Effective condition numbers and small sample statistical condition estimation for the generalized Sylvester equation

Abstract In this paper, we investigate the effective condition numbers for the generalized Sylvester equation （AX - YB, DX - YE） = （C,F）, where A,D ∈ Rm×m B,E ∈ Rn×n and C,F ∈ Rm×n. We apply the small sample statistical method for the fast condition estimation of the generalized Sylvester equation, which requires （9（m2n ＋ mn2） flops, comparing with （-O（m3 ＋ n3） flops for the generalized Schur and generalized Hessenberg- Schur methods for solving the generalized Sylvester equation. Numerical examples illustrate the sharpness of our perturbation bounds.

Toward accurate and efficient dynamic computational strategy for heterogeneous catalysis:Temperature-dependent thermodynamics and kinetics for the chemisorbed on-surface CO

Computational tools on top of first principle calculations have played an indispensable role in revealing the molecular details,thermodynamics,and kinetics in catalytic reactions.Here we proposed a highly efficient dynamic strategy for the calculation of thermodynamic and kinetic properties in heterogeneous catalysis on the basis of efficient potential energy surface(PES)and MD simulations.Taking CO adsorbate on Ru(0001)surface as the illustrative model system,we demonstrated the PES-based MD can efficiently generate reliable two-dimensional potential-of-mean-force(PMF)surfaces in a wide range of temperatures,and thus temperature-dependent thermodynamic properties can be obtained in a comprehensive investigation on the whole PMF surface.Moreover,MD offers an effective way to describe the surface kinetics such as adsorbate on-surface movement,which goes beyond the most popular static approach based on free energy barrier and transition state theory(TST).We further revealed that the dynamic strategy significantly improves the predictions of both thermodynamic and kinetic properties as compared to the popular ideal statistic mechanics approaches such as harmonic analysis and TST.It is expected that this accurate yet efficient dynamic strategy can be powerful in understanding mechanisms and reactivity of a catalytic surface system,and further guides the rational design of heterogeneous catalysts.

A Fault Sample Simulation Approach for Virtual Testability Demonstration Test

Virtual testability demonstration test has many advantages,such as low cost,high efficiency,low risk and few restrictions.It brings new requirements to the fault sample generation.A fault sample simulation approach for virtual testability demonstration test based on stochastic process theory is proposed.First,the similarities and differences of fault sample generation between physical testability demonstration test and virtual testability demonstration test are discussed.Second,it is pointed out that the fault occurrence process subject to perfect repair is renewal process.Third,the interarrival time distribution function of the next fault event is given.Steps and flowcharts of fault sample generation are introduced.The number of faults and their occurrence time are obtained by statistical simulation.Finally,experiments are carried out on a stable tracking platform.Because a variety of types of life distributions and maintenance modes are considered and some assumptions are removed,the sample size and structure of fault sample simulation results are more similar to the actual results and more reasonable.The proposed method can effectively guide the fault injection in virtual testability demonstration test.