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

Geomagnetically induced currents (GICs) have the potential to severely disrupt power grid operations, and hence their impact needs to be assessed through planning studies. This paper presents a methodology for determining the sensitivity of the GICs calculated for individual and/or groups of transformers to the assumed quasi-dc electric fields on the transmission lines that induce the GICs. Example calculations are provided for two small systems and for the North American Eastern Interconnect model. Results indicate that transformer GICs are mostly due to the electric fields on nearby transmission lines, implying localized electric field models may be appropriate for such studies.

/pdf/power-grid-sensitivity-analysis-of-geomagnetically-induced-2a21p7p9ed.pdf

Power Grid Sensitivity Analysis of Geomagnetically Induced Currents

This paper describes a user-friendly power simulation program for teaching power system operations and control. The motivation for the development of the program is to provide students with a simple and useable tool for gaining an intuitive feel for power system operations. This Microsoft Windows based program simulates power system operation over a specified time period (of typically several hours to a day). Students dynamically interact with the simulated system through various windows, including a one-line display. The use of data files and option windows allows the program to simulate a wide variety of different power systems and operating problems. Efficient programming results in a modest program size of just 450 k, allowing for easy distribution to students.

A user-friendly simulation program for teaching power system operations

The goal of achieving 20% wind power penetration by 2030 in the US has stimulated the installation of large scale wind farms in recent years, both on-shore and off-shore. Collector systems consolidate the power generated by turbine units distributed over the geographical area of the wind farm to a substation from where the generated power is transmitted to the electric grid. Design of a wind farm collector system must take into consideration the economics and reliability of operation. Most modern day large scale wind farms consist of hundreds of wind turbines and are generally electrically connected in a radial feeder cable configuration or daisy chains. While these configurations are generally accepted as convention, not much research has been done to analyze other cable layout configurations. This paper proposes a clustering based algorithm for cable layout of a large scale wind power plant. Comparison of the proposed method with the radial feeder cable configuration shows that real power losses in collector system are lowered and greater reliability is achieved with the proposed design. An economic analysis has also been done to compare the cost of generated energy associated with the proposed design and the conventional configuration.

/pdf/a-clustering-based-wind-farm-collector-system-cable-layout-p6e240xek9.pdf

A clustering based wind farm collector system cable layout design

Geomagnetically induced currents (GICs) can cause half cycle saturation of transformers and consequently affect the power grid with harmonics and reactive power losses. To effectively mitigate the negative GIC impacts in large-scale power systems, the present paper considers the problem of placing blocking devices in transformer neutrals. The placement problem of multiple blocking devices is first considered by analytically quantifying the associated reactive power losses. A linear sensitivity analysis is further provided for the case of blocking a single transformer, and it has been observed that the effects of blocking transformer neutral currents to be mostly local. This motivates us to propose the scheme that selects multiple substations to block all high voltage level transformers therein, based on a linearized approximation model. The effectiveness of such scheme has been demonstrated using both a 20-bus GIC test case and a realistically sized larger power system.

Blocking Device Placement for Mitigating the Effects of Geomagnetically Induced Currents

Distributed flexible AC transmission system (D-FACTS) devices offer many potential benefits to power system operations. This paper examines the impact of installing D-FACTS devices by studying the linear sensitivities of power system quantities such as voltage magnitude, voltage angle, bus power injections, line power flow, and real power losses with respect to line impedance. Using these linear sensitivities, nonlinear problems such as real power loss minimization and voltage control may be solved; these applications are discussed in this paper.

/pdf/some-applications-of-distributed-flexible-ac-transmission-l0endoiz6n.pdf

Thomas J. Overbye

Papers

Power Grid Sensitivity Analysis of Geomagnetically Induced Currents

A user-friendly simulation program for teaching power system operations

A clustering based wind farm collector system cable layout design

Blocking Device Placement for Mitigating the Effects of Geomagnetically Induced Currents

Some applications of Distributed Flexible AC Transmission System (D-FACTS) devices in power systems