Global existence and propagation speed for a generalized Camassa-Holm model with both dissipation and dispersion

In this paper, we study a generalized Camassa–Holm (gCH) model with both dissipation and dispersion, which has (N+1)-order nonlinearities and includes the following three integrable equations: the Camassa–Holm, the Degasperis–Procesi, and the Novikov equations, as its reductions. We first present the local well-posedness and a precise blow-up scenario of the Cauchy problem for the gCH equation. Then, we provide several sufficient conditions that guarantee the global existence of the strong solutions to the gCH equation. Finally, we investigate the propagation speed for the gCH equation when the initial data are compactly supported

Formation law and criterion of nebulous macroscopic segregation in ZL205A alloy castings

The appearance of macroscopic segregation in ZL205A alloy castings bears a super resemblance to the appearance of shrinkage porosity, and the chemical composition of the segregation is Al2Cu whose microstructure is in the form of dentrite or skeleton crystal. According to the characteristic of nebulous segregation, the formation process could be divided into two steps by the eutectic temperature of Al2Cu. Then a criterion for each of the two steps is brought forward on the basis of the shrinkage porosity criterion of low pressure casting

A CLT for the LSS of large dimensional sample covariance matrices with diverging spikes

In this paper, we establish the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix when the population covariance matrices are not uniformly bounded, which is a nontrivial extension of the Bai-Silverstein theorem (BST) (2004). The latter has strongly influenced the development of high-dimensional statistics, especially in applications of random matrix theory to statistics. However, the assumption of uniform boundedness of the population covariance matrices has seriously limited the applications of the BST. The aim of this paper is to remove the barriers for the applications of the BST. The new CLT, allows spiked eigenvalues to exist, which may be bounded or tend to infinity. An important feature of our result is that the roles of either spiked eigenvalues or the bulk eigenvalues predominate in the CLT, depending on which variance is nonnegligible in the summation of the variances. The CLT for LSS is then applied to compare four linear hypothesis tests: The Wilk's likelihood ratio test, the Lawly-Hotelling trace test, the Bartlett-Nanda-Pillai trace test, and Roy's largest root test. We also derive and analyze their power function under particular alternatives.Comment: Comparing with the old manuscript, we modified the title of the paper. arXiv admin note: text overlap with arXiv:2205.07280. arXiv admin note: text overlap with arXiv:2205.0728

Research and Application of PDM Borehole Technology for HDD

AbstractBy introducing the structure character and working principle of PDM, borehole technologies of PDM directional drilling were studied in this text, including borehole technology principle, directional method, technology flow, drilling technology parameters, branch borehole technology etc. Shaanxi Tingnan Coal .Ltd field application was taken as an example to do a simple introduction on PDM matching equipment and technology promotion. The borehole technology and related result can be used as reference for horizontal directional drilling research and construction