测量圆盘转动惯量产生误差的曲线研究

结合三线摆实验的基本过程,进行实验数据的采集。利用投影法来测量圆盘的转角大小,借助于matlab的cftool工具箱,对数据进行曲线拟合,对测出来的二组数据拟合,得到转角与百分差曲线图。通过误差的大小比较,得出圆盘转动惯量测量值与理论值的百分差随转角变化最接近于三次曲线。     

An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD

We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd.     

A fourth-order approximate projection method for the incompressible Navier–Stokes equations on locally-refined periodic domains

In this follow-up of our previous work [30], the author proposes a high-order semi-implicit method for numerically solving the incompressible Navier–Stokes equations on locally-refined periodic domains. Fourth-order finite-volume stencils are employed for spatially discretizing various operators in the context of structured adaptive mesh refinement (AMR). Time integration adopts a fourth-order, semi-implicit, additive Runge–Kutta method to treat the non-stiff convection term explicitly and the stiff diffusion term implicitly. The divergence-free condition is fulfilled by an approximate projection operator. Altogether, these components yield a simple algorithm for simulating incompressible viscous flows on periodic domains with fourth-order accuracies both in time and in space. Results of numerical tests show that the proposed method is superior to previous second-order methods in terms of accuracy and efficiency. A major contribution of this work is the analysis of a fourth-order approximate projection operator.     

Concurrent multiresponse non-linear screening: Robust profiling of webpage performance

Profiling engineered data with robust mining methods continues attracting attention in knowledge engineering systems. The purpose of this article is to propose a simple technique that deals with non-linear multi-factorial multi-characteristic screening suitable for knowledge discovery studies. The method is designed to proactively seek and quantify significant information content in engineered mini-datasets. This is achieved by deploying replicated fractional-factorial sampling schemes. Compiled multi-response data are converted to a single master-response effectuated by a series of distribution-free transformations and multi-compressed data fusions. The resulting amalgamated master response is deciphered by non-linear multi-factorial stealth stochastics intended for saturated schemes. The stealth properties of our method target processing datasets which might be overwhelmed by a lack of knowledge about the nature of reference distributions at play. Stealth features are triggered to overcome restrictions regarding the data normality conformance, the effect sparsity assumption and the inherent collapse of the ‘unexplainable error’ connotation in saturated arrays. The technique is showcased by profiling four ordinary controlling factors that influence webpage content performance by collecting data from a commercial browser monitoring service on a large scale web host. The examined effects are: (1) the number of Cascading Style Sheets files, (2) the number of JavaScript files, (3) the number of Image files, and (4) the Domain Name System Aliasing. The webpage performance level was screened against three popular characteristics: (1) the time to first visual, (2) the total loading time, and (3) the customer satisfaction. Our robust multi-response data mining technique is elucidated for a ten-replicate run study dictated by an L₉(3⁴) orthogonal array scheme where any uncontrolled noise embedded contribution has not been necessarily excluded.     

Corrigendum to: on the inheritance of the strongly π-extending property

In this corrigendum, we provide correct versions of Theorem 2.8 and Corollary 3.2, retract two consequences of the previous form of the Theorem 2.8. To this end, the main results of the article remain after the aforementioned changes.     

An optimal perturbation bound

Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well.     

用于考察外源添加剂对卷烟常规烟气指标影响的样品制备因子筛选

为筛选用于考察外源添加剂对卷烟常规烟气指标影响的样品制备关键控制因子,采用L_8(2~7)正交试验设计进行香兰素及乙基麦芽酚的添加实验.卷烟常规烟气指标变化数值通过极差分析、方差分析,结果显示:参比卷烟种类是影响卷烟烟气总粒相物、焦油、水分的高度显著因子,就试验采用的1R5F和3R4F参比卷烟而言,添加剂在高焦油3R4F卷烟中对常规烟气指标的影响比其在低焦油1R5F卷烟中的影响大;添加剂种类与浓度的交互作用不仅对卷烟烟气总粒相物有高度显著影响,而且对总粒相物中的水分也有显著影响;因此,规范样品制备,可减少误差、保证后续外源添加剂加入对卷烟常规烟气指标影响评价结果和推断的可靠性及科学性.     

关于全国大学生数学竞赛决赛试题的解析与思考

本文对二道全国大学生数学竞赛决赛试题(数学类)给予了诠释与解析.     

A multivariate evolutionary credibility model for mortality improvement rates

The present paper proposes an evolutionary credibility model that describes the joint dynamics of mortality through time in several populations. Instead of modeling the mortality rate levels, the time series of population-specific mortality rate changes, or mortality improvement rates are considered and expressed in terms of correlated time factors, up to an error term. Dynamic random effects ensure the necessary smoothing across time, as well as the learning effect. They also serve to stabilize successive mortality projection outputs, avoiding dramatic changes from one year to the next. Statistical inference is based on maximum likelihood, properly recognizing the random, hidden nature of underlying time factors. Empirical illustrations demonstrate the practical interest of the approach proposed in the present paper.