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Let A be a commutative semisimple F-algebra with identity, and let D 0 , D 1 , ⋯ {D_0},{D_1}, \cdots be a system of derivations from A into the algebra of all continuous functions on the spectrum of A. It is shown that the transformations D 0 , D 1 , ⋯ {D_0},{D_1}, \cdots are necessarily continuous. This result is used to obtain a characterization of derivations on Hol ( Ω ) {\text {Hol}}(\Omega ) where Ω \Omega is an open polynomially convex subset of C n {C^n} .

Lens opacities result from exposure of the rabbit eye to 2450-mc continuous wave radiation. Threshold for a single damaging exposure is determined by power density and duration. Opacities may also result as a cumulative effect of repeated subthreshold exposures. Intraocular temperature increases during irradiation, the extent and rate of increase being related to power density. Inasmuch as a particular temperature critical for opacity induction cannot be identified, it is suggested that the intraocular thermal response may be coincident with, rather than the cause of, induction of opacities. Lens damage may result from irradiation at power levels not sufficient to cause discomfort to nonanesthetized animals. Pulsed radiation with high peak intensities appears to be more potent in inducing lens opacities than continuous wave radiation of equal average power. Since ocular temperature is related to average rather than to peak power, these findings further suggest the possibility of a nonthermal biological effect of microwave radiation.

Confirmation of the astronomical unit reported by muhleman, using radar observations of mercury

After microwave irradiation the first change to occur in the lens appears to be a drop in the level of ascorbic acid. The depression in lens ascorbate does not occur immediately but is observed 6–18 hours after irradiation. Consequently, the loss in ascorbic acid does not appear to be a direct thermal effect. There is no corresponding change in the ascorbate level of the aqueous humor.

Venus may rotate in a direction opposite to that of the earth at a rate of only one revolution in 240 days. The estimated period is accurate within 20 percent if the axis of rotation of Venus is perpendicular to the plane of the planet's orbit.

During the period 13 August to 22 August, day-to-day determinaitions of the average orbital elements of the 100-foot Echo I balloon, based on observations taken at the Jet Propulsion Laboratory's Goldstone tracking station, indicated a decrease in perigee height of 3.0 km/day and an increase in the eccentricity of 0.00038 per day.

Drift scans were made of a selected track on the sky to search for small- scale anisotropy in thw microwave background radiation. The observations were made with the 64-m antenna at Goldstone, California, operating at 3.56 cm. The half-power beam width was 2'.3. The scans were approximately 1 deg in length. The upper bound on the small anisotropy along our track is DELTA T/T < 7.15x 10/ sup -4/ (90 percent confidence). Some implications of this result are discussed. (auth)

Let B be an F-algebra and A be a commutative semisimple F-algebra such that the spectrum of A contains no isolated points. We prove that any homomorphism of B onto A is necessarily continuous. Let A be a commutative semisimple algebra. We prove that there is at most one topology with respect to which A is an F-algebra. Introduction. Let A be a semisimple algebra over the complex numbers. It was shown by Gelfand [3, Satz 17] that if A is commutative and has an identity, then there is at most one norm (up to equivalence) which makes A into a Banach algebra. C. E. Rickart gave several extensions of this result in the paper [6]. In [4] B. E. Johnson proved that the norm is unique in any semisimple Banach algebra. E. A. Michael [5, ?14] extended the theorem on uniqueness of topology to certain types of F-algebras. In particular it is proved in [5] that the topology is unique for commutative semisimple Falgebras in which every homomorphism of the algebra onto the complex numbers is continuous. (Whether all homomorphisms of a commutative F-algebra onto the complex numbers are continuous is one of the outstanding questions which remain open for F-algebras.) In this paper we show that if A is a commutative semisimple algebra, then there is at most one topology with respect to which A is an Falgebra. We also show that if 0 is a homomorphism of an F-algebra B onto a commutative semisimple F-algebra A whose spectrum contains no isolated points, then 4 is necessarily continuous. Uniqueness of topology. A commutative F-algebra is a commutative algebra over the complex numbers which is a complete T2 topological space with respect to a topology determined by a countable family of multiplicative seminorms { II Ii}, i = 1, 2, * . . . No generality is lost if the seminorms are assumed to be increasing. That is, we may assume II| Ii

In [1] Johnson considered commutative semisimple F-algebras with identity which are also Q-algebras. (A Q-algebra is an algebra in which the set of invertible elements is open.) For an algebra A of this type, Johnson proved that any derivation of A into A^, the algebra of all Gelfand transforms of elements of A, is continuous. The difficulty with this theorem is that the standard examples of F-algebras with derivations are not Q-algebras. In particular, neither the algebra CG (0, 1), nor the algebra Hol (Q), each with the standard F-algebra topology, is a Q-algebra. Here Co (0, 1) denotes the algebra of all complex valued infinitely differentiable functions on (0, 1), and Hol (Q) is the algebra of all functions which are holomorphic on an open subset Q of the complex plane. In fact, one often turns to F-algebras in order to avoid the restrictions (such as every element having a compact spectrum) placed on an algebra by requiring the algebra to be a Q-algebra. Tihe purpose of this note is to show how Johnson's techniques can be used to prove that every derivation of an F-algebra A into the algebra A is continuous, where it is only assumed that A is commutative, semisimple, and has an identity. From this fact, we can conclude that every derivation of A into A' is continuous, since any such derivation can be factored through A. In particular, we have that any derivation of a Frechet function algebra into itself is continuous. A will denote a commutative semisimple F-algebra with identity. For an element a of A, aA will denote the Gelfand transform of the element a, and A' will denote the algebra of all Gelfand transforms of elements of A. If B is an F-algebra, then we will use Spec B to denote the space of all continuous homomorphisms of B onto the complex numbers, where the space of homomorphisms is given the Gdelfand topology. We fix a sequence {Bn} of Banach algebras such that A is the inverse limit of the Banach algebras