The perturbation theory for the Drazin inverse and its applications

AbstractLet A and E be n × n matrices and B = A + E. Denote the Drazin inverse of A by AD. We give an upper bound for the relative error ∥BD − AD∥∥AD∥ under certain circumstances. An error bound for the solution for the singular equations Ax = b [b ∈ R(A)] is also considered

Self-Similar Tilings of Fractal Blow-Ups

New tilings of certain subsets of $\mathbb{R}^{M}$ are studied, tilings associated with fractal blow-ups of certain similitude iterated function systems (IFS). For each such IFS with attractor satisfying the open set condition, our construction produces a usually infinite family of tilings that satisfy the following properties: (1) the prototile set is finite; (2) the tilings are repetitive (quasiperiodic); (3) each family contains self-similartilings, usually infinitely many; and (4) when the IFS is rigid in an appropriate sense, the tiling has no non-trivial symmetry; in particular the tiling is non-periodic

Maintenance Decision Method Based on Risk Level

Maintenance decision method of the mechanical equipment still has some deficiencies and shortcomings, including unreasonable maintenance methods, surplus or insufficient repair, and unscientific inspection and repair intervals, especially for equipment with different risks. As a consequence, more frequent failures and higher maintenance costs of the mechanical equipment occur along with some major safety accidents and economic losses in the process of production. To overcome these problems, a framework for maintenance decision method based on risk level is presented for mechanical equipment in the petrochemical industry. First, 10 evaluation indexes and a set of scoring criteria quantifying the subjective evaluation are defined to evaluate the risk level of each mechanical equipment. Based on the analytic hierarchy process (AHP), the weight of the evaluation indexes and the evaluation model of the risk levels were established. Then, the subjective effects in the scoring process were removed using the Monte Carlo simulation (MCS) approach. Next, maintenance decision-making trees of the mechanical equipment were formulated by referencing the logic decision tree of reliability-centered maintenance. Finally, the feasibility of the framework was effectively verified by testing a well-control system in the oil field, for which the risk level and maintenance methods were obtained

Beam energy distribution influences on density modulation efficiency in seeded free-electron lasers

The beam energy spread at the entrance of undulator system is of paramount importance for efficient density modulation in high-gain seeded free-electron lasers (FELs). In this paper, the dependences of high harmonic micro-bunching in the high-gain harmonic generation (HGHG), echo-enabled harmonic generation (EEHG) and phase-merging enhanced harmonic generation (PEHG) schemes on the electron energy spread distribution are studied. Theoretical investigations and multi-dimensional numerical simulations are applied to the cases of uniform and saddle beam energy distributions and compared to a traditional Gaussian distribution. It shows that the uniform and saddle electron energy distributions significantly enhance the performance of HGHG-FELs, while they almost have no influence on EEHG and PEHG schemes. A numerical example demonstrates that, with about 84keV RMS uniform and/or saddle slice energy spread, the 30th harmonic radiation can be directly generated by a single-stage seeding scheme for a soft x-ray FEL facility

Lift force, drag force, and tension response in vortex-induced vibration for marine risers under shear flow

An experiment was performed in a deep-water basin to investigate VIV mechanisms under shear flow. Lift force, drag force, and tension response were obtained. Results show that multiple frequencies are appeared for nonuniform vortex shedding frequency and interaction between the IL and CF vibrations. Beat phenomenon is observed in time history of lift force, and decreased with the increasing riser pretension. Dominant frequencies of riser tension are consistent with the IL and CF dominant frequency, and amplitudes of the tension are not uniform. VIV is inhibited with increasing riser pretension and the dominant frequencies also increase with increasing riser tension

Effect of drilling pipe rotation on vortex induced vibration response of drilling riser

An experiment was carried out in a basin to investigate rotation of drilling pipe on vortex induced vibration response of drilling riser. Vibration displacement time-history and frequency are obtained. Results show that dominant vibration frequency in the in-line direction is almost twice as high as that in the cross-flow direction. The vibration amplitudes in both the cross-flow and in-line direction increase with an increase in rotation speed of drilling pipe under the experimental conditions. However, the influence of rotation speed drilling pipe on drilling riser vibration amplitude is insignificant. Dominant frequencies are invariant with variation of drilling pipe rotation under experimental conditions

Experimental study of the vortex-induced vibration of marine risers under middle flow

A considerable number of studies for vortex induced vibration (VIV) under uniform flow have been performed. However, investigation of VIV under middle flow is scarce. An experiment for VIV under middle flow was conducted in a deep-water offshore basin. Various measurements were obtained by the fiber Bragg grating strain sensors placed on the riser, and VIV under the effect of middle flow with was investigated. Results show that the riser vibrates at different order natural frequencies along the water depth in the CF and IL directions appearing as the multi-frequencies under middle flow. The variation vortex shedding frequencies along the riser under middle flow may generate different wake modes and vibration modals as the corresponding vortex shedding frequencies approach the riser natural frequencies. The dominant vibration frequency of the entire riser is consistent, and determined by high order natural frequency and the corresponding closing vortex shedding frequencies under the middle flow. Meanwhile, the vibration modal under middle flow appears multi-modals and other lower modal have effect on riser vibration. The VIV mechanism under middle flow possesses some aspects similar to those of uniform flow and several unique features

A theoretical study on the mechanism of the addition reaction between cyclopropenylidene and ethylene

The reaction mechanism between cyclopropenylidene and ethylene has been systematically investigated employing the MP2/6-311+G* level of theory to better understand the cyclopropenylidene reactivity with unsaturated hydrocarbons. Geometry optimization, vibrational analysis, and energy property for the involved stationary points on the potential energy surface have been calculated. Energies of all the species are also further refined by the CCSD(T)/6-311+G* single-point calculations. Firstly, one important reaction intermediate (INTa) has been located via a transition state (TSa). After that, the common intermediate (INTb) for the two pathways (1) and (2) has been formed via TSb. At last, two different products possessing three- and four-membered ring characters have been obtained through two reaction pathways. In the reaction pathway (1), a three-membered ring alkyne compound has been obtained. As for the reaction pathway (2), a four-membered ring conjugated diene compound has been formed, which is the most favorable reaction to occur from the kinetic and thermodynamic viewpoints