Geometric inequalities for initial data with symmetries

We consider a class of initial data sets (Σ,h,K) for the Einstein constraint equations which we define to be generalized Brill (GB) data. This class of data is simply connected, U(1)²-invariant, maximal, and four-dimensional with two asymptotic ends. We study the properties of GB data and in particular the topology of Σ. The GB initial data sets have applications in geometric inequalities in general relativity. We construct a mass functional M for GB initial data sets and we show:(i) the mass of any GB data is greater than or equals M, (ii) it is a non-negative functional for a broad subclass of GB data, (iii) it evaluates to the ADM mass of reduced t − φi symmetric data set, (iv) its critical points are stationary U(1)²-invariant vacuum solutions to the Einstein equations. Then we use this mass functional and prove two geometric inequalities: (1) a positive mass theorem for subclass of GB initial data which includes Myers-Perry black holes, (2) a class of local mass-angular momenta inequalities for U(1)²-invariant black holes. Finally, we construct a one-parameter family of initial data sets which we show can be seen as small deformations of the extreme Myers- Perry black hole which preserve the horizon geometry and angular momenta but have strictly greater energy.

Development of calix[4]arene-functionalized microcantilever array sensing system for the rapid, sensitive and simultaneous detection of metal ions in aqueous solutions

The work described in this thesis was conducted with the aim of: 1) investigating the binding capabilities of calix[4]arene-functionalized microcantilevers towards specific metal ions and 2) developing a new16-microcantilever array sensing system for the rapid, and simultaneous detection of metal ions in fresh water. Part I of this thesis reports on the use of three new bimodal calix[4]arenes (methoxy, ethoxy and crown) as potential host/guest sensing layers for detecting selected ions in dilute aqueous solutions using single microcantilever experimental system. In this work it was shown that modifying the upper rim of the calix[4]arenes with a thioacetate end group allow calix[4]arenes to self-assemble on Au(111) forming complete highly ordered monolayers. It was also found that incubating the microcantilevers coated with 5 nm of Inconel and 40 nm of Au for 1 h in a 1.0 M solution of calix[4]arene produced the highest sensitivity. Methoxy-functionalized microcantilevers showed a definite preference for Ca²⁺ ions over other cationic guests and were able to detect trace concentration as low as 10⁻¹² M in aqueous solutions. Microcantilevers modified with ethoxy calix[4]arene displayed their highest sensitivity towards Sr²⁺ and to a lesser extent Ca²⁺ ions. Crown calix[4]arene-modified microcantilevers were however found to bind selectively towards Cs⁺ ions. In addition, the counter anion was also found to contribute to the deflection. For example methoxy calix[4]arene-modified microcantilever was found to be more sensitive to CaCl₂ over other water-soluble calcium salts such as Ca(NO₃)₂ , CaBr₂ and CaI₂. These findings suggest that the response of calix[4]arene-modified microcantilevers should be attributed to the target ionic species as a whole instead of only considering the specific cation and/or anion. Part II presents the development of a 16-microcantilever sensor setup. The implementation of this system involved the creation of data analysis software that incorporates data from the motorized actuator and a two-axis photosensitive detector to obtain the deflection signal originating from each individual microcantilever in the array. The system was shown to be capable of simultaneous measurements of multiple microcantilevers with different coatings. A functionalization unit was also developed that allows four microcantilevers in the array to be coated with an individual sensing layer one at the time. Because of the variability of the spring constants of different cantilevers within the array, results presented were quoted in units of surface stress unit in order to compare values between the microcantilevers in the array.

Improving safety of nursing staff: challenges and solutions regarding safety for nursing staff in acute care psychiatric settings

Workplace violence is defined as an act of abuse, threatening behaviour, intimidation, or assault on a person in his or her place of employment. Unfortunately, such violence is a reality for nurses. These take the form of physical, verbal, and threating behaviours, and harassment. Violence, particularly verbal abuse, is so prevalent that it is often considered “part of the job” and can contribute to many negative professional and personal effects for nurses. Therefore, it is important to understand what influences an individual to become violent in order to suggest and support initiatives to decrease it. A literature review and consultations with key stakeholders were conducted to gather relevant information regarding violence committed by patients and others visiting mental health care settings. Through data analysis, two relevant themes were revealed: reporting and interventions. Reporting incidents of workplace violence is important to track and quantify aggressive episodes, thus emphasizing its seriousness. Nurses may differ in the perception of what constitutes violence, underreport incidents, and feel a sense of futility when reported violence continues. In addition, cumbersome methods of reporting can be a hindrance to the reporting process. Six areas of potential interventions were identified to increase safety for nurses. These are staffing, de-escalation training, environmental considerations, addictions services, organizational support, and consequences. All findings were summarized in a document to be presented to the leadership of the Mental Health and Addictions program within the local health care authority. The goal is to offer recommendations to lead to a decrease in workplace aggression and increased safety for nurses in the acute care psychiatric setting.