Canonical Coordinates and Natural Equation for Lorentz Surfaces in R13

We consider Lorentz surfaces in R13 satisfying the condition H2−K≠0, where K and H are the Gaussian curvature and the mean curvature, respectively, and call them Lorentz surfaces of general type. For this class of surfaces, we introduce special isotropic coordinates, which we call canonical, and show that the coefficient F of the first fundamental form and the mean curvature H, expressed in terms of the canonical coordinates, satisfy a special integro-differential equation which we call a natural equation of the Lorentz surfaces of a general type. Using this natural equation, we prove a fundamental theorem of Bonnet type for Lorentz surfaces of a general type. We consider the special cases of Lorentz surfaces of constant non-zero mean curvature and minimal Lorentz surfaces. Finally, we give examples of Lorentz surfaces illustrating the developed theory.

“Unfrenchifying” Quebec

In keeping with the overall theme of the contested nature of British rule, this chapter investigates the establishment of the first French-language newspaper, Le Canadien, demonstrating the way in which the French Canadian political opposition appropriated the tenets of classical republicanism to break the natural equation between Britishness and liberty. Because of this move, the English press was compelled to embrace Court Whig political discourse so that political allegiances and ideologies were now synonymous with two ethnic political factions. The discourse of political opposition was not derived from the model of the American Republic, as historians have previously contended, but was adapted from a longstanding mode of political argument within the colony and was driven by an often stridently anti-Catholic and anti-French British nationalism.

Lines on the surface in the quasi-hiperbolic space 11^S1/3

Quasi-hyperbolic spaces are projective spaces with decaying abso­lute. This work is a continuation of the author's work [7], in which surfac­es in one of these spaces are examined by methods of external forms and a moving frame. The semi-Chebyshev and Chebyshev net­works of lines on the surface in quasi-hyperbolic space are considered. In this pa­per we use the definition of parallel transfer adopted in [6]. By analogy with Euclidean geometry, the semi-Chebyshev network of lines on the surface is the network in which the tangents to the lines of one family are carried parallel along the lines of another family. A Che­byshev network is a network in which tangents to the lines of each family are carried parallel along the lines of another family. We proved three theorems. In Theorem 1, we obtain a natural equa­tion for non-geodesic lines that are part of a conjugate semi-Chebyshev network on the surface so that tangents to lines of another family are transferred in parallel along them. In Theorem 2, the natural equation of non-geodesic lines in the Chebyshev network is obtained. In Theorem 3 we prove that conjugate Chebyshev networks, one family of which is nei­ther geodesic lines, nor Euclidean sections, exist on surfaces with the lati­tude of four functions of one argument.

Half conformally flat generalized quasi-Einstein manifolds of metric signature (2,2)

We provide classification results for and examples of half conformally flat generalized quasi-Einstein manifolds of signature [Formula: see text]. This analysis leads to a natural equation in affine geometry called the affine quasi-Einstein equation that we explore in further detail.

The Financier Himself: Dreiser and C. T. Yerkes

In his Trilogy of Desire, Theodore Dreiser presented a virtual biography of the model (Charles T. Yerkes, Jr.) for his central character (Frank A. Cowperwood). Dreiser's connection with Yerkes dated from the 1880's in Chicago, continued through the 1890's when both men moved to New York, and extended past 1905, when Yerkes died, and 1910, when The Financier was begun. Yerkes, a man of many facets, was selected by Dreiser as model for the generic millionaire principally because the dissolution of his estate after 1905 demonstrated Dreiser's theory of the natural “Equation Inevitable” in action. The events portrayed in The Financier, The Titan, and The Stoic followed verbatim the events of Yerkes' life as established in Dreiser's working notes and verified by newspapers, periodicals, and books of the era. In this central fictional figure also is found a clear, though submerged, portrait of Dreiser's own hopes and desires.