By Professor Dr. Vladmir G. Makhankov, Professor Yurii P. Rybakov, Professor Valerii I. Sanyuk (auth.)

The December 1988 factor of the foreign magazine of contemporary Physics A is devoted to the reminiscence of Tony Hilton Royle Skyrme. It includes an informative account of his lifestyles through Dalitz and Aitchison's reconstruction of a conversation by way of Skyrme at the starting place of the Skyrme version. From those pages, we research that Tony Skyrme used to be born in England in December 1922. He grew up in that state in the course of a interval of accelerating fiscal and political turbulence in Europe and in other places. In 1943, after Cambridge, he joined the British conflict attempt in making the atomic bomb. He was once linked to army initiatives through the conflict years and started his profession as a tutorial theoretical physicist purely in 1946. in the course of 1946-61, he used to be linked to Cambridge, Birmingham and Harwell and was once engaged in wide-ranging investigations in nuclear physics. It was once this study which finally culminated in his reports of nonlinear box theories and his amazing proposals for the outline of the nucleon as a chiral soliton. In his speak, Skyrme defined the explanations at the back of his striking sug gestions, which while first made should have appeared extraordinary. in line with him, rules of this kind return many a long time and take place within the paintings of Sir William Thomson, who later turned Lord Kelvin. Skyrme had heard of Kelvin in his youth.

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**Example text**

18) is equal to the identity element. 4. 18) is called the Poincare fundamental or the first homotopy group. It is denoted by 7rl(P). To compute the fundamental group for any manifold P means to establish an isomorphism between 7rl (p) and the group (or any subgroup) of integers 71.. The results of calculation - established isomorphisms - tell us what arithmetic can be applied when one adds homotopy classes. , it means that homotopy classes possess the addition operation just as ordinary integer numbers.

Jp. 56) on which we focus in the subsequent discussion of the rotating Skyrmion and in quantization procedure. 5 Skyrme's Results and Conjectures Leaving a more detailed treatment of the final version of the Skyrme model for subsequent chapters, let us outline to what extent Skyrme managed to study the proposed theory by himself. The equally important aim of this section is to list the main suggestions and hypotheses of Skyrme, which were expressed in his papers {Skyrme 1961a, 1962, 1971) and became the subject of great interest among particle physicists during the 1980's.

Ut = ]I. = I~I; If I = ± sin e; ¢>o=cose. 29) In what follows we will write down formulas for dynamical quantities of the Skyrme model using both of these parametrizations. The next step is to find the form of the boundary conditions one should impose on the mesonic fields ¢>p in order to provide a description of extended objects localized in space with finite dynamical characteristics. It is obvious that these conditions should be analogous to the Eq. 30) --+ 00. 29) it is clear that corresponding boundary conditions on U and on e look like the following: U(z) --+]1; e(z) --+ 0, as Izl --+ 00.