Home Rule in New York: The Need for a Change

This article is intended to provide a practical lens into how Home Rule issues unfold in complex matters involving the City, and to suggest how a much-needed Home Rule constitutional amendment could re-shape or, at the very least, clarify Home Rule standards. Section II will provide some historical and legal background on Home Rule; Section III will analyze some of the more well-known Home Rule cases that the Law Department litigated during the Bloomberg Administration; and Section IV will discuss insights gleaned with respect to, and will offer several recommendations for, the future of Home Rule in New York

Global (in Time) Solutions to the 3D-Navier-Stokes Equations on R^3

A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time solutions to the three-dimensional Navier-Stokes equations. (These equations describe the time evolution of the fluid velocity and pressure of an incompressible viscous homogeneous Newtonian fluid in terms of a given initial velocity and given external body forces.) A related problem is to provide conditions under which we can be assured that the numerical approximation of these equations, used in a variety of fields from weather prediction to submarine design, have only one solution. In earlier papers, we solved this problem for a bounded domain. In this paper, we use an approach based on additional physical insight, that allows us to prove that there exists unique global in time solutions to the Navier-Stokes equations on R^3

Everything’s Bigger in Texas: Examining the Mandatory (and Additional) Financial Burden of Postsecondary Education

Student fees remain an under-researched aspect of postsecondary education and finance (Kelchen, 2016). This study examines the mandatory and additional fees charged to full-time, in-state undergraduate students by public and private not-for-profit four-year institutions in Texas (n=96). Findings demonstrate the average four-year institution in Texas charges over $1,500 per academic year in mandatory fees,$500 higher than the national average. Moreover, private institutions charge an average of $1,100 less than publics, while fees comprise 6.8% of the total cost of attendance at private and 29.1% at publics. Institutions of higher education compose fee explanations above the 12th-grade reading level and only 5.2% of the sample provided fee explanations in a language other than English, thus further marginalizing non-English speaking language populations in Texas. Implications for policy makers, practitioners, and future research are addressed.Educatio

Implementation of a point-of-care ultrasound skills practicum for hospitalists

Introduction Point-of-care ultrasound is recognized as a safe and valuable diagnostic tool for patient evaluation. Hospitalists are prime candidates for advancing the point-of-care ultrasound field given their crucial role in inpatient medicine. Despite this, there is a notable lack of evidence-based ultrasound training for hospitalists. Most research focuses on diagnostic accuracy rather than the training required to achieve it. This study aims to improve hospitalists' point-of-care ultrasound knowledge and skills through a hands-on skills practicum. Methods Four skill practicums were conducted with pre-course, post-course, and six-month evaluations and knowledge assessments. Results The mean pre- vs. post-course knowledge assessment scores significantly improved, 41.7% vs. 75.9% (SD 16.1% and 12.7%, respectively, p < 0.0001). The mean ultrasound skills confidence ratings on a 10-point Likert scale significantly increased post-course (2.60 ± 1.66 vs. 6.33 ± 1.63, p < 0.0001), but decreased at six months (6.33 ± 1.63 vs. 4.10 ± 2.22, p < 0.0001). The greatest limitations to usage pre-course and at six months were knowledge/skills and lack of machine access. While knowledge/skills decreased from pre-course (82.0%) as compared to six-months (64.3%), lack of machine access increased from pre-course (15.8%) to six-months (28.6%) (p = 0.28). Conclusion Hospitalists agree that point-of-care ultrasound has utility in the diagnostic and therapeutic management of patients, though the lack of training is a significant limitation. Our study demonstrated that a brief skills practicum significantly improves hospitalists’ confidence and knowledge regarding ultrasound image acquisition and interpretation in the short term. Long-term confidence and usage wanes, which appears to be due to the lack of machine access

Matrix Algebras with a Certain Compression Property I

An algebra $\mathcal{A}$ of $n\times n$ complex matrices is said to be projection compressible if $P\mathcal{A}P$ is an algebra for all orthogonal projections $P\in\mathbb{M}_n(\mathbb{C})$. Analogously, $\mathcal{A}$ is said to be idempotent compressible if $E\mathcal{A}E$ is an algebra for all idempotents $E\in\mathbb{M}_n(\mathbb{C})$. In this paper we construct several examples of unital algebras that admit these properties. In addition, a complete classification of the unital idempotent compressible subalgebras of $\mathbb{M}_3(\mathbb{C})$ is obtained up to similarity and transposition. It is shown that in this setting, the two notions of compressibility agree: a unital subalgebra of $\mathbb{M}_3(\mathbb{C})$ is projection compressible if and only if it is idempotent compressible. Our findings are extended to algebras of arbitrary size in the sequel to this paper.Comment: 23 page