A sharpened version of Moser’s ‘modifying terms’ KAM theorem is derived, and it is shown how this theorem can be used to investigate the persistence of invariant tori in general situations, including those where some of the Floquet exponents of the invariant torus may vanish. The result is ‘structural’ and works for dissipative, Hamiltonian, reversible and symmetric vector fields. These results...

A modification of the Dai-Yuan conjugate gradient algorithm is proposed. Using the exact line search, the algorithm reduces to the original version of the Dai and Yuan computational scheme. For inexact line search the algorithm satisfies both the sufficient descent and conjugacy condition. A global convergence result is proved when the Wolfe line search conditions are used. Computational result...

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

We provide the first effectively computable, modulo a mild conjecture, complete invariant for simultaneous conjugacy in Garside groups. This invariant generalizes the notion of super summit set of a conjugacy class, and provides a solution of the simultaneous conjugacy problem in Garside groups, of complexity a small degree polynomial in the sizes of the invariant and the input parameters. Comp...

Subgroups H1 and H2 of a group G are said to be locally conjugate if there is a bijection f : H1 → H2 such that h and f(h) are conjugate in G. We study local conjugacy among subgroups of GL2(Z/pZ), where p is an odd prime, building on Andrew Sutherland’s categorizations of subgroups of GL2(Z/pZ) and local conjugacy among them. We obtain a classification of locally conjugate subgroups of GL2(Z/p...

A reanalysis of Budescu et al.’s (2009) data on numerical interpretations of the Intergovernmental Panel on Climate Change (IPCC 2007) fourth report’s verbal probability expressions (PE’s) revealed that negative wording has deleterious effects on lay judgements. Budescu et al. asked participants to interpret PE’s in IPCC report sentences, by asking them to provide lower, “best” and upper estima...

A state amalgamation of a directed graph is a node contraction which is only permitted under certain configurations of incident edges. In symbolic dynamics, state amalgamation and its inverse operation, state splitting, play a fundamental role in the the theory of subshifts of finite type (SFT): any conjugacy between SFTs, given as vertex shifts, can be expressed as a sequence of symbol splitti...

If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop. This statement is also shown to be true for some weak Smarandache loops(inverse property, weak inverse property) but...

many results were proved on the structure of finite groups with some‎ ‎restrictions on their real elements and on their conjugacy classes‎. ‎we‎ ‎generalize a few of these to some classes of infinite groups‎. ‎we study groups in which real elements are central‎, ‎groups in which real elements are $2$-elements‎, ‎groups in which all non-trivial classes have the same finite size and $fc$-groups w...

The Weyl groups are important for Lie algebras. Lie algebras arise in the study of Lie groups, coming from symmetries of differential equations, and of differentiable manifolds. The Weyl groups have been used to classify Lie algebras up to isomorphism. The Weyl group associated to a Lie algebra of type Bn and the group of graph automorphisms of the n-cube Aut(Qn) are known to be isomorphic to Z...