Lowering topological entropy over subsets revisited

Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\subseteq X$, respectively. $(X, T)$ is called D-{\it lowerable} (resp. {\it lowerable}) if for each $0\le h\le h (T, X)$ there is a subset (resp. closed subset) $K_h$ with $h^B (T, K_h)= h$ (resp. $h (T, K_h)= h$); is called D-{\it hereditarily lowerable} (resp. {\it hereditarily lowerable}) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable). In this paper it is proved that each topological dynamical system is not only lowerable but also D-lowerable, and each asymptotically $h$-expansive system is D-hereditarily lowerable. A minimal system which is lowerable and not hereditarily lowerable is demonstrated.Comment: All comments are welcome. Transactions of the American Mathematical Society, to appea

Local entropy theory for a countable discrete amenable group action

In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation between these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for finite Borel covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool

Deep Learning Based on Orthogonal Approximate Message Passing for CP-Free OFDM

Channel estimation and signal detection are very challenging for an orthogonal frequency division multiplexing (OFDM) system without cyclic prefix (CP). In this article, deep learning based on orthogonal approximate message passing (DL-OAMP) is used to address these problems. The DL-OAMP receiver includes a channel estimation neural network (CE-Net) and a signal detection neural network based on OAMP, called OAMP-Net. The CE-Net is initialized by the least square channel estimation algorithm and refined by minimum mean-squared error (MMSE) neural network. The OAMP-Net is established by unfolding the iterative OAMP algorithm and adding some trainable parameters to improve the detection performance. The DL-OAMP receiver is with low complexity and can estimate time-varying channels with only a single training. Simulation results demonstrate that the bit-error rate (BER) of the proposed scheme is lower than those of competitive algorithms for high-order modulation.Comment: 5 pages, 4 figures, updated manuscript, International Conference on Acoustics, Speech and Signal Processing (ICASSP 2019). arXiv admin note: substantial text overlap with arXiv:1903.0476

Exploration on Intelligent Teaching of Probability and Statistics in Universities

Starting from the concept of Intelligent Teaching, this paper briefly introduces the meaning of intelligent classroom, then gives the description about tools of Intelligent teaching. Taking Probability and Statistics as an example, this paper explores the mild Intelligent teaching with Mosotech as the tool of Intelligent teaching which can be used before, during and after class under the Intelligent teaching mode. Keywords: Intelligent teaching, Intelligent teaching tools, Probability and statistics DOI: 10.7176/JEP/12-27-03 Publication date:September 30th 202

A Survey and Study on the Current Status of Mathematics Study Habits of Rural Junior High School Students in China

The research is supported by the research project of higher education reform in Jiangsu Province. Nos. 2019JSJG257, 2017JSJG212, Special research project on Rural Education in Yancheng City. No. XCZX21090, and Yancheng educational science planning project in 2021. No. 2021-L-136. (Sponsoring information) Abstract Based on the relevant theories, the article adopts literature research, questionnaire survey, and interview records to first analyze and summarize the research related to " mathematics study habits" and to define and classify the concepts related to "mathematics study habits." Take rural junior high school students in a school in China as the target group, and analyze the current situation of mathematics study habits of rural junior high school students in this school through a questionnaire survey based on the results. Furthermore, through personal interviews with rural junior high school students, teachers, and parents in the region, we completed the analysis of the factors that contribute to the formation of good mathematics study habits in rural junior high school students from the perspectives of students, teachers, and parents. Finally, combined with the current situation and influencing factors of mathematics learning habits of rural junior high school students in the region, corresponding countermeasures are proposed for the cultivation of good mathematical learning habits from the three perspectives of students, teachers and parents. Keywords: Rural junior high school students, Mathematics study habits, Influence factors, Habit development measures DOI: 10.7176/JEP/13-29-04 Publication date:October 31st 202

An Empirical Research of the Network Public Opinion Impact on the Information Openness of Government Affairs – Take “Hide and Seek” and “Deng Yujiao” Events for Example

The influence network public opinion on the information openness of government affairs is studied after comparing the events of hide-and-seek and Deng Yujiao . The linear dependence relationship exists between variation of information publicity about government affairs and the total number of the network public opinion, moreover, variation of information publicity about government affairs and the ratio that negative comments in total number of the network public opinion presences linear relation. Both total number and negative comment ratio play an improving role in the process of e-government publicly: total number and degree of e-government information openness exists stable positive correlation, while the positive correlation relationship between negative comments ratio and e-government information openness is instability