Rothberger gaps in fragmented ideals

The~\emph{Rothberger number} $\mathfrak{b} (\mathcal{I})$ of a definable ideal $\mathcal{I}$ on $\omega$ is the least cardinal $\kappa$ such that there exists a Rothberger gap of type $(\omega,\kappa)$ in the quotient algebra $\mathcal{P} (\omega) / \mathcal{I}$. We investigate $\mathfrak{b} (\mathcal{I})$ for a subclass of the $F_\sigma$ ideals, the fragmented ideals, and prove that for some of these ideals, like the linear growth ideal, the Rothberger number is $\aleph_1$ while for others, like the polynomial growth ideal, it is above the additivity of measure. We also show that it is consistent that there are infinitely many (even continuum many) different Rothberger numbers associated with fragmented ideals.Comment: 28 page

Apollo experience report the command and service module milestone review process

The sequence of the command and service module milestone review process is given, and the Customer Acceptance Readiness Review and Flight Readiness Review plans are presented. Contents of the System Summary Acceptance Documents for the two formal spacecraft reviews are detailed, and supplemental data required for presentation to the review boards are listed. Typical forms, correspondence, supporting documentation, and minutes of a board meeting are included

Educational Program to Improve Care for the Lesbian, Gay, Bisexual and Transgender (LGBT) Patient

focus of this capstone project is to explore the impact of registered nurses’ bias and lack of knowledge associated with the care of the LGBT patient. A Quasiexperimental design was used to evaluate the cause-and-effect relationship of an educational intervention. This intervention provided LGBT cultural knowledge and provides evidence regarding how homophobia and transphobia among nurses creates and perpetuates disparities among LGBT people. Attitude and knowledge assessment tools were used to collect responses from participant’s pre and post intervention. Using parametric and descriptive statistics, the participants’ data were analyzed. There were no statistically significant differences between the pre and post intervention scores. Although statistical significance was lacking, clinical significance was inferred by the participants’ knowledge gap in their posed questions at the conclusion of the educational intervention. The implementation of similar training sessions, offered in a recurring fashion, will likely be necessary to effectively decrease the healthcare disparities currently being experienced by the LGBT population

Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page

Separating cardinal characteristics of the strong measure zero ideal

Let $\mathcal{SN}$ be the $\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{SN}$ after finite support iterations. This is applied to force that the four cardinal characteristics associated with $\mathcal{SN}$ are pairwise different: $$\mathrm{add}(\mathcal{SN})<\mathrm{cov}(\mathcal{SN})<\mathrm{non}(\mathcal{SN})<\mathrm{cof}(\mathcal{SN}).$$ Furthermore, we construct a forcing extension satisfying the above and Cicho\'n's maximum (i.e. that the non-dependent values in Cicho\'n's diagram are pairwise different)

A Preliminary List of the Flora of the Perkiomen Region

41 page annotated list of vascular plants collected by the authors in and around the Perkiomen Creek in Montgomery County, Pennsylvania. About the year 1915 Dr. Kline, Brendle and Mumbauer began to make weekly collecting trips. This preliminary catalogue rests mostly upon the work done on these trips. [from the Foreword]https://digitalcommons.ursinus.edu/faculty_books/1011/thumbnail.jp

Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat