Rigidity for pp-Laplacian type equations on compact Riemannian manifolds

In this paper, we obtain two rigidity results for $p$-Laplacian type equations on compact Riemannian manifolds by using of the carr\'e du champ and nonlinear flow methods, respectively, where rigidity means that the PDE has only constant solution when a parameter is in a certain range. Moreover, an interpolation inequality is derived as an application.Comment: 14 page

Women and Matrimony: A Study of Mona Lisa Smile

This study intended to use the film Mona Lisa Smile (1993) as an example to examine how women in the traditional generation of 1950 were gender stereotyped and used to trade themselves off through marriage in consideration of a cost-and-benefit analysis. However, as the change of women’s gender consciousness from the conservative to the feminist in the USA of 1950, women began to realize their potential and subjectivity, hence questing for liberal spirit and autonomy to choose their career and husbands based on love. The researchers used the qualitative method, with both the primary and secondary data, to facilitate a latent-content analysis. After conducting a content analysis of the film and the script of Mona Lisa Smile, the researchers took notes regarding gender stereotyping and conventional gender norms in social interactions and conducted a literature review of Becker’s side bet theory and Homan’s social exchange theory to investigate how women in America in the 1950s were disciplined to meet the expectation of social norms to fit the notion of conventional matrimony, and how people, both men and women, while choosing their mates, seek the maximum interest and minimum cost. The film Mona Lisa Smile lets readers have a chance to see the transformation of a marital relationship from the old days to modern ones. With raised gender consciousness, women may now subject their choices to their own will and, hence, apply a different definition to the word “marriage.

Vibrational analysis of planetary gear trains by finite element method

Planetary gear trains produce several advantages, including high speed reduction, compactness, greater load sharing and higher torque to weight ratio, which are used widely in wind turbine, automobiles, robot and other applications. In some important transmission applications, the noise and vibration are key concerns in design. In this paper, a 3D dynamic contact and impact analysis model of planetary gear trains has been proposed. Tooth surface friction, backlash, tolerance of peg hole, and time-varying stiffness were considered in this dynamic model. The ANSYS / LS-DYNA were utilized to analyze the dynamic responses of gear transmission of the planetary gears. The vibration behavior of an actual gear set under dynamic loading was simulated in the dynamic model. The stiffness and elastic deformation of gear teeth are calculated using the finite element method with actual geometry and positions of the gears. The time-varying position of the carrier defined as the vibration and noise source. After impact analysis, the numerical results of vibration of carrier involved with the transient and steady states. Through the Fast Fourier Transform (FFT) methods, frequency spectrums of the transient and steady states of the calculated vibration of planet carrier are obtained for the gearbox designer to avoid the resonance zone