Parameter Estimation of Sub-/Super-synchronous Oscillation Based on Interpolated All-phase Fast Fourier Transform with Optimized Window Function

In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and frequencies,as well as the mutual interferences among SsO modes with close frequencies,the accurate parameter estimation of SsO has become a particularly challenging topic.To solve this issue,this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision.First,by aiming at the sidelobe characteristics of the window function as evaluation criteria,a combined cosine function is optimized using a genetic algorithm(GA).Furthermore,the obtained window function is self-convolved to extend its excellent characteristics,which have better performance in reducing mutual interference from other SSO modes.Subsequently,a new form of interpolated all-phase fast Fourier transform(IpApFFT)using the optimized window function is proposed to estimate the parameters of SsO.This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience.The performance of the pro-posed method is demonstrated under various conditions,com-pared with other estimation methods.Simulation results validate the effectiveness and superiority of the proposed method.

THERMODYNAMIC FORMALISM FOR SUBADDITIVE SEQUENCE OF DISCONTINUOUS FUNCTIONS

The topological pressure for subadditive sequence of discontinuous functions is defined on any invariant subset having a nested family of subsets in the compact metric space. Two subadditive variational principles associated with two different relatively weak conditions are developed for the defined topological pressure. As an application, we give an example on systems with nonzero Lyapunov exponents.

Comparative analysis of interdecadal precipitation variability over central North China and sub Saharan Africa

The interdecadal variability of precipitation over sub-Saharan Africa (SSA) and central North China (CNC) is examined and compared in this study. Previous studies have found that the two regions have similar interdecadal dry–wet evolution in the past 100 years. The results show obvious decadal precipitation fluctuations in the two regions. In CNC, a persistent negative precipitation anomaly is detected from the early 1970s to the 2000s. In SSA, a negative precipitation anomaly is apparent since the late 1970s, while a distinct upward trend is found since the 1990s although the precipitation anomaly is still negative. Significant correlation is found between the decadal precipitation anomalies in SSA and the SST modes (Atlantic Multidecadal Oscillation (AMO) and Pacific Decadal Oscillation (PDO)), as well as the North Atlantic Oscillation (NAO), while in CNC the decadal precipitation is influenced by the NAO and PDO. The EOF results show that the total explained variance of the first four EOFs in SSA is smaller than that of CNC. The fourth and third modes in SSA are significantly associated with the AMO and PDO respectively, while the first, third, and fourth modes are significantly associated with the NAO. The first mode in CNC is significantly associated with the NAO. The first mode of the precipitation anomaly in SSA fluctuates out of phase with that in CNC, while in-phase changes are apparent among the third and the fourth modes.

Advanced unconventional techniques for sub-100 nm nanopatterning

Patterned nanostructures with ultrasmall features endow functional devices with unique nanoconfinement and performance enhancements.The increasing demand for miniaturization has stimulated the development of sub-100 nm nanopatterning techniques.Beyond conventional lithography—which is limited by unavoidable factors—advanced patterning techniques have been reported to produce nanoscale features down to molecular or even atomic scale.In this review,unconventional techniques for sub-100 nm nanopatterning are discussed,in particular the principles by which to achieve the desired patterns(among other important issues).Such techniques can be classified into three categories:template-replica,template-induced,and template-free techniques.Moreover,multi-dimensional nanostructures consist of various building materials,the unique properties of which are summarized.Finally,the remaining challenges and opportunities for large-scale patterning,the improvement of device perfor-mance,the multi-dimensional nanostructures of biocompatible materials,molecular-scale patterning,and the carbon footprint requirements for future nanofabrication processes are discussed.

ON SET-VALUED MARTINGALES, SUBMARTINGALES AND SUPERMARTINGALES

Based on Refs. [1—8], we discuss the following problem in this note.Let (Ω, A, P)be a complete probability space and X be a separable Banach space with the dual X~*.