摘要:

LetLbe a linear differential operator of thenth order whose coefficientspi(x) are continuous in a semi‐infinite intervalI: [a, ∞). A functionH(x, &zgr;) is said to be a one‐sided Green's function for the operatorLif it satisfies the four conditions: (1)His continuous and its firstnderivatives with respect toxare continuous inI. (2)H&agr;(&zgr;, &zgr;)=0 for &agr;=0, 1, …,n−2. (3)Hn−1(&zgr;, &zgr;)=1/p0(&zgr;). (4)LH=0. (The subscript on theHrefers to partial differentiation with respect to the first argument, andp0(x) is the coefficient ofdn/dxnin the expression forL.) It is shown thatHis unique and ifu(x)=∫axH(x, &zgr;)f(&zgr;)d&zgr;, thenLu=f(x) andu(&agr;)(a)=0, &agr;=0, 1, …,n−1. Furthermore, ifHis given, a fundamental system of solutions ofLu=0 can be written down explicitly in terms ofHand its derivatives evaluated at the end pointa. The converse problem is trivial. Other properties ofHare also considered, for example, its relation to the impulsive response of a network.

ISSN:0021-8979    

DOI:10.1063/1.1700100

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

In the performance of antenna measurements the antenna is usually placed over a large conducting screen. The assumption is then made that the measurements are in close agreement with those that would be obtained if the screen were of infinite size. Recent experimental work, however, indicates that the finiteness of the ground screen may influence the measurements to a considerable extent.It is therefore desirable to solve this problem theoretically in order to determine the extent of the change introduced by the use of a finite screen. This paper treats the problem of an antenna erected vertically in the center of a circular screen. An integral equation is obtained for the electric field in the plane of the screen, outside the screen. This equation is solved approximately by the use of a variational principle, and a formula is obtained for the change of antenna impedance as a function of the diameter of the screen. The formula may be used to give a simple and accurate estimate of the changes introduced by the use of a finite screen.

ISSN:0021-8979    

DOI:10.1063/1.1700101

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

The expected number of times the functione(t)=at+eN(t) crosses thetaxis in a positive direction prior to any given time is calculated, whereeN(t) is a random noise function of arbitrary power spectrum. The solution is given as the product of two functions. Curves are presented for the two functions.

ISSN:0021-8979    

DOI:10.1063/1.1700102

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

A method for measuring the gas flow velocity in hot high velocity exhaust flames is described. This method is based on the doppler shift of wavelength of the sodium or lithium spectral radiation from the flame when viewed at different angles relative to the flame axis. The same apparatus may be used to measure the gas pressure from the pressure shift of wavelength of the sodium radiation. A Fabry‐Perot interferometer and camera assembly was used to determine the small shift in wavelengths. It was concluded that the absolute accuracy of any one velocity measurement by this method is about ±1.5×104cm/sec, while that of any one pressure measurement is about ±0.3 atmosphere. The method is therefore applicable to flames of very high velocity and to pressures of at least a few atmospheres.

ISSN:0021-8979    

DOI:10.1063/1.1700103

出版商:AIP    

年代:1951

数据来源: AIP

摘要:

The NOL 12×12‐cm hyperballistics wind tunnel No. 4, which operates in a Mach number range up to eleven, is briefly described. Experiments performed in this tunnel indicate that a fraction of the air condenses at or shortly after reaching the dew line for air condensation unless the supply air is preheated. The measured effects of air condensation on the flow at high Mach numbers for a variety of supply temperatures and pressures are given. It is found that of the flow parameters commonly measured in supersonic wind tunnels, only static‐pressure and shock‐angle measurements are sensitive to liquefaction effects. A simple thermodynamic analysis assuming a reversible condensation process allows interpretation of some of the observations.

ISSN:0021-8979    

DOI:10.1063/1.1700104

出版商:AIP    

年代:1951

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1700106

出版商:AIP    

年代:1951

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1700107

出版商:AIP    

年代:1951

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1700108

出版商:AIP    

年代:1951

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1700110

出版商:AIP    

年代:1951

数据来源: AIP

ISSN:0021-8979    

DOI:10.1063/1.1700111

出版商:AIP    

年代:1951

数据来源: AIP