Multiply Warped Products with Non-Smooth Metrics

In this article we study manifolds with $C^{0}$-metrics and properties of Lorentzian multiply warped products. We represent the interior Schwarzschild space-time as a multiply warped product space-time with warping functions and we also investigate the curvature of a multiply warped product with $C^0$-warping functions. We given the {\it{Ricci curvature}} in terms of $f_1$, $f_2$ for the multiply warped products of the form $M=(0,\ 2m)\times_{f_1}R^1\times_{f_2} S^2$.Comment: LaTeX, 7 page

Study of quasi-optical circuit techniques in varactor multipliers

Quasi-optical circuit techniques in varactor multiplier

Infinite slabs and other weird plane symmetric space-times with constant positive density

We present the exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with constant positive density located below $z=0$. This solution depends essentially on two constants: the density $\rho$ and a parameter $\kappa$. We show that this space-time finishes down below at an inner singularity at finite depth. We match this solution to the vacuum one and compute the external gravitational field in terms of slab's parameters. Depending on the value of $\kappa$, these slabs can be attractive, repulsive or neutral. In the first case, the space-time also finishes up above at another singularity. In the other cases, they turn out to be semi-infinite and asymptotically flat when $z\to\infty$. We also find solutions consisting of joining an attractive slab and a repulsive one, and two neutral ones. We also discuss how to assemble a "gravitational capacitor" by inserting a slice of vacuum between two such slabs.Comment: 8 page

Study of quasi-optical circuit techniques in varactor multipliers

Quasi-optical circuit techniques in varactor multiplier

NUT-Charged Black Holes in Gauss-Bonnet Gravity

We investigate the existence of Taub-NUT/bolt solutions in Gauss-Bonnet gravity and obtain the general form of these solutions in $d$ dimensions. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet gravity that contain these solutions in the limit that the Gauss-Bonnet parameter $\alpha$ goes to zero. Furthermore there are no NUT solutions in Gauss-Bonnet gravity that yield non-extremal NUT solutions to Einstein gravity having a curvature singularity at $r=N$ in the limit $$. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions with non-trivial fibration only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature. Indeed, when the base space has at most one positively curved two dimensional space as one of its factor spaces, then Gauss-Bonnet gravity admits extreme NUT solutions, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet gravity with any base space with factor spaces of zero or positive constant curvature. The only case for which one does not have bolt solutions is in the absence of a cosmological term with zero curvature base space.Comment: 20 pages, referrence added, a few typos correcte

The Effects Of Training In Timing And Rhythm On Reading Achievement

This study investigated the relationship between improvement in students’ timing/rhythmicity and reading achievement. Two hundred eighty high school-age participants completed pre- and post-test measures from the Woodcock-Johnson Tests of Achievement-III (Woodcock, McGrew, & Mather, 2001). Students in the experimental group participated in a timing/rhythm intervention designed to reduce their latency response to a reoccurring metronome beat. Students in the control group participated in traditional classroom activities. The results from the study indicate that after treatment, the experimental group’s post-test Broad Reading and Reading Fluency scores were statistically significantly higher than the non-treatment control group’s post-test scores

Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity

We present a class of higher dimensional solutions to Gauss-Bonnet-Maxwell equations in $2k+2$ dimensions with a U(1) fibration over a $2k$-dimensional base space $\mathcal{B}$. These solutions depend on two extra parameters, other than the mass and the NUT charge, which are the electric charge $q$ and the electric potential at infinity $V$. We find that the form of metric is sensitive to geometry of the base space, while the form of electromagnetic field is independent of $\mathcal{B}$. We investigate the existence of Taub-NUT/bolt solutions and find that in addition to the two conditions of uncharged NUT solutions, there exist two other conditions. These two extra conditions come from the regularity of vector potential at $r=N$ and the fact that the horizon at $r=N$ should be the outer horizon of the black hole. We find that for all non-extremal NUT solutions of Einstein gravity having no curvature singularity at $r=N$, there exist NUT solutions in Gauss-Bonnet-Maxwell gravity. Indeed, we have non-extreme NUT solutions in $2+2k$ dimensions only when the $2k$-dimensional base space is chosen to be $\mathbb{CP}^{2k}$. We also find that the Gauss-Bonnet-Maxwell gravity has extremal NUT solutions whenever the base space is a product of 2-torii with at most a 2-dimensional factor space of positive curvature, even though there a curvature singularity exists at $r=N$. We also find that one can have bolt solutions in Gauss-Bonnet-Maxwell gravity with any base space. The only case for which one does not have black hole solutions is in the absence of a cosmological term with zero curvature base space.Comment: 23 pages, 3 figures, typos fixed, a few references adde

The Efroimsky formalism adapted to high-frequency perturbations

The Efroimsky perturbation scheme for consistent treatment of gravitational waves and their influence on the background is summarized and compared with classical Isaacson's high-frequency approach. We demonstrate that the Efroimsky method in its present form is not compatible with the Isaacson limit of high-frequency gravitational waves, and we propose its natural generalization to resolve this drawback.Comment: 7 pages, to appear in Class. Quantum Gra

Effect of alirocumab on lipids and lipoproteins in individuals with metabolic syndrome without diabetes: Pooled data from 10 phase 3 trials.

AimsThis analysis assessed the efficacy and safety of alirocumab, a proprotein convertase subtilisin/kexin type 9 inhibitor, in patients with or without metabolic syndrome (MetS) using pooled data from 10 phase 3 ODYSSEY trials.Materials and methodsData from 4983 randomized patients (1940 with MetS; 1642 with diabetes excluded) were assessed in subgroups by MetS status. Efficacy data were analysed in 4 pools per study design: 2 placebo-controlled pools (1 using alirocumab 150 mg every 2 weeks [Q2W], 1 using 75/150 mg Q2W) with background statin, and 2 ezetimibe-controlled pools (both alirocumab 75/150 mg Q2W), 1 with and 1 without background statin. Alirocumab 75/150 mg indicates possible dose increase from 75 to 150 mg at Week 12 based on Week 8 LDL-C.ResultsLDL-C percentage reduction from baseline at Week 24 with alirocumab was 63.9% (MetS) and 56.8% (non-MetS) in the pool of alirocumab 150 mg Q2W, and 42.2% to 52.2% (MetS) and 45.0% to 52.6% (non-MetS) in 3 pools using 75/150 mg Q2W. Levels of other lipid and lipoprotein parameters were also improved with alirocumab treatment, including apolipoprotein B, non-high-density lipoprotein cholesterol (non-HDL-C), lipoprotein(a) and HDL-C. Overall, the percentage change at Week 24 in LDL-C and other lipids and lipoproteins did not vary by MetS status. Adverse event rates were generally similar between treatment groups, regardless of MetS status; injection-site reactions occurred more frequently in alirocumab vs control groups.ConclusionsAcross study pools, alirocumab-associated reductions in LDL-C, apolipoprotein B, and non-HDL-C were significant vs control, and did not vary by MetS status