Sharpening and generalizations of Shafer's inequality for the arc tangent function

In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined

A Comparison of Student Growth Percentile and Value-added Models on School Quality Measures

Under Every Student Succeeds Act (ESSA), all public schools are required to include student growth measures in addition to student achievement in the school accountability system. The two most popular growth models that are widely used by states are Student Growth Percentiles (SGPs) and Value-added models (VAMs). Growth models are designed to capture the quality of a school in promoting student learning. According to current research, there are indications of disadvantaged schools that are underrepresented in the growth metric compared to advantaged schools. The purpose of this dissertation is to fill in two gaps in the literature: first, current research on growth modeling is mostly focused on elementary and middle schools. This dissertation is an extension of current research to evaluate growth measures used in high schools to provide new evidence on the utility of growth models. Secondly, this dissertation assessed the impact of school demographic variables on model outputs. In other words, it identified which types of schools would receive a different result that is proportional to the student composition within a school. The results showed that growth measures have lower correlations with school poverty compared to achievement measures, which levels the playing field for disadvantaged schools to an extent. However, there are meaningful differences between models in term of the representation of disadvantaged schools in the top quartile of the growth measures

Qubit state tomography in superconducting circuit via weak measurements

The standard method of "measuring" quantum wavefunction is the technique of {\it indirect} quantum state tomography. Owing to conceptual novelty and possible advantages, an alternative {\it direct} scheme was proposed and demonstrated recently in quantum optics system. In this work we present a study on the direct scheme of measuring qubit state in the circuit QED system, based on weak measurement and weak value concepts. To be applied to generic parameter conditions, our formulation and analysis are carried out for finite strength weak measurement, and in particular beyond the bad-cavity and weak-response limits. The proposed study is accessible to the present state-of-the-art circuit-QED experiments.Comment: 7 pages,5figure