We show that the sequence ? jIm(z n)j is never monotone when z is a non-real complex number, and ? jRe(z n)j is never monotone, unless z = re ii , where = k m for some odd m, and r is suuciently large or suuciently small. Similar results hold for the length of the projection of z n onto any line through the origin. The purpose of this note is to prove a simple, amusing and apparently new applic...

A 23-year old man was presented with multiple papules andnodules (25 lesions) on the trunk and proximal extremities(Figure 1). Two or three lesions were appeared at childhood andincreased to 25 lesions in early adulthood. There were variationsin size from several millimeters to 2 cm with spontaneous andinducible pain especially in exposure to the cold environment.Same lesions were present in hi...

compound n2, n3, n7, n8, 1, 4, 5, 6, 9, 10-decaphenyltetradecahydrodipyrazino [2, 3-b: 2, 3-e] pyrazine-2, 3, 7, 8-tetraamine (4) was prepared by condensation of 1, 1′, 2, 2′-tetrakis (phenylamino) ethane (1d) and glyoxal in etoh or i-proh. also, reaction of 1d with glyoxal in equimolare in etoh resulted 5,6-bis (ethoxy)-n2, n3, 1, 4-tetraphenylhexahydro-2, 3-pyrazinediamine (5). the natures of...

The topic of this lecture is the application of triangulations to shortest path problems. Only simple polygons will be considered. Given two points inside a polygon, the goal is to find the shortest path lying inside the polygon between the two points; see Fig. 1. One can think of the shortest path as a taut string connecting the two points. We begin with some definitions. Let P be a simple pol...

The virtually unprecedented popularity of Harriet Beecher Stowe's Uncle Tom's Cabin (1852) in the United States and England was no less marked in France, as evidenced among other things by the commercial success of the eleven French translations that were produced within the period of ten months after its original publication. This and other indications of the significance of Stowe's novel for ...