Book review of Aya Fujiwara. Ethnic Elites and Canadian Identity: Japanese, Ukrainians, Scots, 1919-1971. U Manitoba P, 2012. Studies in Immigration Culture 7, edited by Royden Loewen. xii, 260 pp. Tables. Notes. Selected Bibliography. Index. $27.95, paper.

Abstract We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that heat semigroup is ultracontractive we unique solvability non-empty subgraphs with respect to vertex boundary and provide analytic probabilistic representations solutions. A second result deals canonically compactifiable graphs Royden provides conditions representations.

Essentially nothing found here is original except for a few mistakes and misprints here and there. These lecture notes are based on material from the following books: H. Royden " Real Analysis " , L. Evans and R. Gariepy " Measure Theory and Fine Properties of Functions " , J. Duoandikoetxea " Fourier Analysis " , and M. Pinsky " Introduction to Fourier Analysis and Wavelets " .

We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold (M, J) admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in M and to give a sufficient condition for the complete hyperbolicity of a domain in (M, J).

It is well-known that the Hölder-Rogers inequality implies the Minkowski inequality. Infantozzi [6] observed implicitely and Royden [15] proved explicitely that the reverse implication is also true. In this note we discuss and give a new proof of this perhaps surprising fact. Mathematics subject classification (2000): 26D15.

The Kobayashi indicatrix (infinitesimal unit ball) of a domain in IE n is known to be a biholomorphic invariant. In particular, if a domain is biholomorphic to a ball, then the indicatrix is the ball. Until the recent deep results of Lempert [4], it was not known to what extent the indicatrix characterizes the domain. Sibony had shown earlier that the indicatrix of any pseudoconvex circular dom...