Bouncing universe models in an extended gravity theory

Some bouncing models are investigated in the framework of an extended theory of gravity. The extended gravity model is a simple extension of the General Relativity where an additional matter geometry coupling is introduced to account for the late time cosmic speed up phenomena. The dynamics of the models are discussed in the background of a flat FRW universe. Some viable models are reconstructed for specifically assumed bouncing scale factors. The behavior of the models are found to be decided mostly by the parameters of the respective models. The extended gravity based minimal matter-geometry coupling parameter has a role to remove the omega singularity occurring at the bouncing epoch. It is noted that the constructed models violate the energy conditions, however, in some cases this violation leads to the evolution of the models in phantom phase. The stability of the models are analyzed under linear homogeneous perturbations and it is found that, near the bounce, the models show instability but the perturbations decay out smoothly to provide stable models at late times.     

Study on propagation efficiency and fidelity of subthreshold signal in feed-forward hybrid neural network under electromagnetic radiation

Nonlinear Dynamics - The hybrid neural model provides a computationally effective and biophysics-based neuron behavior model, which maintains its simplicity by incorporating the dynamics...     

“Quad-band flexible magnesium zinc ferrite (MgZnFe2O4)-based double negative metamaterial for microwave applications”

This article presents vertically coupled, rectangular complementary split-ring resonator-shaped quad-band double-negative (DNG) metamaterial unit cells, that is, having both negative permittivity and permeability, which redirect negative refractive and also are not found in nature. The metamaterial is fabricated on magnesium zinc ferrite-based flexible microwave substrates, and the flexible substrates are chosen with two different concentrations of magnesium (Mg) denoted by Mg₃₀ and Mg₅₀ for 30% and 50% of Mg, which possess dielectric constants of 4.32 and 3.15 and loss tangents of 0.003 and 0.005, respectively. The proposed metamaterials are demonstrated by utilizing the CST microwave simulator, and their effective parameters are extracted according to the Nicolson-Ross-Wire method. With Mg_30, the prepared, flexible metamaterial shows measured resonances at 3.70 GHz, 7 GHz, 8.60 GHz, and 9.78 GHz, whereas with Mg₅₀ it shows the measured resonances at 4.10 GHz, 7.70 GHz, 9.33 GHz, and 10.62 GHz. Very good effective medium ratios (EMR) along with DNG properties are obtained, namely 6.5 and 5.85 for Mg₃₀ and Mg_50, respectively, with a physical dimension of 12.5 × 9.5 mm² for both of the unit cells_. Also, the electric field, magnetic field, and surface current distribution at different resonances and the polarization insensitivity at different polarization angles were observed. Thus, the designed new flexible substrate microwave materials based on DNG metamaterials are potential candidates for S-, C- and X-band applications, as well as for flexible microwave technologies.     

New existence of multi-spike solutions for the fractional Schrödinger equations

Science China Mathematics - We consider the following fractional Schrödinger equation: (0.1) $${\left( { - \Delta } \right)^s}u + V\left( y \right)u = {u^p},\,\,\,\,\,\,u >...     

A no expanding breather theorem for noncompact Ricci flows

Annals of Global Analysis and Geometry - In this note we show that, under certain curvature positivity conditions (the weak $${\text {PIC}}-2$$ condition or the nonnegative bisectional curvature...     

Synthesis and properties of novel N,C,N terdentate skeleton based on 1,3-di(pyridin-2-yl)benzene moiety-new tricks for old dogs

Utilization of intermolecular Friedel-Crafts and intramolecular condensation reaction,novel 1,3-di-(pyridine-2-yl)benzene(N,C,N terdentate) skeleton with electro-withdrawing group in 6' position of pyridyl and a cyclization between 6' position of pyridyl and 6 position of benzyl ring were firstly designed and synthesized.The structures of these novel N,C,N terdentate were confirmed by NMR,MS and X-ray single crystalanalyses.The photophysical properties of these compounds were briefly explored.