Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Determination,residue and risk assessment of trifloxystrobin,trifloxystrobin acid and tebuconazole in Chinese rice consumption

A simple and rapid analytical method for the detection of trifloxystrobin, trifloxystrobin acid and tebuconazole in soil, brown rice, paddy plants and rice hulls was established and validated by liquid chromatography with tandem mass spectrometry. Acceptable linearity (R² > 0.99), accuracy (average recoveries of 74.3–108.5%) and precision (intra- and inter-day relative standard deviations of 0.9–8.8%) were obtained using the developed determination approach. In the field trial, the half-lives of trifloxystrobin and tebuconazole in paddy plants were 5.7–8.3 days in three locations throughout China, and the terminal residue concentrations of trifloxystrobin and tebuconazole were <100 and 500 μg/kg (maximum residue limits set by China), respectively, at harvest, which indicated that, based on the recommended application procedure, trifloxystrobin and tebuconazole are safe for use on rice. The risk assessment results demonstrated that, owing to risk quotient values of both fungicides being <100%, the potential risk of trifloxystrobin and tebuconazole on rice was acceptable for Chinese consumers. These data could provide supporting information for the proper use and safety evaluation of trifloxystrobin and tebuconazole in rice.     

Optical fiber acoustic sensing multiplexing system based on TDM/SFDM

We propose a system of time-division multiplexing(TDM) and spatial frequency-division multiplexing(SFDM). Extrinsic Fabry–Perot interferometric sensors are applied to detect weak acoustic signals. The broadband source is employed, the light from it is modulated by a pulse signal sequence and is efficiently amplified by semiconductor optical amplifiers. Experimental results show that the equivalent noise pressure spectrum level is-97.2 d B re 1 rad/√Hz below 1250 Hz, and the cross talk between two sensors in one TDM channel is-32.7 d B with a cavity length difference of 60 μm. The number of sensors in this multiplexing system can theoretically reach 160.