numerical examples according to the theoretical results, in the case of using the Euler implicit method, and a better numerical behaviour than the predicted theoretically, showing order two in time and order N −2 log 2 N in space, if the Crank-Nicolson scheme is used to discretize the time variable. Finally, we construct a numerical algorithm by combining a third order A-stable SDIRK with two stages and a third order HODIE difference scheme, showing its uniformly convergent behaviour, reaching order three, up to a logarithmic factor. c (Year) John Wiley & Sons, Inc.

Neurotransmission mediated by gamma-aminobutyric acid type A (GABA(A)) receptors in the mammalian medial preoptic area (mPOA) plays a pivotal role in the expression of hormone-sensitive behaviors. Hand in hand with GABAergic control of reproduction, hormone treatments that activate gonadal steroid signaling pathways in gonadectomized rats are known to regulate the expression of specific GABA(A) receptor subunit mRNAs. While the effects of exogenous hormone treatments have been well documented, little information is available as to how GABA(A) receptor-mediated transmission in the mPOA is altered by endogenous changes in hormonal state in gonadally-intact adult animals or if those changes can be ascribed to hormone-dependent changes in receptor subunit composition. In the present study, we found that both the peak amplitudes of GABA(A) receptor-mediated synaptic currents in the mPOA, as well as the ability of the endogenous neurosteroids to modulate those currents, varied as a function of the estrous cycle. Moreover, we found that the degree of neurosteroid modulation was also significantly different between wild-type and the androgen-insensitive testicular feminization (Tfm) mutant male mice. Semiquantitative RT-PCR analysis performed to assess levels of GABA(A) receptor subunit mRNAs indicated that levels of specific subunits varied over the course of the estrous cycle and between wild-type and Tfm male mice. The variations in GABA(A) receptor expression and function in the mPOA that are associated with differences in gonadal steroid signaling may contribute to the dynamic nature of GABAergic control of neuroendocrine pathways.

A battery of behavioral tasks in C57BL/6J mice was used to assess changes in affective components of behavior after systemic exposure to the anabolic-androgenic steroid (AAS) 17alpha-methyltestosterone (7.5 mg/kg). Gonadal weight in both sexes was reduced after 16 days of AAS exposure. Changes in discrete components of social behaviors were observed. No changes were recorded in the elevated plus-maze, the light-dark transition, and defensive behavior tests on exposure to 17alpha-methyltestosterone. When compared with controls, AAS-exposed females received a greater number of shocks, and AAS-exposed males displayed a shorter recovery time to consume water after a negative reinforcer in the modified Vogel conflict test. Results show that systemic exposure to a single AAS modified social behaviors, whereas minimal effects on anxiety-related behaviors were observed according to sex.

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Abstract. In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting, alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge-Kutta method, which is called the fractional step Runge-Kutta method, and a standard space discretization which can be of type finite differences, finite elements or spectral methods among others. Spectral methods have been chosen here to complete the analysis of convergence of a totally discrete scheme of this type of improved fractionary steps. The numerical experiences performed also show the increase of accuracy that this technique provides.

In this paper we consider numerical schemes for multidimensional evolutionary convection-diffusion problems, where the approximation properties are uniform in the diffusion parameter. In order to obtain an efficient method, to provide good approximations with independence of the size of the diffusion parameter, we have developed a numerical method which combines a finite difference spatial discretization on a special mesh and a fractional step method for the time variable. The special mesh allows a correct approximation of the solution in the boundary layers, while the fractional steps permits a low computational cost algorithm. Some numerical examples confirming the expected behavior of the method are shown.

Anabolic androgenic steroids have become a major class of drugs of abuse among a growing population of male and female adolescents. Although the rewarding and reinforcing properties of androgens have been demonstrated in male rodents, it is unknown whether these properties are apparent in female rats. In this study, conditioned place preference and self-administration paradigms showed that the endogenous androgen metabolite 3alphaDIOL is rewarding and reinforcing in ovariectomized female rats. Because 3alphaDIOL can be synthesized de novo in the brain, it is hypothesized that this neurosteroid provides a permissive neurochemical environment that modulates reward processes.