Independent Internationalism and Nationalistic Pragmatism: The United States and Mexico Relations during the 1920s

Villarreal Ríos, Rodolfo, M.A., Autumn 2008 History Independent Internationalism and Nationalistic Pragmatism: The United States and México Relations during the 1920s. Chairperson: Michael S. Mayer During the 1920s, relations between the United States and Mexico revealed the extent to which the U.S. actively engaged in foreign affairs and demonstrated the process by which México defined a new era of its international relations while facing a reconstruction in internal politics. Decades ago, William Appleman Williams refuted the stereotype of American isolationism, arguing that the administrations of Presidents Harding, Coolidge, and Hoover engaged in diplomacy, even where they conducted diplomacy through public silence and backstage negotiations. Later, Joan Hoff defined American foreign policy as independent internationalism, characterized by an amalgamation of ideological and economic considerations. On the Mexican side, presidents, Obregón, Elías Calles, and Portes Gil, approached diplomacy with a nationalistic pragmatism that recognized the need for new rules governing the participation of foreigners in the economy and in religious matters. Despite their seemingly draconian nature, these new rules left room for negotiations. Three main issues influenced U.S.-Mexican relations. The rights of American oil companies in México were settled in 1923 through the Bucareli Agreements. In 1927, when a new Petroleum law was enacted, American Ambassador Dwight Morrow conducted the negotiations which lead the Mexican Supreme Court to eliminate the provisions that placed time limits on foreign concessions, and the Mexican Congress invalidated the retroactivity of such laws. A second point of contention was the Church-State controversy in México. American Catholics demanded direct U.S. intervention, but Coolidge instructed Morrow to work with representatives of the Catholic Church and the Mexican State to achieve a solution that allowed each to function while respecting the other’s field of influence. The successful conclusion of the religious dispute in Mexico allowed Coolidge to avoid the insertion of a potentially poisonous issue into the 1928 presidential elections. These events demonstrated that the U. S. was anything but isolationist in the 1920s. The religious controversy offered an example of how domestic determinants influenced foreign policy and, at the same time, demonstrated how foreign policy could enter the American domestic political arena. The American intervention in the religious conflict of the 1920s shaped United States-México relations for the rest of the 20th Century

The gap between a variational problem and its occupation measure relaxation

Recent works have proposed linear programming relaxations of variational optimization problems subject to nonlinear PDE constraints based on the occupation measure formalism. The main appeal of these methods is the fact that they rely on convex optimization, typically semidefinite programming. In this work we close an open question related to this approach. We prove that the classical and relaxed minima coincide when the dimension of the codomain of the unknown function equals one, both for calculus of variations and for optimal control problems, thereby complementing analogous results that existed for the case when the dimension of the domain equals one. In order to do so, we prove a generalization of the Hardt-Pitts decomposition of normal currents applicable in our setting. We also show by means of a counterexample that, if both the dimensions of the domain and of the codomain are greater than one, there may be a positive gap. The example we construct to show the latter serves also to show that sometimes relaxed occupation measures may represent a more conceptually-satisfactory "solution" than their classical counterparts, so that -- even though they may not be equivalent -- algorithms rendering accessible the minimum in the larger space of relaxed occupation measures remain extremely valuable. Finally, we show that in the presence of integral constraints, a positive gap may occur at any dimension of the domain and of the codomain.Comment: 46 pages, 10 figure