Module 10: Introduction to Fusion 360 Part II

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Introduction to Part II of the Special Issue

We are appreciative of the voices that are constantly being raised around the world, and the public discourse centered on unsettling systemic racism, anti-Blackness practices, discrimination and other related prevailing social issues. We believe that these voices in conversation signal that the stronghold of silencing among activists, abolitionists, and all other allies and co-conspirators in this space is being dismantled as we speak and write. We are also aware that dialogues must move to actions and concrete strategies for justice. We developed this two-part special issue around the themes of anti-racist and racial justice praxis to illuminate actions happening locally, nationally and globally, and how the work of anti-racism/racial justice might be adapted, integrated or used as guides for ongoing racial justice and social progress. These articles represent a call for a participatory, action oriented and decolonial liberatory standpoint rather than a bystander or deficit approach

Generalized geometry lectures on type II backgrounds

The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some past and recent results on the generalized complex structure of supersymmetric type II vacua in various dimensions.Comment: 34 pages, 5 figure

Introduction to Diophantine Approximation. Part II

In the article we present in the Mizar system [1], [2] the formalized proofs for Hurwitz’ theorem [4, 1891] and Minkowski’s theorem [5]. Both theorems are well explained as a basic result of the theory of Diophantine approximations appeared in [3], [6]. A formal proof of Dirichlet’s theorem, namely an inequation |θ−y/x| ≤ 1/x2 has infinitely many integer solutions (x, y) where θ is an irrational number, was given in [8]. A finer approximation is given by Hurwitz’ theorem: |θ− y/x|≤ 1/√5x2. Minkowski’s theorem concerns an inequation of a product of non-homogeneous binary linear forms such that |a1x + b1y + c1| · |a2x + b2y + c2| ≤ ∆/4 where ∆ = |a1b2 − a2b1| ≠ 0, has at least one integer solution.Suginami-ku Matsunoki 3-21-6 Tokyo, JapanGrzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi: 10.1007/978-3-319-20615-8 17.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191-198, 2015. doi: 10.1007/s10817-015-9345-1.G.H. Hardy and E.M. Wright. An Introduction to the Theory of Numbers. Oxford University Press, 6th edition, 2008.Adolf Hurwitz. Ueber die angenäherte Darstellung der Irrationalzahlen durch rationale Brüche. Mathematische Annalen, 39(2):279-284, B.G.Teubner Verlag, Leipzig, 1891.Hermann Minkowski. Diophantische Approximationen: eine Einf¨uhrung in die Zahlentheorie. Teubner, Leipzig, 1907.Ivan Niven. Diophantine Approximation. Dover, 2008.Tetsuya Tsunetou, Grzegorz Bancerek, and Yatsuka Nakamura. Zero-based finite sequences. Formalized Mathematics, 9(4):825-829, 2001.Yasushige Watase. Introduction to Diophantine approximation. Formalized Mathematics, 23(2):101-106, 2015. doi: 10.1515/forma-2015-0010.25428328

Gender Equality and Customary Marriage: Bargaining in the Shadow of Post-Apartheid Legal Pluralism

This Report represents the culmination of a year-long project undertaken by the Crowley Program in International Human Rights at the Fordham Law School to study issues surrounding women and customary law marriages in South Africa in light of its international legal commitments. This Report presents the findings of this research effort. Following this introduction, Part I of this Report describes South Africa\u27s international and domestic legal obligations regarding culture and gender equality, particularly with respect to marriage, divorce, and family formation. Part I then sketches two distinct approaches to the tension between customary law and gender equality, both of which may be found in the domestic law regulating the family. Part II evaluates the effectiveness of the two approaches with reference to data collected in the course of several hundred interviews with South African men and women in May and June 2006. Part II also offers tentative conclusions and suggestions for reform