Abstract: The speaker‐verification problem is defined and contrasted with the speaker‐identification problem. A speaker‐verification experiment is performed using eight known speakers and 32 impostors. Formant frequencies, voicing pitch period, and speech energy—all as functions of time—are used in verification. Proper time normalization is shown to be an important factor in improving verification error performance. Nonlinear time normalization is performed by maximizing the correlation between sample and reference second‐formant profiles through a piecewise linear continuous transformation of time. Average error rates after time normalization were: for pitch, 0.05; for formants, 0.04; for energy, 0.04; and over‐all, 0.015. This over‐all error rate is four times less than that obtained using only utterance endpoint alignment.

Abstract: The normalization technique usually employed in "analytic platforms" in which quaternions are used to update the orientation of the vehicle is the one which divides the components of the quaternion by its magnitude. In this correspondence, it is analytically shown that this is the "best" normalization technique. A geometrical interpretation of this result is also given.

Abstract: The height and width of a binary input pattern are measured and the pattern is loaded into a read/write memory. The height and width signals select stored vertical and horizontal normalization vectors which address specific locations in the read/write memory so as to transfer certain of the input-pattern bits to an output memory for subsequent recognition. Each normalization vector has a series of digits for specifying addresses within the read/write memory. Horizontal and vertical registration signals may also be combined with the normalization-vector elements to modify the selected read-write memory locations, in order to move the input pattern to a reference location in the output memory.

Abstract: The properties of a two-dimensional display whose coordinates are the Euclidean distances from two points in a multivariate space are presented. When used in conjunction with three linear normalization procedures, this display is a useful tool in both supervised and unsupervised classification problems. In addition, some geometric structure is preserved by this mapping. Examples using well-known Iris data are presented to demonstrate the display characteristics.

Abstract: Using a formula derived from equations given by Furry for the normalization integral of the wavefunction corresponding to a bound state, we derive the normalization factor for the higher‐order phase‐integral approximations introduced by N. Froman. The present treatment is based on the method developed by N. Froman and P.O. Froman, in which one uses exact formulas in the calculations and makes the approximations in the final stage. We particularize the resulting general formula to the case of a single‐well potential previously discussed by the present author and to the case of a double‐well potential, which has been treated in a series of papers from this institute.

Abstract: A method is proposed for the analysis of variance of ranked data from a factorial experiment of size 2n which may be replicated or not. A test of the hypothesis that a given linear contrast of means is zero is based on the corresponding contrast of the ranks of the observations in each replicate. An approximate critical region for the test is based on the rank sum test, which is equivalent to the new test under certain null hypotheses. Two other forms of test are also suggested. Estimates of the population contrasts may be obtained by means of an ad hoc procedure for resolving the ambiguity in the mean of the test statistic, together with normalization.

Abstract: Vectorcardiography is an important area of human and machine pattern recognition. The wide range of interclass variation in observed VCGs is attributed to variations in body structure. Intra-class differences can be minimized and interclass differences maximized if a linear normalization procedure is used to eliminate variations due to individual body differences.

Abstract: The stringent test of Dodson's normalization equation was made for the isotopic fractionation arising from the evaporation of sample from the filament As an extension of recent papers of Kanno(4)and of Ozard and Russel(6), a new normalization equation has been proposed ΔMit logrjt/R0jt=kii·ΔMit logrit/R0it where rit is the observed isotopic abundance ratio of isotope i to reference isotope t, R0it is the corresponding true isotope ratio, ΔMit is mass difference between isotopes t and i, and kij is the correction factor, which is determined experimentally from a log-log plot of rit and rjt

Abstract: Teichmüller's relation between the coefficients of extremal schlicht functions and quadratic differentials is extended. The coefficient normalization hypothesis in his theorem is dropped with the result that the new coefficient relations become more complex. This completes the partial result in this direction which is contained in Jenkins' General Coefficient Theorem. A modification of the version of the length-area method used by Teichmüller and Jenkins is introduced in our proof.

Abstract: 1. Quantitative analysis of chromatograms by internal normalization of the products of the width of the peak by the retention time, without the introduction of correction coefficients, is possible only with a practically constant value of the efficiency of the column, calculated from the parameters of the different peaks. In the case of the analysis of braod fractions, when the efficiency varies considerably with a transition from the first component to the last, the results of a calculation employing normalization of the products h · tR can only be in the nature of an estimate. 2. The value of the correction coefficient, in a calculation using normalization of the products h · tR, is equal to the square root of a height equivalent to a theoretical plate.