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If H is a Hermitian matrix and W = AH + HA ∗ is positive definite, then A has as many eigenvalues with positive (negative) real part as H has positive (negative) eigenvalues [5]. Theorems of this type are known as inertia theorems. In this note the rank of the controllability matrix of A and W is used to derive a new inertia theorem. As an application, a result in [8] and [4] on a damping problem of the equation M x + (D + G) xdot; + Kx = 0 is extended.

Generalizing a result of Schwarz [4], an inertia theorem for tridiagonal matrices is proved. This theorem is used to deduce a criterion of Wall which relates root location of polynomials to continued fractions.

Rats were allowed to drink water while a stream of amyl acetate vapor was directed towards the end of the drinking spout. Toxicosis was then induced via the injection of lithium chloride after delays of 0, 0.5, 1, 4, and 12 hr for different groups. When compared with no-toxicosis controls, it was found that significant aversions were obtained for all groups except the 12 hr group.

(1953). Quantitative Studies on the Function of Smell. Acta Oto-Laryngologica: Vol. 43, No. 6, pp. 537-544.

In einem Hochvakuumspektrometer mit gebogenem Kristall werden die LinienKα 2,α 1,α′, α 3,α′ 3, undα 4 von kristallisiertem Silicium, Karborund SiC und Siliciumdioxyd SiO2 registriert. Die Wellenlangen sind relativ zu CuKα 1 IX und CoKα 1 VIII . ermittelt. Der Unterschied der Spektren des reinen Elements und der Verbindungen wird untersucht.

The equation of the title is attacked via Taylor's formula for matrix functions. This approach contrasts with that of Lancaster [1], who used methods of contour integration suggested by functional analysis. The paper is designed as a supplement to his, being organized around a number of generalizations of his theorems. Solutions of the target equation are expressed in terms of component matrices of A and B and in terms of contour integrals.

Summary The clinical results of using preserved ox cartilage grafts in 125 patients (144 operations) are given (see Table I). It is stated that the probability of success is 95 per cent. in grafting to the nose, 50 per cent, in grafting to the ear (the best results being in total reconstructions), and 80 per cent. in restoring other facial contours. As these figures correspond very well to what one could expect from any other grafting material to these regions, and as histologically the same sort of capsule formation takes place in successful grafts, it seems justifiable to recommend preserved ox cartilage for routine plastic procedures, particularly for reconstruction of the nose.