Point out that the results will be the same for the single epoch positioning in single differential model or double differential model using least square method.
The experimental results show that in ordinary laboratory condition, without constant temperature, the shift of phase measurement is about 15 nm. Calibration with differential dual-frequency interferometer gives the linealy correlation coefficient of 0.9999 and nonlinearity of about 10 nm.
This paper aims at the request of detectinging and measuring the earth tide, introduces the composing and principle of high precision vertical pendulum tiltmeter and discusses in detail the application of the differential capacity micrometry sensor to the vertical pendulum tiltmeter.
The best noise level which we can acquire in the design of displacement detecting circuit is making it be the on thermal noise level of bridge resistance. However, the thermal noise of bridge resistance depend on parameters of sensor unit, exciting voltage, temperature and quality factor of differential transformer.
In our paper [KR] we began a systematic study of representations of the universal central extension[InlineEquation not available: see fulltext.] of the Lie algebra of differential operators on the circle.
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We express them in terms of generatorsEij ofU(gl(n)) and as differential operators on the space of matrices These expressions are a direct generalization of the classical Capelli identities.
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Quantum integrable systems and differential Galois theory
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This paper is devoted to a systematic study of quantum completely integrable systems (i.e., complete systems of commuting differential operators) from the point of view of algebraic geometry.
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In particular, we show that the differential Galois group of this eigenvalue problem is reductive at generic eigenvalues.