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For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)2/cod(χ), when χ varies among the irreducible characters of G. [ABSTRACT FROM AUTHOR]

The pressure increasing process within a twin screw multiphase pump, under the condition of high gas volume fractions (GVFs), induces large temperature and pressure changes that cause the rotors to deform. Rotor deformations heavily influence the backflow of the multiphase fluid through clearances within the twin screw multiphase pump and these deformations may even lead to pump failures. An accurate temperature and pressure distribution on the screw rotors need be obtained before the deformation analysis can be carried out. By means of small temperature and pressure sensors embedded into the groove at the root of the rotors, the temperatures of 12 points on the rotors and the pressure distributions of a twin screw multiphase pump under high GVFs conditions were recorded. Temperature test results were adopted to perform a heat transfer analysis for determining the temperature distribution on the screw rotors. Then deformation analyses, including thermal deformation, force deformation, and total deformation, were conducted according to the pressure and temperature distributions. Deformation analysis for different materials was also conducted under the same boundary conditions. A material was suggested for the manufacturing of rotors in a twin screw multiphase pump under the condition of high gas volume fractions. [ABSTRACT FROM AUTHOR]