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.     

Limit for the Euler-genus distributions of ladder-like sequences of graphs

Journal of Algebraic Combinatorics - In this paper, we demonstrate a method for calculating the production matrices for the Euler-genus polynomials of H-linear families of graphs. Particularly, for...     

n-APR tilting and $$\tau $$ τ -mutations

Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that...     

Characters of unipotent radicals of standard parabolic subgroups with 3 parts

Journal of Algebraic Combinatorics - This paper gives explicit constructions of all irreducible representations of unipotent radicals $$N_{n_1,n_2,n_3}({\mathbb {F}}_q)$$ of the standard parabolic...     

Electrochemical synthesis of α,α-dihaloacetophenones from terminal alkyne derivatives

By virtue of electrochemistry, a series of α,α-dihaloacetophenones were easily obtained with good to excellent yields. This electrochemical procedure was taken in a divided cell with constant current in aqueous media. The reaction can be carried out smoothly at room temperature under metal and oxidant free condition, which provides an eco-friendly synthesis for the α,α-dihaloacetophenone derivatives.     

Oxidation of aromatic sulfides with molecular oxygen: Controllable synthesis of sulfoxides or sulfones

The recent development of selective oxidation of aromatic sulfides with molecular oxygen was highlighted. The sulfoxides and sulfones could be obtained by simply switching the reaction media, i.e., bis(2-butoxyethyl)ether (BBE) or poly(ethylene glycol)dimethyl ether (PEGDME). The application of the high-boiling-point polyether as an initiator and green media can eliminate the need of large quantities of additives and volatile solvents. This strategy represents an economic and eco-friendly method that could find potential applications.     

An adaptive smooth unsaturated bistable stochastic resonance system and its application in rolling bearing fault diagnosis

An adaptive smooth unsaturated bistable stochastic resonance (ASUBSR) system for bearing fault signal detection is established. Based on the problem of output saturation and poor low-frequency suppression performance of classical bistable stochastic resonance (CBSR) system, an SUBSR with unsaturated characteristics is proposed. An ASUBSR system is designed by extracting the envelope spectrum of the input signal and resampling it to satisfy the adiabatic approximation condition, combining high-pass filter to filter out low-frequency interference, and using genetic algorithm to select the optimal system parameters. Through simulations and experiments, we found that the system can effectively suppress the interference of low-frequency and high-frequency, indicates that the system performs like a band-pass filter, and the output signal-to-noise ratio is better than that of the CBSR system. The proposed ASUBSR system has great application in the field of fault detection of rolling bearings.