We describe an algorithm that can fit the properties of the dwarf galaxy progenitor of a tidal stream, given the properties of that stream. We show that under ideal conditions (the Milky Way potential, the orbit of the dwarf galaxy progenitor, and the functional form of the dwarf galaxy progenitor are known exactly), the density and angular width of stars along the stream can be used to constrain the mass and radial profile of both the stellar and dark matter components of the progenitor dwarf galaxy that was ripped apart to create the stream. Our provisional fit for the parameters of the dwarf galaxy progenitor of the Orphan Stream indicates that it is less massive and has fewer stars than previous works have indicated.

From 1985–1994, the Skull Base Unit at St. Vincent's Hospital, Sydney, operated on 61 patients with tumours involving the jugular foramen. Pre-operative assessment by a Speech Pathologist and the institution of swallowing techniques prior to surgery have improved post-operative morbidity. Ancillary procedures at the time of surgery were not required in the majority of cases. An individual assessment of each patient early in the postoperative period was found to be more important with regard to the benefits of supplementary surgery. The majority of patients with dysphagia settled with conservative management and only a few underwent ancillary surgery. It is perceived that the cortical and subcortical control of swallowing is a major factor in the rehabilitation of these patients.

Corresponding to every graph, bipartite graph, or directed bipartite graph there exists a directed graph which is connected if and only if the original graph is connected.

In this paper, it is shown that for every directed graph there exists a certain bipartite graph such that the directed graph is connected if and only if the bipartite graph is irreducible. Other connections between reducibility and connectivity are established.

Euler (6) in 1782 first studied orthogonal latin squares. He showed the existence of a pair of orthogonal latin squares for all odd n and conjectured their non-existence for n = 2(2k + 1). MacNeish (8) in 1921 gave a construction of n — 1 mutually orthogonal latin squares for n = p with p prime and of n(v) mutually orthogonal squares of order v where

with p1 p2, … , Pr being distinct primes and

In [1] G. Birkhoff stated an algorithm for expressing a doubly stochastic matrix as an average of permutation matrices. In this note we prove two graphical lemmas and use these to find an upper bound for the number of permutation matrices which the Birkhoff algorithm may use.

A doubly stochastic matrix is a matrix of non-negative elements with row and column sums equal to unity and is there - fore a square matrix. A permutation matrix is an n × n doubly stochastic matrix which has n2-n zeros and consequently has n ones, one in each row and one in each column. It has been shown by Birkhoff [1],Hoffman and Wielandt [5] and von Neumann [7] that the set of all doubly stochastic matrices, considered as a set of points in a space of n2 dimensions constitute the convex hull of permutation matrices.