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摘要： Given a nonnegative self-adjoint operator H acting on a separable Hilbert space and an orthogonal projection P such that H-P := ((HP)-P-1/2)((HP)-P-1/2) is densely defined, we prove that lim(n ->infinity)(Pe(-itH/n)P)(n) = e(-itHP) P holds in the strong operator topology. We also derive modifications of this product formula and its extension to the situation when P is replaced by a strongly continuous projection-valued function satisfying P(0) = P.

关键词： boundary behavior   quasilinear elliptic system   large solution  

摘要： In this paper, we study the existence, uniqueness and boundary behavior of positive boundary blow-up solutions to the quasilinear system Delta(infinity)u=a(x)u(p)v(q), Delta(infinity)v=b(x)u(r)v(s) in a smooth bounded domain Omega subset of R-N, with the explosive boundary condition u=v=+infinity on partial derivative Omega, where the operator Delta(infinity) is the infinity-Laplacian, the positive weight functions a(x), b(x) are Holder continuous in Omega, and the exponents verify p, s > 3, q, r > 0, and (p - 3)(s - 3) > qr.

关键词： Ageostrophic circulations   Kinetic energy   Ocean circulation   Ocean dynamics   Pressure  

摘要： We investigated the mean kinetic energy (MKE) and eddy kinetic energy (EKE) in the South China Sea to illustrate the dynamics of the vertically rotating cyclonic-anticyclonic-cyclonic (CAC) circulation in the upper, middle, and deep layers. We found that strong MKE along the basin slope and the associated EKE arising from the vertical shear and stratification of the mean current characterize the circulation. In the upper layer, the external MKE input from the Kuroshio intrusion and wind forcing drive the cyclonic circulation, with the wind forcing providing most of the EKE. External forcing, however, does not directly provide the MKE and EKE of the CAC circulation in the semi-enclosed middle and deep layers, where the internal pressure work near Luzon Strait and the vertical buoyancy flux (VBF) in the southern basin and along the western slope maintain the MKE and EKE. The internal pressure work is formed by ageostrophic motion and pressure gradient field associated with circulation. The VBF is generated by vertical motion induced by the geostrophic cross-isobath transport along the slope where variable density field is maintained by the external flow and the internal mixing. The kinetic energy pathway in the CAC circulation indicates that the external forcing dominates upper-layer circulation and the coupling between internal and external dynamics is crucial for maintaining the circulation in the middle and deep layers. This study provides a new interpretation to the maintenance of CAC circulation from energy prospect.

关键词： Torsional buckling   Multi-walled carbon nanotubes   Molecular mechanics   Density functional theory   Mechanical properties  

摘要： In this paper, quantum and molecular mechanics are used to study the quantum effects of fine scaling on the buckling strength of multi-walled carbon nanotubes (MWCNTs), as well as the effects of changes in length, diameter, chirality, wall number and length-to-diameter ratio of the structure under torsional loading. To this end, the total potential energy of the system is calculated with the consideration of both bond stretching and bond angular variations. The density functional theory (DFT) along with the generalized gradient approximation (GGA) function is used to obtain the relevant elastic constants of the nanotubes. The study shows that the quantum effects of fine scaling cause more buckling strength of the structure against external torsional loadings. Also, with any longitudinal change as well as the changes in the structural arrangement that reduce the quantum effects of fine scaling, the strength of the structure decreases sharply. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Baroclinic flows   Mass fluxes   transport   Turbulence   Salinity   Estuaries  

摘要： Asymmetric tidal turbulence (ATT) strongly influences estuarine health and functioning. However, its impact on the three-dimensional estuarine dynamics and the feedback of water motion and salinity distribution on ATT remain poorly understood, especially for short estuaries (estuarine length << tidal wavelength). This study systematically investigates the abovementioned interactions in a short estuary for the first time, considering periodically weakly stratified conditions. This is done by developing a three-dimensional semi-analytical model (combining perturbation method with finite element method) that allows a dissection of the contributions of different processes to ATT, estuarine circulation, and salt transport. The generation of ATT is dominated by (i) strain-induced periodic stratification and (ii) asymmetric bottom-shear-generated turbulence, and their contributions to ATT are different both in amplitude and phase. The magnitude of the residual circulation related to ATT and the eddy viscosity-shear covariance (ESCO) is about half of that of the gravitational circulation (GC) and shows a "reversed" pattern as compared to GC. ATT generated by strain-induced periodic stratification contributes to an ESCO circulation with a spatial structure similar to GC. This circulation reduces the longitudinal salinity gradients and thus weakens GC. Contrastingly, the ESCO circulation due to asymmetric bottom-shear-generated turbulence shows patterns opposite to GC and acts to enhance GC. Concerning the salinity dynamics at steady state, GC and tidal pumping are equally important to salt import, whereas ESCO circulation yields a significant seaward salt transport. These findings highlight the importance of identifying the sources of ATT to understand its impact on estuarine circulation and salt distribution.

关键词： Laplacian flow   G(2)-structure   Extremally Ricci-pinched  

摘要： We explicitly describe the solution of the G(2)-Laplacian flow starting from an extremally Ricci-pinched closed G(2)-structure on a compact 7-manifold and we investigate its properties. In particular, we show that the solution exists for all real times and that it remains extremally Ricci-pinched. This result holds more generally on any 7-manifold whenever the intrinsic torsion of the extremally Ricci-pinched G(2)-structure has constant norm. We also discuss various examples.

关键词： eigenvalue   inequality   sub-Laplacian   CR manifold  

摘要： The sub-Laplacian plays a key role in CR geometry. In this paper, we investigate eigenvalues of the sub-Laplacian on bounded domains of strictly pseudoconvex CR manifolds, strictly pseudoconvex CR manifolds submersed in Riemannian manifolds. We establish some Levitin-Parnovski-type inequalities and Cheng-Huang-Wei-type inequalities for their eigenvalues. As their applications, we derive some results for the standard CR sphere S2n+1 in Cn+1, the Heisenberg group H-n, a strictly pseudoconvex CR manifold submersed in a minimal submanifold in R-m, domains of the standard sphere S-2n and the projective space FPm.

关键词： Hierarchical dispersion entropy   improved Laplacian score   rolling bearing   health condition identification  

摘要： Since bearing fault signal under complex running status is usually manifested as the characteristics of nonlinear and non-stationary, which implies it is difficult to extract accurate affluent features and achieve effective fault identification via conventional signal processing tools. In this article, a hybrid intelligent fault identification scheme, the combination of hierarchical dispersion entropy and improved Laplacian score, is proposed to address this problem, which is mainly composed of three procedures. First, the particle swarm optimization-based optimized hierarchical dispersion entropy is adopted to excavate multilevel fault symptoms from low-frequency and high-frequency components, which can both solve the shortcoming of missing of high-frequency feature information existing in the recently presented multiscale dispersion entropy and artificial parameter selection issue of hierarchical dispersion entropy. Second, an improved feature selection strategy based on improved Laplacian score is proposed to select the sensitive features to establish a low-dimensional feature data set by incorporating the weight coefficient into Laplacian score. Finally, the established low-dimensional feature data set is fed to a Softmax classifier to automatically identify different health conditions of rolling bearing. The efficacy of the proposed method is validated by two experimental cases. Results show that our approach is highly effective in recognizing different fault categories and severities of rolling bearing. Meanwhile, our approach exhibits higher accuracy and better identification performance than some similar entropy-based hybrid approaches and other identification methods reported in this article.

关键词： Lost circulation   Gelation kinetics   Polyacrylamide   Polyethylenimine   Crosslinking   Rheology  

摘要： The problem of lost circulation is a direct consequence of the presence of fractures or high permeability. Lost circulation material (LCM) is used to treat the loss that occurs or proactively strengthen the wellbore of the potential loss zones. The polyacrylamide (PAM)/Polyethylenimine (PEI) cross-linkable polymer gel is proven to work best in zone-sealing and plugging applications. In addition to their thermal stability, the fact that these gels are flexible gives them the advantage of deforming and sealing-off multiple and complex near wellbore fractures. The primary objective of this study is to investigate the gelation kinetics of the PAM/PEI cross-linkable polymer to be used in drilling fluids formulations to enhance wellbore stability and strength. Different combinations of polymers and crosslinkers were evaluated;potential polymers were screened for gelation kinetics and gel strength in typical drilling mud formulations. The gelation time of the polymer-based drilling mud formulation is determined in salt-free and in saline systems. The results on rheological properties and gelation kinetics were used to prepare a gelling mud formulation using PAM/PEI cross-linkable polymer as LCM. The produced gel was thermally stable under high-temperature-high-pressure reservoir conditions, which will result in enhanced wellbore strengthening.

关键词： Reagents   Chemical reactions   Energy   Kinetic parameters   Collisions  

摘要： Despite several studies in the literature, the detailed quantum state-to-state level mechanism of the astrophysically important exoergic barrierless H + LiH+ -> H-2 + Li+ reaction is yet to be understood. In this work, we have investigated the energy disposal mechanism of the reaction in terms of integral reaction cross section, product internal state distributions, differential cross section, and rate constant. Fully converged and Coriolis coupled quantum mechanical calculations based on a time-dependent wave packet method have been performed at the state-to-state level on the ab initio electronic ground state potential energy surface (PES) constructed by Martinazzo et al. (J. Chem. Phys. 2003,119, 11241-11248). The agreement between the present quantum mechanical and previous quasi-classical results is found even at very low relative translational energies of reagents. A non-statistical inverse Boltzmann vibrational distribution for the product is found. This is attributed to the "attractive" nature of the underlying PES, which facilitates the excess energy release mostly as product vibration (60-80%). The energy disposal in products is found to be unaffected by the rovibrational excitation of the reagent diatom due to the weak coupling between the vibrational modes of the reagent and the product. The mild effect of collision energy on the product energy disposal is ascribed to the effective coupling between the translational modes of the reagent and the product. It is found that the collisions lead to the formation of the product H-2 in its rovibrationally excited levels.