Crystal frameworks, symmetry and affinely periodic flexes

Symmetry equations are obtained for the rigidity matrices associated with various forms of infinitesimal flexibility for an idealised bond-node crystal framework \C in \bR^d. These equations are used to derive symmetry-adapted Maxwell-Calladine counting formulae for periodic self-stresses and affinely periodic infinitesimal mechanisms. The symmetry equations also lead to general Fowler-Guest formulae connecting the character lists of subrepresentations of the crystallographic space and point groups which are associated with bonds, nodes, stresses, flexes and rigid motions. A new derivation is also given for the Borcea-Streinu rigidity matrix and the correspondence between its nullspace and the space of affinely periodic infinitesimal flexes.Comment: This preprint has some new diagrams and clarifications. A final version will appear in the New York Journal of Mathematic

Apartheid Baltimore Style: The Residential Segregation Ordinances of 1910-1913

On May 15, 1911, Baltimore Mayor J. Barry Mahool signed into law an ordinance for “preserving the peace, preventing conflict and ill feeling between the white and colored races in Baltimore City.” This ordinance provided for the use of separate blocks by African American and whites and was the first such law in the nation directly aimed at segregating black and white homeowners. This article considers the historical significance of Baltimore’s first housing segregation law