Some new results on irradiation characteristics of synthetic quartz crystals and their application to radiation hardening

The paper reports some new results on irradiation characteristics of synthetic quartz crystals and their application to radiation hardening. The present results show how the frequency shift in quartz crystals can be influenced by heat processing prior to irradiation and how this procedure can lead to radiation hardening for obtaining precise frequencies and time intervals from quartz oscillators in space

Some new results on the frequency characteristics on quartz crystals irradiated by ionizing and particle radiations

The frequency behavior of AT-cut quartz crystals irradiated by X -, gamma rays and fast neutrons. Initial instability in frequency for gamma and neutron irradiated crystals was found. All the different radiations first give a negative frequency shift at lower doses which are followed by positive frequency shift for increased doses. Results are explained in terms of the fundamental crystal structure. Applications of the frequency results for radiation hardening are proposed

Classification into two multivariate normal distributions with different covariance matrices

Linear procedures for classifying an observation as coming from one of two multivariate normal distributions are studied in the case that the two distributions differ both in mean vectors and covariance matrices. We find the class of admissible linear procedures, which is the minimal complete class of linear procedures. It is shown how to construct the linear procedure which minimizes one probability of misclassification given the other and how to obtain the minimax linear procedure; Bayes linear procedures are also discussed

Large deviations of the sample mean in general vector spaces

Let X1, X2, ··· be a sequence of i.i.d. random vectors taking values in a space V, let X-n = (X1 + ··· + Xn)/n, and for J ⊂ V let an(J) = n-1log P(X-n∈ J). A powerful theory concerning the existence and value of limn→∞ an(J) has been developed by Lanford for the case when V is finite-dimensional and X1 is bounded. The present paper is both an exposition of Lanford's theory and an extension of it to the general case. A number of examples are considered; these include the cases when X1 is a Brownian motion or Brownian bridge on the real line, and the case when X-n is the empirical distribution function based on the first n values in an i.i.d. sequence of random variables (the Sanov problem)