Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals

The equations for the three-dimensional incompressible flow of liquid crystals are considered in a smooth bounded domain. The existence and uniqueness of the global strong solution with small initial data are established. It is also proved that when the strong solution exists, all the global weak solutions constructed in [16] must be equal to the unique strong solution

Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions

Let \phi\ be a Dirichlet or Neumann eigenfunction of the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We prove lower bounds for the size of the nodal set {\phi=0}.Comment: 7 page

Correlation of the Subjective Hip Value with Validated Patient-Reported Outcome Measurements for the Hip

Background: The subjective hip value (SHV) was developed as a patient-reported outcome measurement (PROM) that is easily and quickly performed and interpreted. The SHV is defined as a patient's subjective hip measurement tool expressed as a percentage of an entirely normal hip joint, which would score 100%. The hypothesis is that results of the subjective hip value correlate with the results of the modified Harris hip score and the International Hip Outcome Tool in patients with hip-related diseases. Methods: 302 patients completed the modified Harris hip score (mHHS), the International Hip Outcome Tool (iHot-33) as well as the SHV. The SHV consist of only one question: "What is the overall percent value of your hip if a completely normal hip represents 100%?". The patients were divided into five different groups depending on the diagnosis. Pearson correlation was used to evaluate the correlation between the different PROMs and linear regression analysis was used to calculate R2. Results: 302 complete datasets were available for evaluation. There was a high correlation between the SHV and the iHOT-33 (r = 0.847; r2 = 0.692, p < 0.001) and the mHHS (r = 0.832; r2 = 0.717, p < 0.001). The SHV showed a medium (r = 0.653) to high (r = 0.758) correlation with the mHHS and the iHOT-33 in all diagnosis groups. Conclusion: The SHV offers a useful adjunct to established hip outcome measurements, as it is easily and quickly performed and interpreted. The SHV reflects the view of the patient and is independent of the diagnosis. Further research with prospective studies is needed to test the psychometric properties of the score

Nonlinear Hodge maps

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models certain kinds of compressible flow. Conditions are found under which singular sets of prescribed dimension cannot occur. Various degrees of smoothness are proven for the sonic limit, high-dimensional flow, and flow having nonzero vorticity. The gradient flow of solutions is estimated. Implications for other quasilinear field theories are suggested.Comment: Slightly modified and updated version; tcilatex, 32 page

Academic activism and its impact on individual-level mobilization, sources of learning, and the future of academia in Turkey

In January 2016, academics in Turkey distributed a peace petition calling for an end to hostilities and to restart negotiations with the Kurdish movement. The Turkish government responded by opening legal cases, jailing academics, and dismissing them from universities. In the state of emergency following the July 2016 coup attempt in Turkey, the government's extended powers allowed them to fire thousands of civil servants from every branch of government, including thousands of academics. This increased the number of academics who organized to form and teach in academic collectives. The current study evaluates how politicization occurs in scholars removed from the university environment. Traditional approaches to collective action and politicization suggest that empowerment is an important catalyst in politicization and continuation of collective political engagement. With the social and political restrictions that decree law dismissals place on scholars, what is it that motivates them to politicize? The current study was conducted through semistructured interviews with nine academics who work in these collectives. Participants described their politicization in terms of previous practice, reaction to injustice, and ideals of academia and academic freedom. They further evaluated current and prospective functions and possible barriers to academic collectives. Finally, although somewhat ambivalent, participants discussed feelings of efficacy, psychosocial support, and senses of solidarity and liberation in terms of being empowered. Their perspectives provide an opportunity to understand how and where academics engage in scholar activism for an independent and free academia in the context of consolidated political oppression.</p

Regularity of higher codimension area minimizing integral currents

This lecture notes are an expanded version of the course given at the ERC-School on Geometric Measure Theory and Real Analysis, held in Pisa, September 30th - October 30th 2013. The lectures aim to explain the main steps of a new proof of the partial regularity of area minimizing integer rectifiable currents in higher codimension, due originally to F. Almgren, which is contained in a series of papers in collaboration with C. De Lellis (University of Zurich).Comment: This text will appear in "Geometric Measure Theory and Real Analysis", pp. 131--192, Proceedings of the ERC school in Pisa (2013), L. Ambrosio Ed., Edizioni SNS (CRM Series