This monograph deals with random forests and aims to show that, despite the outward simplicity of the forest graph design, the problems emerging in relation to the phenomenon are challenging, and their solution often requires subtle mathematical methods. The book focuses on forests formed by simply generated trees. While the notion of the simply generated family of trees covers many known tree classes, this approach to the study of random forests gives a chance to obtain results for various forest types in a uniform way. The main objective of the book is to provide the full description of the limit behaviour of the random forest's most important characteristics: maximum tree size and number of trees of a given size and height. The main probability methods used in the book are the generalized allocation scheme and methods of the branching process theory. This monograph should be of value and interest to researchers in probabilistic methods and discrete mathematics.

Although it took some time to establish the word, photonics is both widely accepted and used throughout the world and a major area of activity concerns nonlinear materials. In these the nonlinearity mainly arises from second-order or third-order nonlinear optical processes. A restriction is that second-order processes only occur in media that do not possess a centre of symmetry. Optical fibres, on the other hand, being made of silica glass, created by fusing SiO molecules, are made of material with a centre of z symmetry, so the bulk of all processes are governed by third-order nonlinearity. Indeed, optical fibre nonlinearities have been extensively studied for the last thirty years and can be truly hailed as a success story of nonlinear optics. In fact, the fabrication ofsuch fibres, and the exploitation oftheir nonlinearity, is in an advanced stage - not least being their capacity to sustain envelope solitons. What then ofsecond-order nonlinearity? This is also well-known for its connection to second-harmonic generation. It is an immediate concern, however, to understand how waves can mix and conserve both energy and momentum ofthe photons involved. The problem is that the wave vectors cannot be made to match without a great deal of effort, or at least some clever arrangement has to be made - a special geometry, or crystal arrangement. The whole business is called phase matching and an inspection ofthe state-of-the-art today, reveals the subject to be in an advanced state."

It's time for a savior... In a land that has long been occupied and oppressed by foreign dictators, the time for heroes is ripe, it is time for legends to arise and free their country from tyranny. Two adolescent teenagers accustomed to the laid back life of their small and peaceful village of Pavanti where little excitement happens, is about to change. An ensuing attack by an expeditionary force from the main Rakirian army turns their tranquil village into a smoldering ruin and throws the boys into opposite ends of their world, which is suffering under the yoke of oppression. Meanwhile, an evil is approaching that threatens to destroy their world, to face it they must have the courage, to fight it they must have brawn, and to defeat it they must have wisdom. Aided by a beautiful foreign princess and a wise peasant girl, the youths from Pavanti must rise and incite revolt.