Let g be a finite dimensional complex semi-simple Lie algebra with Weyl group W and simple reflections S. For I ⊆ S let g I be the corresponding semi-simple subalgebra of g. Denote by W I the Weyl group of g I and let w • and w I • be the longest elements of W and W I , respectively. In this paper we show that the answer to Kostant's problem, i.e. whether the universal enveloping algebra surjec...

As the theory of identification assumed increasing importance in Freud’s work, it came to be a cornerstone of psychoanalytic theory. Yet because the difficulties contained in Freud’s views on this question have not, with the exception of Lacan, been properly appreciated, post— Freudian theory has employed a theoretical construct of questionable coherence. Although Freud wavered over what was id...

We consider the one-armed bandit problem of Woodroofe [J. Amer. Statist. Assoc. 74 (1979) 799–806], which involves sequential sampling from two populations: one whose characteristics are known, and one which depends on an unknown parameter and incorporates a covariate. The goal is to maximize cumulative expected reward. We study this problem in a minimax setting, and develop rate-optimal police...

For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In [J. Graph Theory, 11 (1987), 399-407], Broersma and Veldman proposed an open problem: For a given positive integer k, determine the value s for which the statement Let G be a k-triangular graph. Then L(G), the line graph of G, is s-hamiltonian if and only L(G) is (s + 2)-connected is...

This short note is a contribution to the solution of the problem of indifference in Austrian economics (“Nozick’s problem”). The problem is divided into two questions: (i) Can the stock of a commodity be defined without a reference to indifference? (ii) What is the praxeological interpretation of the fact that one unit of a homogenous stock is chosen over another? It is argued that the answer t...

Let R be a ring (commutative with unity, in what follows). For an integer n > 1 define gR(n) to be the least integer s for which every element of R is a sum of s nth powers of elements of R, if such an integer exists, or ∞ otherwise. Waring’s problem for R is the problem of deciding whether gR(n) is finite and estimating it for all n. Note that what is usually called Waring’s problem is not wha...