Complete Set Of Observables Research Articles

A Parameter Estimation Criterion for Multiresponse Models Applicable when Some Observations are Missing

Box and Draper (1965) have presented a parameter estimation criterion applicable to k‐response models when n complete sets of observations of all k responses are available. In practice, however, the data are often incomplete, and when the missing values are few in number, Box, Draper and Hunter (1970) have suggested that these missing values be added to the problem as additional parameters to be estimated. The purpose of this note is to present an alternative criterion which is more practicable when there are a large number of such missing values, and the procedure is illustrated with an example.

Complete sets of observables

The concept of a complete set of observables is formulated in the Hilbert space formalism in a manner which agrees with Dirac's original intuitive formulation. Theorems are derived which relate the completeness of a commuting set of observables to the existence of a cyclic vector. It is shown that any operator which commutes with a complete set of observables is a function of those observables.

Complete Sets of Observables and Pure States

It was shown in (1) that a complete set of bounded observables is metrically complete. However, an extra axiom was needed to prove this result (1, footnote, p. 436). In this note we prove the above-mentioned result without the extra axiom. We also show that there is an abundance of pure states if M is closed in the weak topology and give a necessary and sufficient condition for the latter to be the case.

Polarization of Thermal Emission from Venus.

Abstract : Thermal emission from a specific locale on a planetary surface is, in general, polarized, because the emissivities parallel and perpendicular to the plane of incidence are unequal. A radio telescope unable to resolve the planet will observe a net polarization in the thermal emission for appropriate asymmetries in the surface distribution of temperature, T, or dielectric constant, epsilon. Illustrative calculations indicate that the integrated polarization of the 3-cm radiation from Venus is probably between 0.35 and 2 per cent, which is close to or slightly below the capability of existing radio telescopes. A possibly more promising method of determining the polarization of Venus radio emission is provided by interferometry. Under certain, probably valid, approximations, a complete set of observations with one-dimensional resolution across the planetary disk can obtain the two-dimensional distribution of epsilon and T across the disk, and the obliquity of the axis of rotation. The observed integrated brightness-temperature phase effect requires a surface temperature difference between subsolar and antisolar point approximately 400 K. An analysis is made of the incomplete set of interferometric observations of Venus obtained at Owens Valley Radio Observatory by Clark and Spencer. These observations are shown to be consistent with the radar reflectivity and microwave phase effect of Venus if the surface temperature varies markedly (approximately 500 K) between the subsolar point and the pole. (Author)

Polarization of Thermal Emission from Venus.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Polarization of Thermal Emission from Venus. Pollack, J. B. ; Sagan, C. Abstract Thermal emission from a specific locale on a planetary surface is, in general, polarized, because the emissivities parallel to and perpendicular to the plane of incidence are unequal. A radio telescope unable to resolve the planet will observe a net polarization in the thermal emission for appropriate asymmetries in the surface distribution of temperature T or dielectric constant ~. Illustrative calculations indicate that the integrated polarization of the 3-cm radiation from Venus is probably between 0.35% and 2%, which s close to or slightly below the capability of existing radio telescopes. A possibly more promising method of determining the polarization of Venus radio emission is provided by interferometry. Under certain, probably valid, approximations, a complete set of observations with one-dimensional resolution across the planetary disk can obtain the two-dimensional distribution of E and T across the disk, and the obliquity of the axis of rotation. The observed integrated brightness temperature phase effect requires a surface temperature difference between subsolar and antisolar point 400 K0. An analysis is made of the incomplete set of interferometric observations of Venus obtained at Owens Valley Radio Observatory by Clark and Spencer (1963). These observations are shown to be consistent with the radar reflectivity and microwave phase effect of Venus if the surface temperature varies markedly (=500 K0) between the subsolar point and the pole. Publication: The Astronomical Journal Pub Date: 1965 DOI: 10.1086/109586 Bibcode: 1965AJ.....70R.146P full text sources ADS |

IX. Theory of the measurement of wind by shooting spheres upward

For a purpose such as numerical prediction by finite differences, meteorological observations are useless if they are not very complete. The most complete sets of observations are those which have been made on “international balloon days,” and if one looks at the charts of them issued by V. Bjerknes and R. Wenger from Leipzig one notices the conspicuous gaps where clouds have prevented the measurement of the upper wind by means of pilot balloons. More wind observations above clouds would, no doubt, be useful in ways other than that mentioned above. Some have been obtained recently by sound-ranging or by sending instruments up on kite-balloons. The chief advantages of this new method of observing are: (i) that it can be employed when there is fog or low cloud which would hide a pilot balloon; (ii) that it is much cheaper than sound-ranging or than captive ballooning at least for the height of 650 metres to which experiments have so far extended. Minor advantages are (iii) that the steel sphere is much less affected than a pilot balloon by vertical air currents; (iv) that these projectiles give the wind almost directly overhead, while pilot balloons drift far horizontally from the nominal site of the observation; (v) that the operations are easily performed at night; (vi) that it is well suited to making repeated observations of wind at short intervals of time, either in order to study the variations, or in order to remove them by averaging.

The Thermal Expansions of Mercury and Fused Silica

A more complete set of observations of the relative coefficients of expansion of mercury in silica than those previously published are obtained by the use of an electrically heated oil bath. The observations comprise readings at frequent intervals up to 300°C., and are in good agreement with the earlier observations, which, when applied to the values of the absolute expansion of mercury given by Callendar and Moss, seemed to show that the cylindrical bulbs used were not isotropic. Further experiments made with a spherical bulb negatived this conclusion. Tables are included in the Paper giving representative observations and the final results. From the values of the coefficients of expansion of silica determined by Prof. Callendar upon specimens similar to those from which the bulbs were made, the coefficients of absolute expansion of mercury are calculated. These over the range of the experiments of Chappuis, who used a similar method, but with bulbs of verre dur, are in fair agreement with his results, but differ appreciably from the results of Callendar and Moss obtained by the absolute method. It seems, therefore, that there is some undiscovered fundamental difference in the two methods.

I. On the determination of the specific resistance of mercury in absolute measure

In the hope of paving the way for a more accurate determination of the ohm, the author has for a considerable time been engaged in submitting to the test of experiment certain modifications of the method of Lorenz which occurred to him as likely to lead to increased accuracy and certainty. The experiments have been made in the laboratory of the University College, Cardiff, with apparatus for the most part constructed in the College workshop. Five complete sets of observations were taken in the spring of this year, with the following results for the specific resistance of mercury at 0ºC.