Remarks on an operator Wielandt inequality

Let $A$ be a positive operator on a Hilbert space $\mathcal{H}$ with $0<m\leq A\leq M$ and $X$ and $Y$ are two isometries on $\mathcal{H}$ such that $X^{*}Y=0$. For every 2-positive linear map $\Phi$, define $$\Gamma=\left(\Phi(X^{*}AY)\Phi(Y^{*}AY)^{-1}\Phi(Y^{*}AX)\right)^{p}\Phi(X^{*}AX)^{-p}, \, \, \, p>0.$$ We consider several upper bounds for $\frac{1}{2}|\Gamma+\Gamma^{*}|$. These bounds complement a recent result on operator Wielandt inequality.Comment: 6page

Analysis of Colored Pottery Decoration using Hidden Markov Model Directional Clustering Classification with Deep Learning

Colored pottery decoration is an important cultural artifact that carries significant imagery, symbols, and cultural connotations. This paper presented an in-depth analysis of colored pottery decoration by employing a novel approach, Hidden Markov Model Directional Clustering Classification (HMMDCC), combined with deep learning techniques. The evaluated data comprehensive dataset of colored pottery designs, representing different historical periods and cultural contexts. The imagery, symbols, and cultural connotations embedded in the designs are extracted through a combination of computer vision and image processing techniques. The HMMDCC model is then utilized to perform directional clustering, which identifies spatial relationships and patterns within the decoration elements. To enhance classification accuracy and capture intricate patterns, deep learning techniques are incorporated into the HMMDCC model. The deep learning model is trained on the dataset, enabling it to recognize and classify the imagery, symbols, and cultural connotations present in colored pottery decoration. The findings of this study shed light on the hidden meanings and cultural significance associated with colored pottery decoration. The application of the HMMDCC model with deep learning showcases its effectiveness in analyzing and interpreting complex visual data. The results contribute to a deeper understanding of the historical and cultural contexts in which colored pottery decoration emerged, providing valuable insights for archaeologists, historians, and art enthusiasts

What Role Does School Play in Helping Socioeconomically Disadvantaged Students Succeed against the Odds?

Based on the data of a large scale survey conducted by Collaborative Innovation Center of Assessment Toward Basic Education Quality at Beijing Normal University, this study examined the role of school in reducing education inequality. The results showed that schools concentrated with resilient students had higher mean socioeconomic status (SES) and SES heterogeneity, more education resources, higher teaching quality, and more positive school climate, and these factors also functioned as significant predictors of academic resilience. Provid-ing socioeconomically disadvantaged students with access to both high SES schools and enriched school resources can even the education ine-quality related to family background. In order to promote education equality, policymakers and education practitioners should take measures to reduce the degree of stratification and encourage student integration, promote equal distribution of high quality education resources among schools, enhance teachers’ ability to effectively use individualized, coop-erative and inquiry teaching methods, and build a supportive climate