摘要:

A theory for the detection of pulsed carriers (of constant amplitude) in narrow‐band random noise is described, based on several types of optimum tests of a statistical hypothesis against an alternative (i.e., signal and noisevsnoise). Siegert's concept of the betting curve is introduced, whereby, for a finite integration time, the minimum detectable signal is uniquely defined. Three types of observer are next considered: the Neyman‐Pearson, the Ideal, and the Sequential observer, whose properties are determined by the manner in which the test is carried out. For each observer it is verified that the best second detector is a logI0‐rectifier, which in practice is closely approximated by the usual half‐wave linear envelope‐tracer. In Part II specific betting curves are calculated and the performance of the three observers is analyzed for both the weak (threshold) and strong‐signal cases.

ISSN:0021-8979    

DOI:10.1063/1.1721290

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

In Part I a statistical theory for the detection of a pulsed carrier in noise has been described, where specifically three types of observer are defined: (1) the Neyman‐Pearson, (2) the Ideal, and (3) the Sequential observer. In Part II specific betting curves are determined for the weak‐signal cases, and some approximate curves for strong signals are also included. The input signal‐to‐noise (power) ratio (a02)mincorresponding to the minimum detectable signal at the output (with an arbitrary probability of a correct decision) is found, as expected, to vary asn−½for weak signals and asn−1for strong, wheren=number of pulses integrated. Furthermore, comparison of observers on the basis of the minimum detectable signal reveals the Neyman‐Pearson to be better than the Ideal, by an amount 0 (0.5 db). On the basis of the assumed approximate distributionws(ns) of sample size, the Neyman‐Pearson also appears superior to the Sequential observer, but as indicated in Part I, the latter must always be as good as, if not better than the former. The discrepancy is the result of the approximate nature of the assumed distributions. A lower bound on the errors thus introduced in the calculations of the (a02)minis accordingly provided by the extent to which the Sequential appearsworsethan the Neyman‐Pearson observer for equal probabilities of type I and II errors &agr; and &bgr;. Forws(ns) =&dgr;(ns−<n>) this error is reasonably small 0 (1.5 db), but for a Gaussian distribution ofnsthe effect is 0 (3.0 db) at least. Included also are an analysis of performance and some of the factors affecting it. The paper terminates with a brief account of a statistical theory of the observation process and its relation to the various observers considered here.

ISSN:0021-8979    

DOI:10.1063/1.1721291

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

This paper concerns the numerical solution, in two or more dimensions, of boundary‐value problems arising from linear partial differential equations, of which Laplace's and Poisson's equations furnish simple examples. Only techniques suitable for automatic computing machines are considered. The only method previously applicable to automatic machines is a straightforward iteration of an appropriate difference operator applied to an assumed trial solution on a network of points; as has been repeatedly pointed out, the rate of convergence of this iterative procedure is inordinately slow when the number of net points is large. The present paper shows how the employment of a Tschebyscheff polynomial of this same difference operator can cut the amount of work required in obtaining a solution by a very large factor—a factor of the order of magnitude of √Nin the two‐dimensional case,3Nin the three‐dimensional case, whereNis the number of net points. This method is an outgrowth of that developed by Flanders and Shortley [J. Appl. Phys.21, 1326 (1950)] for employment of such Tschebyscheff‐polynomial operators in the numerical solution ofeigenvalueproblems. The method is illustrated by a simple example involving Poisson's equation.

ISSN:0021-8979    

DOI:10.1063/1.1721292

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The theory of optimum nonlinear filters outlined in this paper is based on the consideration of a sequence of classes of nonlinear filters, designated asN1,N2,N3, …, such that each class in the sequence includes all the preceding classes and, furthermore, the class of linear filters is a subclass of every class in the sequence. A filter of classNmis described in terms of a characteristic function which involvesmage variables andmvalues of the input time‐function. The input‐output relationship for a filter of classNmhas the form of anm‐fold integral of the characteristic function with respect to themage variables. It is shown that the characteristic function of the optimum filter (in the least squares sense) within the classNmsatisfies a linear integral equation of 2mth order. The optimization of filters of classN1is treated in detail, and methods of approximate realization of such filters in the form of nonlinear delay line filters and power series filters are indicated. The results are extended to the case of nonstationary time series.

ISSN:0021-8979    

DOI:10.1063/1.1721293

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

In contrast to other inorganic solids, glasses may be permanently compacted by application of pressures of the order of 104to 105atmospheres. This effect was studied on two simple oxide glasses (SiO2and B2O3) and several silicate glasses. The effect of compacting was studied by measuring the densities, dimensions, and x‐ray diffraction patterns. A definite threshold pressure is observed in vitreous silica and silicate glasses, under which no effect takes place and above which the collapse takes place readily. Vitreous boric oxide behaves in a different manner, collapsing gradually, starting at the lowest pressures. Vitreous boric oxide exhibits also plastic flow with subsequent strain hardening. X‐ray diffraction measurements performed on vitreous silica and boric oxide indicate that the compacting proceeds on the atomic scale, leaving, however, the short‐range order of the basic structural units unchanged. The density of compacted glass can be restored to the original value by annealing to sufficiently high temperatures. Activation energy of this process was determined in the case of vitreous boric oxide.

ISSN:0021-8979    

DOI:10.1063/1.1721294

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The problem of the susceptance of a circular obstacle in a circular wave guide with an incidentTE01mode is solved by a variational method. Theoretical expressions are obtained which are in good agreement with experimental results. Curves of normalized susceptance as a function of relative aperture, guide wavelength, and free‐space wavelength are included.

ISSN:0021-8979    

DOI:10.1063/1.1721295

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The bulk viscosity of the system polystyrene‐diethyl benzene has been measured over the concentration range from 8 to 80 weight percent polymer and a temperature range from 30 to 130°C. A single sample of polymer was used. The activation energy for viscous flow is found to vary from about 2 to 100 kcal/mole as one goes from pure solvent to pure polymer. Using a series of 15 fractions of polystyrene ranging from 50 000 to 106, the molecular weight dependence for the viscosity of this system was measured at two polymer concentrations, 14 and 44 percent. The results are compared in a qualitative way with what one would expect from existing theory.

ISSN:0021-8979    

DOI:10.1063/1.1721296

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The positive and negative ions accompanying the operation of a cathode‐ray tube contribute in a number of ways to tube failure. These ions have been studied in standard sealed‐off tubes. The identities of the most persistent ions have been determined and ion currents measured. Some attempts to limit or control the ions at their sources have been made.The greatest offender is hydrogen which is present as both negative and positive ions. It is shown that aluminized screens offer little protection to the ion bombarded phosphor. Uncertainty in the literature as to whether negative m/e, 26 is C2H2or CN seems resolved in favor of C2H2.

ISSN:0021-8979    

DOI:10.1063/1.1721297

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

The general formula for the effective length of an electrostatic analyzer with ``rounded'' corners is derived using a modified Schwartz transformation. For the dimensions considered the rounded corner effect introduces a correction of about 0.1 percent in the evaluation of the effective length of the analyzer.

ISSN:0021-8979    

DOI:10.1063/1.1721298

出版商:AIP    

年代:1953

数据来源: AIP

摘要:

Rapid breaks of metal‐polymer‐metal adhesive specimens have shown the presence of a charge density on the metallic surface, provided the break occurs at the metal‐polymer interface, and a much smaller charge if it occurs in the interior of the polymer. This is analyzed in terms of the electron atmosphere existing external to the metal in a dielectric region of low barrier. The barrier values in certain cases are otherwise known to be of appropriate order of magnitude. Measured experimental surface charge densities permit estimation of the maximum limit of barrier height. Because of the presence of the charge distribution in the polymer, there is an electrostatic force on the adherend metal directed toward the dielectric polymer, which represents a contribution to the total adhesive forces opposing break. Such electrostatic contributions to adhesion have not previously been considered; their order of magnitude and their relation to the thickness of the adhesive are discussed. The qualitative agreement between the theory and a number of previously unexplained experimental results in the literature is shown.

ISSN:0021-8979    

DOI:10.1063/1.1721299

出版商:AIP    

年代:1953

数据来源: AIP