Abstract:
We discuss the problem of R-separability (separability of variables with a factor R) in the stationary Schr dinger equation on n-dimensional Riemann space. We follow the approach of Gaston Darboux who was the first to give the first general treatment of R-separability in PDE (Laplace equation on E^3). According to Darboux R-separability amounts to two conditions: metric is isothermic (all its parametric surfaces are isothermic in the sense of both classical differential geometry and modern theory of solitons) and moreover when an isothermic metric is given their Lamé coefficients satisfy a single constraint which is either functional (when R is harmonic) or differential (in the opposite case). These two conditions are generalized to n-dimensional case. In particular we define n-dimensional isothermic metrics and distinguish an important subclass of isothermic metrics which we call binary metrics. The approach is illustrated by two standard examples and two less standard examples. In all cases the approach offers alternative and much simplified proofs or derivations. We formulate a systematic procedure to isolate R-separable metrics. This procedure is implemented in the case of 3-dimensional Laplace equation. Finally we discuss the class of Dupin-cyclidic metrics which are non-regularly R-separable in the Laplace equation on E^3.

Abstract:
We discuss the problem of $R$-separability (separability of variables with a factor $R$) in the stationary Schr\"odinger equation on $n$-dimensional Riemann space. We follow the approach of Gaston Darboux who was the first to give the first general treatment of $R$-separability in PDE (Laplace equation on ${\mathbb E}^3$). According to Darboux $R$-separability amounts to two conditions: metric is isothermic (all its parametric surfaces are isothermic in the sense of both classical differential geometry and modern theory of solitons) and moreover when an isothermic metric is given their Lam\'e coefficients satisfy a single constraint which is either functional (when $R$ is harmonic) or differential (in the opposite case). These two conditions are generalized to $n$-dimensional case. In particular we define $n$-dimensional isothermic metrics and distinguish an important subclass of isothermic metrics which we call binary metrics. The approach is illustrated by two standard examples and two less standard examples. In all cases the approach offers alternative and much simplified proofs or derivations. We formulate a systematic procedure to isolate $R$-separable metrics. This procedure is implemented in the case of 3-dimensional Laplace equation. Finally we discuss the class of Dupin-cyclidic metrics which are non-regularly $R$-separable in the Laplace equation on ${\mathbb E}^3$.

Abstract:
We construct perfect fluid metrics corresponding to spacelike surfaces invariant under a 1-dimensional group of isometries in 3-dimensional Minkowski space. Under additional assumptions we obtain new cosmological solutions of Bianchi type II, VI_0 and VII_0. The solutions depend on an arbitrary function of time, which can be specified in order to satisfy an equation of state.

Abstract:
A method of solving perfect fluid Einstein equations with two commuting spacelike Killing vectors is presented. Given a spacelike 2-dimensional surface in the 3-dimensional nonphysical Minkowski space the field equations reduce to a single nonlinear differential equation. An example is discussed.

Abstract:
According to [8] if the stationary Schroedinger equation on n-dim. Riemann space admits R-separation of variables (i.e. separation of variables with a factor R), then the underlying metric is necessarily isothermic. An important sub-class of isothermic metrics are the so called binary metrics. In this paper we study conditions for vanishing of components C_ijkl of Weyl tensor of arbitrary 4-binary metrics. In particular all 4-binary metrics for which C_ijij are the only non-vanishing components are classified into four classes. Finally, conformally flat metrics of the last class are isolated.

Abstract:
Hidden symmetry transformations of D-dimensional vacuum metrics with D-3 commuting Killing vectors are studied. We solve directly the Einstein equations in the Maison formulation under additional assumptions. We relate the 4-dimensional Reissner-Nordstr\"om solution to a particular case of the 5-dimensional Gross-Perry metric.

Abstract:
Studies concerned with the status of Information Systems Development Methodologies usage in many developing countries including the factors that influence and motivate their use, current trends, difficulties, and barriers to adoption are lacking, especially within the higher education sector. This paper examines these identified gaps in a developing country, namely the United Arab Emirates. The initial findings reveal that there is limited knowledge and understanding of the concept of ISDM in federal higher education institutions in the UAE. This is reflected in the quality of the software products being developed and released. However, the analysed data also reveals a trend whereby federal higher education institutions in the UAE are gradually moving towards increased ISDM adoption and deployment.

Abstract:
This paper presents a simple modification to the standard IS curve used, at least implicitly, by policymakers that allows capital flight to have a contractionary effect in emerging market economies. In the standard model, capital flight leads to an expansionary shift in the IS curve through an increase in net exports. However, in the presence of liability dollarization for domestic firms, a currency depreciation triggered by capital flight leads to an investment collapse. A simple adjustment to the standard investment schedule captures this channel and allows for the possibility that capital flight yields a contractionary shift in the IS curve.

This
study tested which of two crucial mechanisms of working memory (WM): attention
control, consisting of focusing attention on the proper task-set as well as
blocking distraction, and the active buffer capacity, related to the number of
chunks that can be actively maintained, plays a more important role in WM’s
contribution to fluid intelligence. In the first study, the antisaccade task
was used, the standard measure of attention control, in a modified variant
which resulted in scores less sensitive to individual differences in the active
buffer capacity, in comparison to the standard variant. In effect, attention
control became a weak predictor of Gf, explaining less than one third of its
variance accounted for by the capacity. In the second study, a variant of another
attention control test, the Stroop task, was applied, which minimized the load
on capacity, and no significant contribution of this task to Gf was found.
Thus, when contribution of control and capacity were unconfounded, attention
control mechanisms of WM contributed to fluid intelligence to a lesser extent
than did the mechanisms related to the active buffer of WM.

Abstract:
G protein-coupled receptor 54 (GPR54) is a Gq/11-coupled 7 transmembrane-spanning receptor (7TMR). Activation of GPR54 by kisspeptin (Kp) stimulates PIP2 hydrolysis, Ca2+ mobilization and ERK1/2 MAPK phosphorylation. Kp and GPR54 are established regulators of the hypothalamic-pituitary-gonadal (HPG) axis and loss-of-function mutations in GPR54 are associated with an absence of puberty and hypogonadotropic hypogonadism, thus defining an important role of the Kp/GPR54 signaling system in reproductive function. Given the tremendous physiological and clinical importance of the Kp/GPR54 signaling system, we explored the contributions of the GPR54-coupled Gq/11 and β-arrestin pathways on the activation of a major downstream signaling molecule, ERK, using Gq/11 and β-arrestin knockout mouse embryonic fibroblasts. Our study revealed that GPR54 employs the Gq/11 and β-arrestin-2 pathways in a co-dependent and temporally overlapping manner to positively regulate ERK activity and pERK nuclear localization. We also show that while β-arrestin-2 potentiates GPR54 signaling to ERK, β-arrestin-1 inhibits it. Our data also revealed that diminished β-arrestin-1 and -2 expression in the GT1-7 GnRH hypothalamic neuronal cell line triggered distinct patterns of gene expression following Kp-10 treatment. Thus, β-arrestin-1 and -2 also regulate distinct downstream responses in gene expression. Finally, we showed that GPR54, when uncoupled from the Gq/11 pathway, as is the case for several naturally occurring GPR54 mutants associated with hypogonadotropic hypogonadism, continues to regulate gene expression in a G protein-independent manner. These new and exciting findings add significantly to our mechanistic understanding of how this important receptor signals intracellularly in response to kisspeptin stimulation.