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

A senior capstone transmission expansion planning project is presented for a large-scale synthetic grid. Parameters such as generation, load, and contingencies are incorporated in the case to create summer peak load cases over a period of seven years. The methodologies to create the load case, containing the seven year load growth projection, and the solution case, containing the proposed upgrades for each year, are presented.

Large-Scale Synthetic Grids in Classroom Planning Studies

This paper presents an overview of the development of an Energy Management Platform (EMP) research testbed for power system monitoring and control. In this work, a testbed utilizes a simulator to mimic power system operations on a synthetic network. By emulating field devices, the simulator is used to further transmit grid data over a supervisory control and data acquisition (SCADA) system to an EMS software. Finally, through the design of oneline diagrams, a node-branch layout algorithm is proposed to develop interface substation displays for controlling the power system networks being used in the testbed.

An Electric Power System Energy Management Platform (EMP) Research Testbed

Discussion of the future of the Smart Grid brings with it issues regarding the current level of distribution system visibility. Phasor Measurement Units (PMU) have been proliferating throughout the electric power grid in order to support future distribution system analysis. One type of PMU is the Frequency Disturbance Recorder (FDR); it records voltage magnitude, frequency, and phase angle at the 120 V outlet level. Previous work has introduced ways in which distribution system events can be read from this voltage data, but this paper focuses on defining similarity measures for comparing detected events. Discrete Signal Processing (DSP) techniques such as correlation and convolution can be used to determine how similar events are, even in the presence of a time delay. Euclidean distance and mean-squared error are used as similarity measurements to help confirm the correctness of the time-delay estimation. Beyond detecting positively and negatively correlated events, the similarity measures support the correlation results by determining that some events aren't correlated at all.

Event analysis of distribution system voltage data

This work is a reliability assessment of Nigeria's existing power system. A probabilistic framework involving Markov reliability models is used to evaluate the ability of available generation to serve Nigeria's existing power demand. Resource planning indices, such as reserve margin and loss of load probability (LOLP), were evaluated. This study also investigates the sensitivity of LOLP to three base load levels (2900, 3100, 3225 MW) and unit availability assumptions (65%, 80%, and 95%). Results show that loss of load probability is extremely sensitive to generation availability. For the 2900 MW base load case, LOLP is reduced from 83.26% to 20.50% moving from 65% to 95% unit availability. Conclusively, in efforts to improve Nigeria's overall system reliability, it behooves resource planners to focus on improving the unit availability levels of existing generation even as new reliable power resources are installed. Such an energy development strategy is likely to be more effective at improving Nigeria's ability to serve its ever-increasing load demand. This work can be improved by considering transmission line effects and evaluating the economic value of reliability in Nigeria.

A resource adequacy assessment of Nigeria's power system

Geomagnetic disturbances (GMDs) are the result of coronal mass ejections (CMEs) from the sun. CMEs, such as solar flares, alter the magnetic and electric field of the earth. These changes induce DC voltage sources superimposed on transmission lines. The voltages result in the introduction of quasi-DC geomagnetically induced currents (GICs) to the AC synchronous power grid. These currents can cause half cycle saturation of transformers, harmonics, reactive power losses, and in extreme situations, widespread power outages. In this work, a planning-based GMD mitigation strategy is developed for large power systems. GIC blocking devices and system topology are leveraged in the design of strategies and systems to maintain preferable system operations despite a GMD. Simulation cases based on GIC blocking device installation and islanding plans will be used to create a strategy to minimize the effects of GMDs on the power grid.

Thomas J. Overbye

Papers

Large-Scale Synthetic Grids in Classroom Planning Studies

An Electric Power System Energy Management Platform (EMP) Research Testbed

Event analysis of distribution system voltage data

A resource adequacy assessment of Nigeria's power system

Undergraduate Research on Design Considerations for a GMD Mitigation System