Michael Reid

Noninvasive blood flow measurements by doppler ultrasound with applications to renal artery flow determination

A description of a new Doppler ultrasound flow measuring instrument is given along with representative measurements of blood flow in the canine renal artery and the human aortic arch, renal artery, and transplanted kidney renal artery. The instrument is briefly described, and a discussion of the limitations of the technique is presented.

On the connectivity of unit distance graphs

For a number field K ⊆ ℝ, consider the graph G(Kd), whose vertices are elements of Kd, with an edge between any two points at (Euclidean) distance 1. We show that G(K2) is not connected whileG(Kd) is connected ford ≥ 5. We also give necessary and sufficient conditions for the connectedness of G(K3) and G(K4).

Abelian Forcing Sets

Many readers of the MONTHLY have encountered particular cases of the following question. Suppose G is a group and n is an integer with the property that (ab) = ab for all a and b in G. Which values of n imply that G is Abelian? Indeed, standard exercises in undergraduate abstract algebra textbooks ([1], [2], [3], [4]) are to show that n = 2 and n = −1 are two such values. Are there others? If n ∈ Z, we say that a group G is n-Abelian if (xy) = xy for all x, y ∈ G. Thus our question may be reformulated as “for which integers n is an n-Abelian group necessarily abelian?” If p is any prime, consider the non-Abelian group

A new tumor model for angiographic investigations: Feline sarcoma virus tumor induction in adult cats

This article describes the first successful virus induction of sarcomas in adult immunosuppressed cats. The method of tumor induction, the immunosuppression regimen, and the gross, histologic, and angiographic findings in these induced sarcomas are described. The simplicity of the model, the rapid and reliable growth of the tumors, and the size of the animals permit repeated angiography. The model is well suited to studies of angiographically directed therapy with embolic agents, radioactive implants, or chemotherapeutic drugs. The use of a feline model permits repeated selective angiography, which is not the case with small laboratory animals, in which such studies are difficult. In this investigation, tumors were induced into the right hepatic lobe because of the relative homogeneity of peripheral hepatic vascularity and the ease with which early neoplastic changes can be detected. There is good evidence to indicate that virus induction sites in other organs would also be successful.