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

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

The 11th edition of Harrison's Principles of Internal Medicine welcomes Anthony Fauci to its editorial staff, in addition to more than 85 new contributors. While the organization of the book is similar to previous editions, major emphasis has been placed on disorders that affect multiple organ systems. Important advances in genetics, immunology, and oncology are emphasized. Many chapters of the book have been rewritten and describe major advances in internal medicine. Subjects that received only a paragraph or two of attention in previous editions are now covered in entire chapters. Among the chapters that have been extensively revised are the chapters on infections in the compromised host, on skin rashes in infections, on many of the viral infections, including cytomegalovirus and Epstein-Barr virus, on sexually transmitted diseases, on diabetes mellitus, on disorders of bone and mineral metabolism, and on lymphadenopathy and splenomegaly. The major revisions in these chapters and many

Harrison's Principles of Internal Medicine

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Convex Analysisの二,三の進展について

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Introduction to Discrete Event Systems is a comprehensive introduction to the field of discrete event systems, offering a breadth of coverage that makes the material accessible to readers of varied backgrounds. The book emphasizes a unified modeling framework that transcends specific application areas, linking the following topics in a coherent manner: language and automata theory, supervisory control, Petri net theory, Markov chains and queuing theory, discrete-event simulation, and concurrent estimation techniques. This edition includes recent research results pertaining to the diagnosis of discrete event systems, decentralized supervisory control, and interval-based timed automata and hybrid automata models.

Introduction to Discrete Event Systems

Lifetime maximization is an important optimization problem specific to Wireless Sensor Networks (WSNs) since they operate with limited energy resources which are therefore eventually depleted. This paper considers first the problem of routing in a WSN with the objective of lifetime maximization based on a simple model for battery dynamics. Specifically, we discuss the equivalence of two different formulations and solutions in the existing literature. We then revisit a related problem, the optimal allocation of a total energy amount over all nodes so as to maximize network lifetime. We prove that this is equivalent to a shortest path problem on a weighted graph and can therefore be efficiently solved. Finally, we present a more realistic model for battery dynamics, and numerically solve the lifetime maximization problem. The empirical results obtained indicate that, while a static routing policy is not expected to be optimal, such a policy is a good approximation of the optimal dynamic routing policy.

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On maximum lifetime routing in Wireless Sensor Networks

The aim of this text is to teach the student what discrete event systems (DES) are about and how they differ from "classical systems"; describe the differences between various modelling approaches; and show how to simulate DES using commercially-available software or from first principles

Discrete event systems : modeling and performance analysis

A decentralized energy-optimal control framework for connected automated vehicles at signal-free intersections

We present a modeling framework for hybrid systems intended to capture the interaction of event-driven and time-driven dynamics. This is motivated by the structure of many manufacturing environments where discrete entities (termed jobs) are processed through a network of workcenters so as to change their physical characteristics. Associated with each job is a temporal state subject to event-driven dynamics and a physical state subject to time-driven dynamics. Based on this framework, we formulate and analyze a class of optimal control problems for single-stage processes. First-order optimality conditions are derived and several properties of optimal state trajectories (sample paths) are identified which significantly simplify the task of obtaining explicit optimal control policies.

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Christos G. Cassandras

Papers

Introduction to Discrete Event Systems

On maximum lifetime routing in Wireless Sensor Networks

Discrete event systems : modeling and performance analysis

A decentralized energy-optimal control framework for connected automated vehicles at signal-free intersections

Optimal control of a class of hybrid systems