Regression quantiles for unstable autoregressive models

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit circle. It involves stochastic integrals in terms of a sequence of independent and identically distributed multivariate Brownian motions with correlated components. The related L-estimator is also discussed. The asymptotic distributions of the RQ and the L-estimator corresponding to the nonstationary componentwise arguments can be transformed into a function of a normal random variable and a sequence of i.i.d. univariate Brownian motions. This is different from the analysis based on the LSE in the literature. As an auxiliary theorem, a weak convergence of a randomly weighted residual empirical process to the stochastic integral of a Kiefer process is established. The results obtained in this paper provide an asymptotic theory for nonstationary time series processes, which can be used to construct robust unit root tests.     

Electromagnetic Field Theory Without Divergence Problems 2. A Least Invasively Quantized Theory

Classical electrodynamics based on the Maxwell–Born–Infeld field equations coupled with a Hamilton–Jacobi law of point charge motion is partially quantized. The Hamilton–Jacobi phase function is supplemented by a dynamical amplitude field on configuration space. Both together combine into a single complex wave function satisfying a relativistic Klein–Gordon equation that is self-consistently coupled to the evolution equations for the point charges and the electromagnetic fields. Radiation-free stationary states exist. The hydrogen spectrum is discussed in some detail. Upper bounds for Born's “aether constant” are obtained. In the limit of small velocities of and negligible radiation from the point charges, the model reduces to Schrödinger's equation with Coulomb Hamiltonian, coupled with the de Broglie–Bohm guiding equation.     

Sugar conjugates of fulvestrant (ICI 182,780): efficient general procedures for glycosylation of the fulvestrant core

We have prepared glucose and cellobiose conjugates at the phenolic 3- and hydroxylic 17-positions of the pure anti-estrogenic compound fulvestrant (ICI 182,780), which has recently been approved in the USA for the treatment of advanced postmenopausal breast cancer. Glycosylation at the 17-position was achieved most effectively using pivaloyl protection of the sugar imidates employed, which we found suppressed the competing transacylation reaction and led to improved yields of the product glycosides.     

Independence and graph homomorphisms graph homomorphisms

A graph with n vertices that contains no triangle and no 5-cycle and minimum degree exceeding n/4 contains an independent set with at least (3n)/7 vertices. This is best possible. The proof proceeds by producing a homomorphism to the 7-cycle and invoking the No Homomorphism Lemma. For k ≥ 4, a graph with n vertices, odd girth 2k+1, and minimum degree exceeding n/(k+1) contains an independent set with at least kn/(2k+1) vertices; however, we suspect this is not best possible. © 1993 John Wiley & Sons, Inc.     

On the free boundary of surfaces with bounded mean curvature: the non-perpendicular case

H?lder continuity up to the free boundary is proved for minimizing solutions if they meet the supporting surface in an angle which is bounded away from zero. The problem is localized by proving the continuity of the distance function, a result which is also true for stationary points. Received: 14 April 1998     

Use of dynamic trees in a network simplex algorithm for the maximum flow problem

Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n ² m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.Research partially supported by a Presidential Young Investigator Award from the National Science Foundation, Grant No. CCR-8858097, an IBM Faculty Development Award, and AT&T Bell Laboratories.Research partially supported by the Office of Naval Research, Contract No. N00014-87-K-0467.Research partially supported by the National Science Foundation, Grant No. DCR-8605961, and the Office of Naval Research, Contract No. N00014-87-K-0467.     

Algebras with Collapsing Monomials

A semigroup S is called collapsing if there exists a positiveinteger n such that for every subset of n elements in S, atleast two distinct words of length n on these letters are equalin S. In particular, S is collapsing whenever it satisfies alaw. Let U(A) denote the group of units of a unitary associativealgebra A over a field k of characteristic zero. If A is generatedby its nilpotent elements, then the following conditions areequivalent: U(A) is collapsing; U(A) satisfies some semigrouplaw; U(A) satisfies the Engel condition; U(A) is nilpotent;A is nilpotent when considered as a Lie algebra.