For a holonomic system with variable mass, the conformal invariance and the conserved quantity of Mei symmetry of Appell equations are investigated. First, by the infinitesimal one-parameter transformation group and the infinitesimal generator vector, the Mei symmetry and the conformal invariance of differential equations of motion for Appell equations in a holonomic system with variable mass are defined, and the determining equation of Mei symmetry and conformal invariance for Appell equations in a holonomic system with variable mass are given. Then, the Mei-conserved quantity corresponding to the system is derived by means of the structure equation to which the gauge function satisfies. Finally, an example is given to illustrate the application of the result.
Atmospheric path radiance is the key factor in the accuracy of objective radiation measurement. In the traditional radiation character measurements, under the help of the atmospheric observation equipment, MODTRAN and other software likewise, the indeterminacy rate could be around 10~20%, it is highly restricts the measurement accuracy of objective radiation. For this reason, it is quite significant to develop the study of measure and calculation in path radiance. The approximate calculation formula for path radiance in close range and horizontal direction is expressed in this article; it is compared with the results of MODTRAN and measurement in experiment. It is revealed that the accuracy of software is 7.8%, and the formula is 4.9%, which could demonstrate the validity of the approximate calculation formula in close range and horizontal direction. In this article, in the process of deducing and experiment, the validity of the approximate calculation formula in close range and horizontal direction is fully proved, which supply a new method in approximate calculation of path radiance for objective radiation measurement.
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