By Ernst Breisach
American revolutionary heritage is the 1st publication to narrate the tale of innovative historical past via all its ameliorations from its emergence within the early 1900s to its death within the 1940s.Focusing his account at the paintings of the movement's most vital representatives—including Charles Beard, James Harvey Robinson, and Carl Becker—Ernst Breisach demonstrates that revolutionary historical past is special via its distinctive mixture of ideals within the goal fact of historic evidence and its religion within the inevitability of the growth of the human race. And even though he discusses at size Frederick Jackson Turner's contributions to the construction of a contemporary American historiography, Breisach units him except the students who formed revolutionary history.While revolutionary historical past is mostly taken care of in isolation from simultanieous pursuits in eu historiography, Breisach exhibits the way it was once formulated within the face of an analogous cultural pressures confronting ecu historians. certainly, it turns into transparent that until eventually the Nineteen Thirties the innovative historians' self assurance within the validity of ancient research and the development of civilization shielded American historians from the skepticism and cultural pessimism which characterised lots of their ecu contempories.Breisach's highly huge and refined research unearths American innovative historical past to be an enormous and cutting edge test within the foreign quest for a brand new background, in addition to a coherent college of proposal in its personal correct.
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Extra resources for American Progressive History: An Experiment in Modernization
Co ~ E E ,:!. '~-~T ~ ~ - - - - - -- - ~ ---- ~o THEORY OF MINIMAL SURFACES 45 Graph of area of minimal surfaces is represented by a many-valued function Figure 33i-j 46 THE PLATEAU PROBLEM: PART ONE in Fig. 33b. Let this thread lie on the film of type Ic freely, that is, no forces act on it. We shall slightly deform the contour. While moving the right-hand circles apart, we see that a part of the film bends to the left, and the thread stretches tight. Similarly, on moving the left-hand circles apart, we see that the film deforms and the thread stretches tight while bending to the right.
The equation describing the critical stationary surfaces is (1 + f~) f)ry - 2 fx fy fxy + (1 + f;) fxx = O. , minimal surfaces, in relation to the nature of the boundary contour. As it happens, for any closed, piecewise-smooth contour "I' whose projection into the convex, closed curve "I on the plane is one-to-one, there exists a minimal surface with given boundary, projected, therefore, onto the domain bounded on the plane by the curve "I. THEORY OF MINIMAL SURFACES 51 The existence and uniqueness of this solution in the indicated class of surfaces admitting of a one-to-one projection is a corollary to the boundary projection being convex.
A mapping of a circle (or system of circles), should be fixed in R3. Thus, the set of all boundary conditions is naturally identified with the space Coo (oM,N) of mappings g: oM-N. Recall that the specification ofa boundary condition g: oM ~ N defines, generally speaking, several extremals fo of the functional F. e. such that fo IaM = g. We associate each boundary condition g: oM--+ N with the set Kg of the extremals fo: M--+N corresponding to it. For each extremal fo E Kg, we calculate the value F(Q, that is, the value of the functional F on the given extremal.