RELATIVE ESSENTIAL SPECTRA INVOLVING RELATIVE DEMICOMPACT UNBOUNDED LINEAR OPERATORS

In this article, we introduce the concept of demicompactness with respect to a closed densely defined linear operator, as a generalization of the class of demicompact operator introduced by Petryshyn in [24] and we establish some new results in Fredholm theory. Moreover, we apply the obtained results to discuss the incidence of some perturbation results on the behavior of relative essential spectra of unbounded linear operators acting on Banach spaces. We conclude by characterizations of the relative Schechter＇s and approximate essential spectrum.

Modeling co-seismic thermal infrared brightness anomalies in petroliferous basins surrounding the North and East of the Qinghai–Tibet Plateau

Co-seismic gas leakage usually occurs on the edge of seismic faults in petroliferous basins,and it may have an impact on the local environment,such as the greenhouse effect,which can cause thermal infrared brightness anomalies.Using wavelet transform and power spectrum estimation methods,we processed brightness temperature data from the Chinese geostationary meteorological satellite FY-C/E.We report similarities between the co-seismic thermal infrared brightness(CTIB)anomalies before,during and after earthquakes that occurred at the edges of the Sichuan,Tarim,Qaidam,and Junggar basins surrounding the North and East of the Qinghai–Tibet Plateau in western China.Additionally,in each petroliferous basin,the area of a single CTIB anomaly accounted for 50%to 100%of the basin area,and the spatial distribution similarities in the CTIB anomalies existed before,during and after these earthquakes.To better interpret the similarities,we developed a basin warming effect model based on geological structures and topography.The model suggests that in a petroliferous basin with a subsurface gas reservoir,gas leakage could strengthen with the increasing stress before,during,and even after an earthquake.The accumulation of these gases,such as the greenhouse gases CH4 and CO2,results in the CTIB anomalies.In addition,we conclude that the CTIB anomalies are strengthened by the high mountains(altitude^5000 m)around the basins and the basins’independent climatic conditions.This work provides a new perspective from which to understand the CTIB anomalies in petroliferous basins surrounding the North and East of the Qinghai–Tibet Plateau.

A relation spectrum inheriting Taylor series:muscle synergy and coupling for hand

There are two famous function decomposition methods in math:the Taylor series and the Fourier series.The Fourier series developed into the Fourier spectrum,which was applied to signal decomposition and analysis.However,because the Taylor series function cannot be solved without a definite functional expression,it has rarely been used in engineering.We developed a Taylor series using our proposed dendrite net(DD),constructed a relation spectrum,and applied it to decomposition and analysis of models and systems.Specifically,knowledge of the intuitive link between muscle activity and finger movement is vital for the design of commercial prosthetic hands that do not need user pre-training.However,this link has yet to be understood due to the complexity of the human hand.In this study,the relation spectrum was applied to analyze the muscle—finger system.One single muscle actuates multiple fingers,or multiple muscles actuate one single finger simultaneously.Thus,the research was focused on muscle synergy and muscle coupling for the hand.The main contributions are twofold:(1)The findings concerning the hand contribute to the design of prosthetic hands;(2)The relation spectrum makes the online model human-readable,which unifies online performance and offline results.Code is available at https://github.com/liugang1234567/Gang-neuron.

A Fiber Tractography Study of Social-Emotional Related Fiber Tracts in Children and Adolescents with Autism Spectrum Disorder

The symptoms of autism spectrum disorder（ASD） have been hypothesized to be caused by changes in brain connectivity. From the clinical perspective, the‘‘disconnectivity＇＇ hypothesis has been used to explain characteristic impairments in ‘‘socio-emotional＇＇ function.Therefore, in this study we compared the facial emotional recognition（FER） feature and the integrity of socialemotional-related white-matter tracts between children and adolescents with high-functioning ASD（HFA） and their typically developing（TD） counterparts. The correlation between the two factors was explored to find out if impairment of the white-matter tracts is the neural basis of social-emotional disorders. Compared with the TD group,FER was significantly impaired and the fractional anisotropy value of the right cingulate fasciculus was increased in the HFA group（P ／ 0.01）. In conclusion, the FER function of children and adolescents with HFA was impaired and the microstructure of the cingulate fasciculus had abnormalities.