Dark Energy with Phantom Crossing and the H0 Tension

We investigate the possibility of phantom crossing in the dark energy sector and the solution for the Hubble tension between early and late universe observations. We use robust combinations of different cosmological observations, namely the Cosmic Microwave Background (CMB), local measurement of Hubble constant (H0), Baryon Acoustic Oscillation (BAO) and SnIa for this purpose. For a combination of CMB+BAO data that is related to early universe physics, phantom crossing in the dark energy sector was confirmed at a 95% confidence level and we obtained the constraint H0=71.0−3.8+2.9 km/s/Mpc at a 68% confidence level, which is in perfect agreement with the local measurement by Riess et al. We show that constraints from different combinations of data are consistent with each other and all of them are consistent with phantom crossing in the dark energy sector. For the combination of all data considered, we obtained the constraint H0=70.25±0.78 km/s/Mpc at a 68% confidence level and the phantom crossing happening at the scale factor am=0.851−0.031+0.048 at a 68% confidence level.     

von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

“普世价值”思潮对大学生的影响及对策

以民主、自由、人权为核心的“普世价值”思潮具有极强的迷惑性,论述了其对当代大学生的价值观念、政治认同所产生的不可忽视的影响。提出高校思想政治教育工作者必须准确把握“普世价值”思潮的内容和实质,批判其理论根基和价值基础,坚持“疏”“导”结合,强化社会主义核心价值观教育,不断提高大学生抵制错误思潮的能力。     

周秦时期体育价值之嬗变

剖析了周秦时期的社会制度及其现象。探讨了东方文化背景下的体育内容与形式在古代社会中的价值，以及个人自我实现价值，认为：体育价值的社会性是推动体育发展的原动力；体育价值的个人自我需要是推动体育发展的辅动力。     

自我价值观与集体主义

马克思主义自我价值观,强调人的自我实现是历史的、社会的. 只有把自我实现与社会发展统一起来,才能实现自我、完善自我. 同时,实现个人的自我价值离不开集体和社会. 只有在集体中,个人才能获得全面发展其才能的手段,才可能有个人的自由.     

On the distribution singular values of Toeplitz matrices

We prove a second order formula concerning distribution of singular values of Toeplitz matrices in some cases when conditions of the H. Widom Theorem are not satisfied.

     

Extremes of deterministic sub‐sampled moving averages with heavy‐tailed innovations

Let {X_k}_k?1 be a strictly stationary time series. For a strictly increasing sampling function g:?→? define Y_k=X_g(k) as the deterministic sub‐sampled time series. In this paper, the extreme value theory of {Y_k} is studied when X_k has representation as a moving average driven by heavy‐tailed innovations. Under mild conditions, convergence results for a sequence of point processes based on {Y_k} are proved and extremal properties of the deterministic sub‐sampled time series are derived. In particular, we obtain the limiting distribution of the maximum and the corresponding extremal index. Copyright © 2003 John Wiley & Sons, Ltd.     

用VC++.NET编写鼠标交互式绘图程序

主要介绍了在面向对象的VC .NET语言环境下,通过使用WM_LBUTTONDOWN, WM_MOUSEMOVE, WM_LBUTTONUP等鼠标事件消息,采用橡皮条绘图法,编写一个鼠标交互式绘图程序.该程序可实现绘制随机的平面图形,也可通过鼠标的拖动画出大小不同的圆,椭圆,矩形,直线等平面图形.     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.