The linear arboricity of planar graphs with no short cycles

AbstractThe linear arboricity of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that ⌈Δ(G)2⌉≤la(G)≤⌈Δ(G)+12⌉ for any simple graph G. In the paper, it is proved that if G is a planar graph with Δ≥7 and without i-cycles for some i∈{4,5}, then la(G)=⌈Δ(G)2⌉

Fault diagnosis of rolling element bearing using Naïve Bayes classifier

The development of machine learning brings a new way for diagnosing the fault of rolling element bearings. However, the method in machine learning with high accuracy often has the poor ability of generalization due to the overuse of feature engineering. To address this challenge, Naïve Bayes classifier is applied in this paper. As the one of the cluster of Bayes classifiers, its ability of classification is very outstanding. In this paper, the method is provided with a detailed description for why and how to diagnose the fault of bearing. Finally, an evaluation of the performance of Naïve Bayes classifier is presented with real world data. The evaluation indicates that Naïve Bayes classifier can achieve a high level of accuracy without any feature engineering

Deterministic realization of collective measurements via photonic quantum walks

Collective measurements on identically prepared quantum systems can extract more information than local measurements, thereby enhancing information-processing efficiency. Although this nonclassical phenomenon has been known for two decades, it has remained a challenging task to demonstrate the advantage of collective measurements in experiments. Here we introduce a general recipe for performing deterministic collective measurements on two identically prepared qubits based on quantum walks. Using photonic quantum walks, we realize experimentally an optimized collective measurement with fidelity 0.9946 without post selection. As an application, we achieve the highest tomographic efficiency in qubit state tomography to date. Our work offers an effective recipe for beating the precision limit of local measurements in quantum state tomography and metrology. In addition, our study opens an avenue for harvesting the power of collective measurements in quantum information processing and for exploring the intriguing physics behind this power.Comment: Close to the published versio

3-(3,4-Dihydroxyphenyl)-1-methoxy-1-oxopropan-2-aminium chloride

In the title compound, C10H14NO4 +·Cl−, the benzene ring makes a dihedral angle of 64.68 (4)° with the methyl­amino­propano­ate unit, which is bonded to the catechol ring via a methyl­ene C atom. A strong intra­molecular O—H⋯O hydrogen bond occurs. In the crystal, O—H⋯O, N—H⋯Cl and O—H⋯Cl hydrogen bonds and weak C—H⋯O inter­actions link the mol­ecules into a three-dimensional network