Floating body, illumination body, and polytopal approximation

Let $K$ be a convex body in $\Bbb R^{d}$ and $K_{t}$ its floating bodies. There is a polytope with at most $n$ vertices that satisfies $$K_{t} \subset P_{n} \subset K$$ where $$n \leq e^{16d} \frac{vol_{d}(K \setminus K_{t})}{t\ vol_{d}(B_{2}^{d})}$$ Let $K^{t}$ be the illumination bodies of $K$ and $Q_{n}$ a polytope that contains $K$ and has at most $n$ $d-1$-dimensional faces. Then $$vol_{d}(K^{t} \setminus K) \leq cd^{4} vol_{d}(Q_{n} \setminus K)$$ where $$ n \leq \frac{c}{dt} \ vol_{d}(K^{t} \setminus K) $

Effects of UN Peacekeeping Missions

Of everything the United Nations does, probably one its most scrutinized programs is its peacekeeping missions across the globe. Even though humanity is experiencing an unprecedented level of peace, deadly civil wars still occur across the world, especially in developing nations. The UN has become involved in many of these conflicts, sending peacekeeping forces to the country in crisis. UN peace efforts are very important because they have the potential to save thousands of lives and preventing the further damages of war. It is for this reason that it is vital to examine the UN peacekeeping missions and evaluate the outcomes these have produced. My research into this question will briefly look at the process of peacekeeping and its results based on reports after peacekeeping missions leave the nation in question. The overall question I seek to answer is “Do UN peacekeeping forces leave a civil war-stricken country in a better or worse condition since they have arrived?”. Essentially I seek to asses the UN’s effectiveness in peacekeeping overall. In order to find an answer to this question, I will examine various scholarly debates and papers all evaluating the UN’s performance in various conflicts. These papers range in backgrounds and hypotheses but they break down these conflicts into various tests in order to identify the outcomes and come to a general conclusion. Each of these studies also highlights specific conflicts as examples in support of their argument, thus providing the research with more credibility, while still showing the vast complication of peacekeeping. UN peacekeeping forces, in the majority of cases, fail to bring about stable peace in civil wars. I believe this because, from what I have seen, there seems to be a lot of civil wars that keep occurring or fail to stop, for example, Syria. While Syria has caught quite the attention and action of the UN, its war has no end in sight. Conflicts in various African nations such as Somalia fail to end as well, thus bringing me to what I hypothesize

Some facts about functionals of location and scatter

Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for $d\geq 2$, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they must be identically 0. Results are stated on existence and differentiability of location and scatter functionals, defined on a weakly dense, weakly open set of laws, via elliptically symmetric t distributions on ${\Bbb{R}}^d$, following up on work of Kent, Tyler, and D\"{u}mbgen.Comment: Published at http://dx.doi.org/10.1214/074921706000000860 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Confronting the Concept of Intersectionality: The Legacy of Audre Lorde and Contemporary Feminist Organizations

Audre Lorde was one of many women to criticize second wave feminism for overlooking issues of intersectionality. This paper examines the ways in which Lorde introduced intersectionality into feminist discourse and how feminist organizations embrace this concept today. Five organizations are examined (National Organization for Women, Grand Valley State University Women’s Center, Ms. Foundation, Third Wave Foundation, and Guerilla Girls) by interviewing representatives and/or evaluating websites to assess organizational mission, vision, values and practices. Analyses reveal that all five organizations have specific policy statements addressing intersectionality. This research can conclusively say that intersectionality is at least considered by all of the organizations. Determining whether or not the current intervention strategies are effective for women experiencing overlapping oppressions is beyond the scope of this study. The different rhetoric used by each organization to address the intersectional issue, however, suggests that intersectionality is “applied” or put into practice differently by different organizations

Construction and analysis of a fourth grade geography test

Thesis (Ed.M.)--Boston Universit

Legal Limits on Religious Conversion in India

In contemporary India, government assessments of the legitimacy of conversions tend to rely on two assumptions: first, that people who convert in groups may not have freely chosen conversion, and second, that certain groups are particularly vulnerable to being lured into changing their religion. These assumptions, which pervade the anticonversion laws as well as related court decisions and government committee reports, reinforce social constructions of women and lower castes as inherently naive and susceptible to manipulation. Here, Jenkins contends to carefully scrutinized the assumptions since like protective laws in many other contexts, such laws restrict freedom in highly personal, individual choices

Refrigerated cutting tools improve machining of superalloys

Freon-12 applied to tool cutting edge evaporates quickly, leaves no residue, and permits higher cutting rate than with conventional coolants. This technique increases cutting rate on Rene-41 threefold and improves finish of machined surface