Array languages and theN-body problem

Array languages and the N-body problem

Few-body Physics – Then and Now

A summary of the XIVth International Conference on Few-body Problems In Physics is given, with an emphasis on the important problems solved recently and the prognosis for the future of the field. Personal remarks and “homework” problem assignments are made.

The Frame Problem, Then and Now

My collaboration with John McCarthy started in 1984. He was interested then in what he called the commonsense law of inertia. That idea is related to actions, such as moving an object to a different location, or, for instance, toggling a light switch. According to this law, whatever we know about the state of affairs before executing an action can be presumed, by default, to hold after the acti...

TheN-Eigenvalue Problem and Two Applications

Consider the following two questions. (1) When does a compact Lie group G ⊂ U(n) have an element g ∈ G possessing exactly two eigenvalues? (2) When does a compact Lie group G ⊂ U(n) have a cocharacter U(1) → G such that the compositionU(1) → U(n) is a representation ofU(1)with exactly two weights? A solution to the second problem gives a family of solutions to the first, by choosing g to be alm...

Shuffle on Array Languages Generated by Array Grammars

Motivated by the studies done by G. Siromoney et al. (1973) and Alexandru Mateescu et al. (1998) we examine the language theoretic results related to shuffle on trajectories by making use of Siromoney array grammars such as (R : R)AG, (R : CF )AG, (CF : R)AG, (CF : CF )AG, (CS : R)AG, (CS : CS)AG and (CF : CS)AG which are more powerful than the Siromoney matrix grammars (1972) and are used to m...