There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

From the Publisher: 
The accessible presentation of this book gives both a general view of the entire computer vision enterprise and also offers sufficient detail to be able to build useful applications. Users learn techniques that have proven to be useful by first-hand experience and a wide range of mathematical methods. A CD-ROM with every copy of the text contains source code for programming practice, color images, and illustrative movies. Comprehensive and up-to-date, this book includes essential topics that either reflect practical significance or are of theoretical importance. Topics are discussed in substantial and increasing depth. Application surveys describe numerous important application areas such as image based rendering and digital libraries. Many important algorithms broken down and illustrated in pseudo code. Appropriate for use by engineers as a comprehensive reference to the computer vision enterprise.

Computer vision : a modern approach = 计算机视觉 : 一种现代的方法

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

미국의 “전국 수학 교사 협의회”(National Council of Teachers of Mathematics, NCTM)는 1989년부터 〈학교 수학의 교육과정과 평가 규준〉(1989), 〈수학 가르침(교수)의 전문성 규준〉(1991), 〈학교 수학의 평가(시험) 규준〉(NCTM, 1995), 〈학교 수학의 원리와 규준〉(2000)을 출판하여 미국의 수학 교육 의 전망(목표, 나아갈 길)과 규준(실행 지침)을 제시하였다. 수학 교사들로 구성된 미국의 NCTM은 학생, 학부모, 학교 행정가 등 많은 사람들과 힘을 합하여 모든 학생들에게 수준 높은 수학 교육을 받을 수 있는 여건(환경, 기회)을 조성하는 데 구심점의 역할을 하였다. 한편 많은 관련 단체들은 여러 배경과 능력을 가진 학생들이 전문성을 지닌 교사(특수 교사를 일컫는 밀이 아니다. 수학 교과를 이해하고 수학의 전문성과 특수성을 가르칠 수 있는 일반 교사를 일컫는 말이다.)로부터 미래를 대비해 평등하고, 진취적이며, 지원이 잘 이루어지고, 공학 도구(IT)가 잘 갖춰진 환경에서 중요한 수학적 아이디어를 이해하면서 학습할 수 있는 수학 교실(미국에서는 우리나라처럼 수학 교사가 수학 시간에 학생의 방(교실: Homeroom)에 찾아가지 않고 학생들이 선생의 방(수학 교실: Classroom)을 찾아온다. 전형적인 수학 교실의 사진은 2쪽에 나와 있다.)을 만들기 위해 함께 힘썼다. NCTM에서 출간한 여러 규준들은 우리나라의 제6차와 제7차 교육과정에도 큰 영향을 미쳤다. 이 글에서는 NCTM(2000)에서 제시한 학습 원리를 간단히 살펴본 다음 이를 중심으로 현재 미국 수학 교육의 교수ㆍ학습 이론의 동향을 살펴본다.

미국 NCTM의 Principles and Standards for School Mathematics에 나타난 수학과 교수,학습의 이론

Power system visualization

This paper presents experimental results associated with human-factors aspects of utilizing color contours to visualize electric power system bus voltage magnitude information. Participants were divided into three groups: the first group saw only one-line numeric data, the second only one-line contour data, while the third saw both. The purpose of the experiment was to determine how quickly participants could both acknowledge low voltage violations and perform corrective control actions. Results indicated the contour-only visualization resulted in the quickest voltage violation acknowledgments, while the numeric-data-only visualization resulted in the quickest solution times. Testing was done using a modified version of the IEEE 118 bus system.

Human factors aspects of power system voltage contour visualizations

At the residential level, devices which are in place now and expected in the future have the ability to provide reactive power support. Inverters which connect distributed generation such as solar panels and pluggable hybrid electric vehicles (PHEVs) to the grid are an example. Such devices are not currently utilized by the power system. We investigate the integration of these end-user reactive-power-capable devices to provide voltage support to the grid via a secure communications infrastructure. We show how to determine effective locations in the transmission system and how to control reactive power resources at those locations. We also discuss how to determine reactive support groups which parallel the regions of the secure communications architecture that is presented. Ultimately, our goal is to present how the Smart Grid can allow the utilization of available end-user devices as a resource to mitigate power system problems such as voltage collapse.

https://tcipg.org/sites/default/files/papers/Rogers_IEEE_Smart_Grid.pdf

Smart-Grid -enabled load and distributed generation as a reactive resource

All players in the US electricity industry must understand how specific generation decisions, wheeling arrangements, and legislative initiatives affect system operations. This article features PowerWorld, a comprehensive power system simulation package developed to help meet this need. The package is designed for the many new players in the power industry who will never operate an actual system but who must have a basic understanding of its operations. The package, which runs in the Microsoft Windows environment, is user friendly, interactive, and menu driven. It effectively uses visualization techniques to present the basics of power system operations and control simply, yet also with a level of detail to accurately model large-scale systems realistically and with the appropriate level of fidelity. The package has been demonstrated to policy makers, legislative analysts, small and large utilities, and regulatory decision makers both nationally and internationally. It has been found to be a very effective tool for communicating the many technical and economic impacts of third-party access.

/pdf/visualizing-power-system-operations-in-an-open-market-53c3c23onc.pdf

Visualizing power system operations in an open market

Despite the current adequacy of the generation and transmission system in Illinois, there is concern that the uncertainties of electricity restructuring warrant a more detailed analysis to determine if there might be pitfalls that have not been identified under current conditions. The problems experienced elsewhere in the country emphasize the need for an evaluation of how Illinois might fare under a restructured electricity market. The Illinois Commerce Commission (ICC) commissioned this study to be undertaken as a joint effort by the University of Illinois at Urbana-Champaign and Argonne National Laboratory to evaluate the Illinois situation in the 2007 period when restructuring is scheduled to be fully implemented in the State. The purpose of this study is to make an initial determination if the transmission system in Illinois and the surrounding region would be able to support a competitive electricity market, would allow for effective competition to keep prices in check, and would allow for new market participants to effectively compete for market share. The study seeks to identify conditions that could reasonably be expected to occur that would enable a company to exercise market power in one or more portions of the State and thereby create undue pressure on themore » prices charged to customers and/or inhibit new market participants from entering the market. The term 'market power' has many different definitions, and there is no universal agreement on how to measure it. For the purposes of this study, the term is defined as the ability to raise prices and increase profitability by unilateral action. A more complete definition is provided later. With this definition, the central question of this analysis becomes: 'Can a company, acting on its own, raise electricity prices and increase its profits?' It should be noted that the intent of the study is not to predict whether or not such market power would be exercised by any company. Rather, it is designed to determine if a set of reasonably expected conditions could allow any company to do so. It should also be emphasized that this study is not intended to be a comprehensive evaluation of the electric power system in the State. Rather, it is intended to identify some issues that may impact the effective functioning of a competitive market.« less

/pdf/evaluating-the-potential-impact-of-transmission-constraints-ol4mwwb7r3.pdf

Thomas J. Overbye

Papers

Power system visualization

Human factors aspects of power system voltage contour visualizations

Smart-Grid -enabled load and distributed generation as a reactive resource

Visualizing power system operations in an open market

Evaluating the potential impact of transmission constraints on the operation of a competitive electricity market in Illinois.