Showing papers in "Bulletin of The London Mathematical Society in 1982"
1,196 citations
TL;DR: In this article, the adjoint action of G on its Lie algebra L(G) was considered and it was shown that W-orbits in L(T) correspond to G-orbit in L (G).
Abstract: The converse was proved by A. Horn [5], so that all points in this convex hull occur as diagonals of some matrix A with the given eigenvalues. Kostant [7] generalized these results to any compact Lie group G in the following manner. We consider the adjoint action of G on its Lie algebra L(G). If T is a maximal torus of G and W its Weyl group, then it is well known that W-orbits in L(T) correspond to G-orbits in L(G). Now fix a G-invariant metric on L(G), so that we can define orthogonal projection. Then Kostant's result isf
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TL;DR: In this article, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, rigid body motion, and the Hamiltonian formalism.
Abstract: In this text, the author constructs the mathematical apparatus of classical mechanics from the beginning, examining all the basic problems in dynamics, including the theory of oscillations, the theory of rigid body motion, and the Hamiltonian formalism. This modern approch, based on the theory of the geometry of manifolds, distinguishes iteself from the traditional approach of standard textbooks. Geometrical considerations are emphasized throughout and include phase spaces and flows, vector fields, and Lie groups. The work includes a detailed discussion of qualitative methods of the theory of dynamical systems and of asymptotic methods like perturbation techniques, averaging, and adiabatic invariance.
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TL;DR: In this article, the first-order statements independent of Peano arithmetic have been found, in an informal sense, purely number-theoretic in character (as opposed to metamathematical or combinatorial).
Abstract: Recently some interesting first-order statements independent of Peano Arithmetic (P) have been found. Here we present perhaps the first which is, in an informal sense, purely number-theoretic in character (as opposed to metamathematical or combinatorial). The methods used to prove it, however, are combinatorial. We also give another independence result (unashamedly combinatorial in character) proved by the same methods.
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TL;DR: In the first case, C bounds a Moebius band in M and K is isotopic to the centre of this band in this paper, where M representing a is either an embedding or a double cover of a one-sided embedded curve K.
Abstract: 1—> M representing a is either an embedding or a double cover of a one-sided embedded curve K In the second case, C bounds a Moebius band in M and K is isotopic to the centre of this band
TL;DR: In this paper, it was shown that the group of automorphisms of a free associative algebra, k(X, Y>, is generated by the automomorphisms of the form
Abstract: Each of these automorphisms sends the commutator (X, Y) = X~ Y' XY to a conjugate of {X, Y) or (X, Y)~K Using this, Nielsen showed further that two elements X', Y' (freely) generate F if and only if (X, Y') is a conjugate of (X, Y) or (X,Y)~. In [1, p. 197] Cohn conjectured that there were analogous results for the free associative algebra on two generators X, Y over a (commutative) field k. This was vindicated when Makar-Limanov [7] (cf [6]) and Czerniakiewicz [3] independently showed that the group of/c-algebra automorphisms of this free /c-algebra, k(X, Y>, is generated by the automorphisms of the form