Cycles through 4 vertices in 3-connected graphs

AbstractS.C. Locke proposed a question: If G is a 3-connected graph with minimum degree d and X is a set of 4 vertices on a cycle in G, must G have a cycle through X with length at least min{2d,|V(G)|}? In this paper, we answer this question

Analysis of Tall Buildings Settlement Observation Process and Data Processing and Forecast

It is necessary to observe the deformation of buildings while they are constructed and utilized. Based on the practical requirements and combined with a real property, the thesis primarily discussed the processing researched for surveying of building settlement. Test and analysis of stability of the datum points. On the basis of the settlement difference calculated at intervals and the cumulative settlements, the curved p-t-s (pressure, time, settlement) diagram is plotted. For the buildings it is better with whole rigidity. By the analysis of settlement data, the mathematical model for the settlement, time and pressure is developed; some valuable results are obtained, which provide certain experiences for the practical projects

A ThDP-dependent enzymatic carboligation reaction involved in Neocarazostatin A tricyclic carbazole formation

Acknowledgements This work was supported by grants from the National Natural Science Foundation of China (31570033 to Y. Y.) and the Leverhulme Trust-Royal Society Africa Award (AA090088 to K. K and H. D.). Open access via RSC Gold 4 Gold.Peer reviewedPublisher PD

Parametric study of unsteady-flow-induced volute casing vibro-acoustics in a centrifugal fan

A numerical parametric analysis of a vibro-acoustic coupling method that considered the influence of vibro-acoustic coupling was carried out to investigate the casing vibrations and feathers of vibrational noise induced by unsteady flow of the centrifugal fan at the best-efficiency point (BEP). There are three important aspects of this method. First, an unsteady flow-field with a whole impeller-volute configuration was solved based on three-dimensional incompressible Navier-Stokes equations and a standard k-ε turbulence mode to obtain the source of the vibro-acoustics. Second, a one-way-flow structural acoustic coupling method was implemented to study the volute vibrations and behaviors of vibrational noise by adoption. The generation mechanism of vibrational noise of the volute casing was revealed. Third, the parametric analysis method was used to explore the parametric relationship between the panel thicknesses (such as front-panel thickness [FT], side-panel thickness [ST], and back-panel thickness [BT]) and the outlet acoustical power of the volute casing surface. The parametric analysis provides a reasonable range of values of three panel thicknesses that result in minimal vibrational sound radiation

A novel classification method combining adaptive local iterative filtering with singular value decomposition for fault diagnosis

As a novel time-frequency analysis method, adaptive local iterative filtering (ALIF) can decompose the time series into several stable components which contain the main fault information. In addition, the amplitude of singular value obtained by singular value decomposition (SVD) can reflect the energy distribution. Naturally, there are certain differences in the energy produced by different faults such as the broken tooth, wearing and normal. Thus, a novel method of mechanical fault classification method based on adaptive local iterative filtering and singular value decomposition is proposed in this paper. Firstly, ALIF method decomposed the original vibration signal into a number of stable components to establish an initial feature vector matrix. Then, the singular values energy corresponding to the feature matrix is employed as a criterion to identify various faults. Compared with the conventional EMD method by simulation experiments, ALIF method has obvious superiority in solving modal aliasing, which is more conducive to the advanced analysis. In this paper, the proposed method is employed to extract the fault information of rolling bearing fault signals from Case Western Reserve University Bearing Data Center. To further verify the effectiveness of the method, the case study is conducted at Drivetrain Diagnostics Simulator. To further illustrate the effectiveness of the method, the results obtained by this method are compared with EMD and EEMD. The results indicated the proposed method performs better in the classification of different mechanical faulty modes