Cohen and multiple Cohen strongly summing multilinear operators

Considering the successful theory of multiple summing multilinear operators as a prototype, we introduce the classes of multiple Cohen strongly p-summing multilinear operators and polynomials. The adequacy of these classes under the viewpoint of the theory of multilinear and polynomial ideals and holomorphy types is discussed in detail.     

A fitting algorithm for real coefficient polynomial rooting

A new algorithm for computing all roots of polynomials with real coefficients is introduced. The principle behind the new algorithm is a fitting of the convolution of two subsequences onto a given polynomial coefficient sequence. This concept is used in the initial stage of the algorithm for a recursive slicing of a given polynomial into degree-2 subpolynomials from which initial root estimates are computed in closed form. This concept is further used in a post-fitting stage where the initial root estimates are refined to high numerical accuracy. A reduction of absolute root errors by a factor of 100 compared to the famous Companion matrix eigenvalue method based on the unsymmetric QR algorithm is not uncommon. Detailed computer experiments validate our claims.     

四川省市州经济发展差异的统计分析

采用因子分析研究四川省21市州之间的相关性,利用主因子计算出各个市州得分,以市州得分作为新变量进行集团排序,再将基于相对位置排序法引入到集团排序中,进而得到最终的市州分类结果,在统计分析的基础上对市州经济发展给出一些建议.     

Assessing the Calibration of High-Dimensional Ensemble Forecasts Using Rank Histograms

Any decision-making process that relies on a probabilistic forecast of future events necessarily requires a calibrated forecast. This article proposes new methods for empirically assessing forecast calibration in a multivariate setting where the probabilistic forecast is given by an ensemble of equally probable forecast scenarios. Multivariate properties are mapped to a single dimension through a prerank function and the calibration is subsequently assessed visually through a histogram of the ranks of the observation’s preranks. Average ranking assigns a prerank based on the average univariate rank while band depth ranking employs the concept of functional band depth where the centrality of the observation within the forecast ensemble is assessed. Several simulation examples and a case study of temperature forecast trajectories at Berlin Tegel Airport in Germany demonstrate that both multivariate ranking methods can successfully detect various sources of miscalibration and scale efficiently to high-dimensional settings. Supplemental material in form of computer code is available online.     

对冷聚变全原子论的进一步探讨

我在一篇论文中提出了一个冷聚变的全原子论，阐明氘原子进入钯晶体间隙位置时扩展成为一个封闭的球形全原子，其价电子完全在球内，围绕氘核运动使氘核对邻近氘核的排斥作用被屏蔽掉，使氘核易于接近而产生聚变。对离子晶体两个负氘离子相互作用是怎样引起聚变的没做详细讨论，本文将对此问题进一步进行详细讨论。     

On the Existence Of Consistent Price Systems

We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS). We use the new condition to show the existence of CPSs for certain processes that fail to have the CFS property. In particular this condition gives sufficient conditions, under which a continuous function of a process with CFS admits a CPS, while the CFS property might be lost.     

The Determination Of Sub Part-Per-Billion Levels Of Volatile Organic Compounds In Air By Pre-Concentration From Small Sample Volumes

Abstract

Trace level Volatile Organic Compounds (VOCs) in ambient air are normally determined according to EPA Method TO-14. This method describes the analysis in ambient air of 41 VOCs, ranging in boiling point from -29 to 215°C. It covers a concentration range from 0.2 to 20 parts per billion, volume/volume (ppb), and specifies sample enrichment of a 400 mL air sample on glass beads at -160°C. While this sample volume provides sub-ppb levels of VOC detection for target analytes when using a quadrupole mass spectrometer detector in SIM mode or when using GC detectors, the identification of non-target analytes may only be done in full scan mode for higher concentrations. Also with this sample volume a Nafion dryer is needed for water removal thereby lowering the recovery of polar VOCs.

Because of the very high sensitivity of the ion trap MS, relatively small air volumes (60 mL) are adequate to obtain the required or lower detection levels. An integrated air analysis system based on a GC-ion-trap MS has been investigated and is described. This system has a built-in cryogenic trap and necessary valving, internal standard gas sampling loop, and is controlled from the GC-MS workstation. The linearity, precision, and method detection levels obtainable with this system when using small volumes are reported. In addition, examples of the quantitative and qualitative analysis of ambient air samples are shown.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.