The notion of a ?xed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of ?xed point theory have been an increasing focus of interest over the last century. These topological methods of ?xed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the ?xed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a ?xed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological ?xed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of ?xed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological ?xed and periodic point theory.
Table Talk was the title Pushkin gave, following the example of William Hazlitt or Samuel Taylor Coleridge, to the collection of historical anecdotes jotted down in the years 1830-1836. Pushkin had in his library the T able Talk of both Hazlitt and Coleridge. The question which book prompted his own title has been much discussed. There can be no doubt that Coleridge occupies a very important position in the list of literary sources which Puskhin utilized. It is curious that in the fall of 1830 at Boldino, hence at the period of his greatest literary activity, when he composed a number of his most splendid masterpieces, Puskhin had Coleridge's works with him; not only had his works, but read them anew. Among the Boldino master pieces was also, as we know, the famous "little tragedy" Mozart and Salieri, of which the ultimate psychological-moral peripeteia revolves about Mozart's remark that "genius and crime are two incompati ble things"--"geny i zlodeystvo dve veschi nesovmestnye ..." When I looked through Coleridge's Table Talk I was struck with the following observation, under the date of the 29th of August, 1827: "genius may co-exist with wildness, idleness, folly, even with crime: but not long, believe me, with selfishness, and the indulgence of an envious disposition. Envy is kdkistos kai dikai6tatos the6s, as I once saw expressed some where in a page of Stobaeus: it dwarfs and withers its worshippers.
The book is devoted to intelligent design of structures as a novel kind of designing based on computational intelligence. The proposed methodology based on computational intelligence has some heuristic and learning attributes typical for natural intelligence. Computer models of the structures are built on the base of the finite element method (FEM), the boundary element method (BEM) or coupling of FEM and BEM. The short description of possible discrete models of structures using these methods is included in the Chapter 2. Various kinds of intelligent approaches using sequential, parallel, distributed, fuzzy and hybrid evolutionary, immune and particle swarm algorithms and neural computing are presented in Chapter 3. Different kinds of optimization such as shape, topology, size and material optimization for structures under static and dynamical mechanical and thermo-mechanical loadings, structures with cracks and composite structures are considered in Chapter 4. Multi-objective optimization for coupled problems is also taken into account. Several numerical examples illustrating these kinds of optimization are presented for 2-D (plane-stress or plane-strain, plates, shells) as well as 3-D structures. Chapter 5 is devoted to special problems related to solving inverse problems in which boundary conditions, defects such as voids or cracks and material characteristics, are unknown. Closing comments summarizing the book are presented in Chapter 6.
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