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A Sobolev gradient of a real-valued functional on a Hilbert space is a gradient of that functional taken relative to an underlying Sobolev norm. This book shows how descent methods using such gradients allow a unified treatment of a wide variety of problems in differential equations. For discrete versions of partial differential equations, corresponding Sobolev gradients are seen to be vastly more efficient than ordinary gradients. In fact, descent methods with these gradients generally scale linearly with the number of grid points, in sharp contrast with the use of ordinary gradients....

This text consists of a sequence of problems which develop a variety of aspects in the field of semigroupsof operators. Many of the problems are not found easily in other books. Written in the Socratic/Moore method, this is a problem book without the answers presented. To get the most out of the content requireshigh motivation from the reader to work out the exercises.The reader isgiven the opportunity to discoverimportant developments of the subject and to quickly arrive at the point of independent research.The compactness of the volume and the reputation of the author lends this consider...

In Hawaii, aumakua is a honored hawaiian spirit ancestor who might assume many forms, including a raven. Many years ago ravens were predominantly found on the Big Island of Hawaii. For unknown reasons they began to die off. The survivors were taken into captivity and are still, to this day, being hand raised so we can continue to enjoy these intelligent, vocal, spiritual, and beautiful black birds. Ravens are known as great imitators of sounds including the human voice. They are spirit guides who aid the deceased. Hawaiian legend says when someone dies they are taken by the sacred raven to...

With the development of Very-Deep Sub-Micron technologies, process variability is becoming increasingly important and is a very important issue in the design of complex circuits. Process variability is the statistical variation of process parameters, meaning that these parameters do not have always the same value, but become a random variable, with a given mean value and standard deviation. This effect can lead to several issues in digital circuit design.

The logical consequence of this parameter variation is that circuit characteristics, as delay and power, also become random...