A colimit of traces of reflection groups

Li-Nadler proposed a conjecture about traces of Hecke categories, which implies the semistable part of the Betti Geometric Langlands Conjecture of Ben-Zvi-Nadler in genus 1. We prove a Weyl group analogue of this conjecture. Our theorem holds in the natural generality of reflection groups in Euclidean or hyperbolic space.Comment: 5 page

Graded character sheaves, HOMFLY-PT homology, and Hilbert schemes of points on C2\mathbb{C}^2

Using a geometric argument building on our new theory of graded sheaves, we compute the categorical trace and Drinfel'd center of the (graded) finite Hecke category $\mathsf{H}_W^\mathsf{gr} = \mathsf{Ch}^b(\mathsf{SBim}_W)$ in terms of the category of (graded) unipotent character sheaves, upgrading results of Ben-Zvi-Nadler and Bezrukavninov-Finkelberg-Ostrik. In type $A$, we relate the categorical trace to the category of $2$-periodic coherent sheaves on the Hilbert schemes $\mathsf{Hilb}_n(\mathbb{C}^2)$ of points on $\mathbb{C}^2$ (equivariant with respect to the natural $\mathbb{C}^* \times \mathbb{C}^*$ action), yielding a proof of a conjecture of Gorsky-Negut-Rasmussen which relates HOMFLY-PT link homology and the spaces of global sections of certain coherent sheaves on $\mathsf{Hilb}_n(\mathbb{C}^2)$. As an important computational input, we also establish a conjecture of Gorsky-Hogancamp-Wedrich on the formality of the Hochschild homology of $\mathsf{H}_W^\mathsf{gr}$

Producing a Standard Dataset of Speed Climbing Training Videos Using Deep Learning Techniques

This dissertation presents a methodology for recording speed climbing training sessions with multiple cameras and annotating the videos with relevant data, including body position, hand and foot placement, and timing. The annotated data is then analyzed using deep learning techniques to create a standard dataset of speed climbing training videos. The results demonstrate the potential of the new dataset for improving speed climbing training and research, including identifying areas for improvement, creating personalized training plans, and analyzing the effects of different training methods.The findings will also be applied to the training process of the Jiangxi climbing team through further empirical research to test the findings and further explore the feasibility of this study.Comment: 2023 3rd International Conference on Innovative Talents Training and Sustainable Developmen

A study on calculation method for mechanical impedance of air spring

This paper proposes an approximate analytic method of obtaining the mechanical impedance of air spring. The sound pressure distribution in cylindrical air spring is calculated based on the linear air wave theory. The influences of different boundary conditions on the acoustic pressure field distribution in cylindrical air spring are analysed. A 1-order ordinary differential matrix equation for the state vector of revolutionary shells under internal pressure is derived based on the non-moment theory of elastic thin shell. Referring to the transfer matrix method, a kind of expanded homogeneous capacity high precision integration method is introduced to solve the non-homogeneous matrix differential equation. Combined the solved stress field of shell with the calculated sound pressure field in air spring under the displacement harmonic excitation, the approximate analytical expression of the input and transfer mechanical impedance for the air spring can be achieved. The numerical simulation with the Comsol Multiphysics software verifies the correctness of theoretical analysis result

E xperimental teaching reform of digital electronic technology course in local colleges and universities under the construction of new engineering

The proposal of “new engineering” is to guide colleges and universities to set up and build engineering disciplines and specialties that face the future development, meet the needs of industry and serve the national development strategy, and cultivate a group of innovative and composite excellent engineering talents. Based on the background of the construction of “new engineering”, the teaching reform of engineering experiment courses in local colleges and universities has been constantly promoted, which helps the construction of “new engineering” from the aspects of experiment content and experimental teaching methods, and helps students develop the ability of innovation and entrepreneurship and interdisciplinary integration. Taking the digital electronic technology course of local colleges and universities as an example, this paper discusses the experimental teaching reform of digital electronic technology course under the background of new engineering construction, and puts forward several teaching reform strategies, hoping to provide some eff ective ideas for promoting the subject construction and experimental teaching reform of local colleges and universities

An Overview of Moving Object Trajectory Compression Algorithms

Compression technology is an efficient way to reserve useful and valuable data as well as remove redundant and inessential data from datasets. With the development of RFID and GPS devices, more and more moving objects can be traced and their trajectories can be recorded. However, the exponential increase in the amount of such trajectory data has caused a series of problems in the storage, processing, and analysis of data. Therefore, moving object trajectory compression undoubtedly becomes one of the hotspots in moving object data mining. To provide an overview, we survey and summarize the development and trend of moving object compression and analyze typical moving object compression algorithms presented in recent years. In this paper, we firstly summarize the strategies and implementation processes of classical moving object compression algorithms. Secondly, the related definitions about moving objects and their trajectories are discussed. Thirdly, the validation criteria are introduced for evaluating the performance and efficiency of compression algorithms. Finally, some application scenarios are also summarized to point out the potential application in the future. It is hoped that this research will serve as the steppingstone for those interested in advancing moving objects mining