It has been shown that when people are asked, in the absence of experimenter feedback, to free classify stimuli into categories that appear natural to them, they tend to sort on the basis of a single dimension (e.g. Medin et al., 1987) rather than by overall similarity. This result is somewhat surprising considering that many natural categories appear to be organized around a number of characte...

We study algebraic and analytic aspects of self-adjoint operators of order four or higher with polynomial coefficients. As a consequence, a systematic way of constructing such operators is given. The procedure is applied to obtain many examples up to order 8; similar examples can be constructed for all even order operators. In particular, a complete classification of all order 4 operators is gi...

We investigate the Ward identities of the W ∞ symmetry in the Liouville theory coupled to the (p, q) conformal matter. The correlation functions are defined by applying the analytic continuation procedure for the matter sector as well as the Liouville one. We then find that the Ward identities are equivalent to the W q algebra constraints deduced from the matrix model.

Automobile manufacturer–distributor partnerships are fundamental to the success of automobile companies. The complexity of the overall partnership model often causes difficulties in partnership study. This paper presents a systematic procedure to evaluate an automobile manufacturer–distributor partnership consisting of a large number of system variables. Firstly, Interpretive Structure Modeling...

A well-known theorem of Frame, Robinson, and, Thrall states that if h is a partition of n, then the number of Standard Young Tableaux of shape h is n! divided by the product of the hook-lengths. We give a new combinatorial proof of this formula by exhibiting a bijection between the set of unsorted Young Tableaux of shape A, and the set of pairs (T, S), where T is a Standard Young Tableau of sha...