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8 (1962), 24433. [37] R. Thorn, Ensembles et morphismes stratifies, Bull. Amer. Math. , 75 (1969) 240-284. [38] A. N. , 37 (1976), 253-262. [39] H. Whitney, Tangents to an analytic variety, Ann. , (2) 81 (1964). 4966549. [40] 0. Zariski, Algebraic surfaces, Erg. math. 61, Springer, 1971. 1 8) Thermodynamics A. Basic Concepts and Postulates’ Thermodynamics traditionally focuses its attention on a particular class of states of a 1583 419 A Thermodynamics given system called (thermal) equilibrium states, although a more recent extension, called the thermodynamics of irreversible processes, deals with certain nonequilibrium states.
By virtue of this fact, the study of singular points constitutes an important aspect of the application of topology to the theory of functions of several complex variables. A singular point z0 of I/ is said to be isolated if, for some open neighborhood MT of z0 in CN, Wn V- {zO} is a smooth submanifold of W{z,,}. In that case, K, is a closed stnooth submanifold of S,, and the diffeomorphism type of (S,, K,) is independent of (sufficiently small) 8 > 0. So far, the topological study of such singular points has been primarily focused on isolated singularities.
The Restricted Three-Body Problem Since the three-body problem is very difficult to handle mathematically, mathematical interest has been concentrated on the restricted three-body problem (in particular, the planar problem) since Hill studied lunar theory in the 19th century. For the restricted three-body problem, the third body, of zero mass, cannot have any influence on the motion of the other 1587 420 Ref. Three-Body two bodies, which are of finite masses and which move uniformly on a circle around the center of mass.