半直线上独立随机环境中的随机游动的常返性

本文主要讨论半直线上随机环境中随机游动的常返性与非常返性,并进一步研究了常返性中的正常返性和零常返性。     

Evaluation of Geometric Attractor Structure and Recurrence Analysis in Professional Dancers

Background: Human motor systems contain nonlinear features. The purpose of this study was to evaluate the geometric structure of attractors and analyze recurrence in two different pirouettes (jazz and classic) performed by 15 professional dancers. Methods: The kinematics of the body’s center of mass (CoM) and knee of the supporting leg (LKNE) during the pirouette were measured using the Vicon system. A time series of selected points were resampled, normalized, and randomly reordered. Then, every second time series was flipped to be combined with other time series and make a long time series out of the repetitions of a single task. The attractors were reconstructed, and the convex hull volumes (CHV) were counted for the CoM and LKNE for each pirouette in each direction. Recurrence quantification analysis (RQA) was used to extract additional information. Results: The CHVs calculated for the LKNE were significantly lower for the jazz pirouette. All RQA measures had the highest values for LKNE along the mediolateral axis for the jazz pirouette. This result underscores the high determinism, high motion recurrence, and complexity of this maneuver. Conclusions: The findings offer new insight into the evaluation of the approximation of homogeneity in motion control. A high determinism indicates a highly stable and predictive motion trajectory.     

Anti-inflammatory catecholic chitosan hydrogel for rapid surgical trauma healing and subsequent prevention of tumor recurrence

Although occupying pillar position in clinical cancer treatments,surgery itself and surgical trauma would elicit series of local/systemic inflammation-related responses that resulted in high rate of tumor recurrence.Herein,chitosan with conjugated gallic acid(CSG) molecules were coordinated with Fe³⁺ to form CSG/Fe³⁺ hydrogel for filling the tumo r-resected cavity with considerable wet-adhesion ability and anti-inflammatory performance.With the assistance of doxorubicin hyd...     

p阶递推式的解公式之注

以文献[1]为基础，我们得到p阶循环方程式之解的一个间明公式，这不论是在理论上，还是实践方面，皆有一定的意义．     

A view on multiple recurrence

In this note we present a proof of multiple recurrence for ergodic systems (and thereby of Szemerédi’s theorem) being a mixture of three known proofs. It is based on a conditional version of the Jacobs–de Leeuw–Glicksberg decomposition and properties of the Gowers–Host–Kra uniformity seminorms.     

A simple algorithm for expanding a power series as a continued fraction

I present and discuss an extremely simple algorithm for expanding a formal power series as a continued fraction. This algorithm, which goes back to Euler (1746) and Viscovatov (1805), deserves to be better known. I also discuss the connection of this algorithm with the work of Gauss (1812), Stieltjes (1889), Rogers (1907) and Ramanujan, and a combinatorial interpretation based on the work of Flajolet (1980).     

Transience of symmetric nonlocal Dirichlet forms

We establish transience criteria for symmetric nonlocal Dirichlet forms on $L^2({\mathbb{R}}^d;\mathrm{d}x)$ in terms of the coefficient growth rates at infinity. Applying these criteria, we find a necessary and sufficient condition for recurrence of Dirichlet forms of symmetric stable-like with unbounded/degenerate coefficients. This condition indicates that both of the coefficient growth rates of small and big jump parts affect the sample path properties of the associated symmetric jump processes.     

分治算法的两种思路和形式

分治算法是程序设计中常用算法之一,是用划分子问题的方法,由较小尺寸的问题的可解导致原问题的解决。介绍了分治算法的两种形式,分析和探讨了它们的不同思路、不同特点和适用场合。