On a product of universal hyperalgebras
Abstract We introduce and study a new operation of product of universal hyperalgebras which lies, with respect to set inclusion, between the cartesian product of the hyperalgebras and the cartesian product of their idempotent hulls. We give sufficient conditions for the validity of the first exponential law and a weak form of the second exponential law for the direct power of universal hyperalgebras with respect to the product introduced.
FOR GENERALIZED ARITHMETIC
. A classical theorem of Fritz John allows one to describe a convex body, up to constants, as an ellipsoid. In this article we establish similar descriptions for generalized (i.e. multidimensional) arithmetic progressions in terms of proper (i.e. collision-free) generalized arithmetic progressions, in both torsion-free and torsion settings. We also obtain a similar characterization of iterated sumsets in arbitrary abelian groups in terms of progressions, thus strengthening and extending recent results of Szemer´edi and Vu.
Shoeless Joe: Fantasy and the Humor of Fellow-Feeling
In his essay on Jean Paul Friedrich Richter, Thomas Carlyle writes of a humor that manifests itself in smile rather than laughter. "Richter is a man of mirth," says Carlyle, whose humor is "capricious . . . quaint . . . [and] heartfelt" (15). The three adjectives represent for Carlyle the essence of what he terms "true humor" because they suggest Richter's enormous respect for humanity. "True humor," he goes on to say, "springs not more from the head than from the heart; it is not contempt, its essence is love; it issues not in laughter, but in still smiles, which lie far deeper" (17). These smiles are not Hobbesian smirks of superiority1 but genuine signs of compassion for, sympathy toward, and empathy with the object of the humor. Carlyle further provides a direct link between humor and both pathos and nobility; the link is the smile of the caring man. For Carlyle, this smile is one of "fellow-feeling":