We provide an alternative, simpler proof of the existence of thick triangulations for noncompact C 1 manifolds. Moreover, this proof is simpler than the original one given in [13], since it mainly uses tools of elementary differential topology. The role played by curvatures in this construction is also emphasized.

We provide an alternative, simpler proof of the existence of thick triangulations for noncompact C 1 manifolds. Moreover, this proof is simpler than the original one given in [1], since it mainly uses tools of elementary differential topology. The role played by curvatures in this construction is also emphasized.

In a previous paper we derived an expression for the di erentials in the Lyndon-Hochschild-Serre spectral sequence of a split extension G = HoQ of nite groups with coe cients in a eld. Here we apply that result to the case where H and Q are elementary abelian 2-groups and char k = 2. We then work out a special case, in which H has rank 4 and Q has rank 2, from a class of examples constructed by...

Consider any nilpotent group G of finite odd order. We ask if we can always find a galois extension K of Q such that Gal(K/Q) ∼= G. This is the famous Inverse Galois Problem applied to nilpotent groups of finite odd order. By solving the Group Extension Problem and the Embedding Problem, two problems that are related to the Inverse Galois Problem, we show that such a K always exists. A major re...

Let rk(n) denote the number of representations of n as a sum of k squares and tk(n) the number of representations of n as a sum of k triangular numbers. We give an elementary, combinatorial proof of the relations rk(8n+ k) = cktk(n), 1 ≤ k ≤ 7, where c1 = 2, c2 = 4, c3 = 8, c4 = 24, c5 = 112, c6 = 544 and c7 = 2368.

This study examines educators’ perceived barriers to technology integration and the relationship to education reform. Educators and administrators from four elementary schools in Washington State were interviewed in their classrooms during a three-month period. The schools differed in size, location, and social economic status and reported variances in their Washington Assessment of Student Lea...

ELEMENTARY CLASSES INDUCED BY TILTING AND COTILTING MODULES HAVE FINITE CHARACTER

Three results dealing with probability distributions (p, q) over a two-element set are presented. The first two give bounds for the entropy function H(p, q) and are referred to as the logarithmic and the power-type bounds, respectively. The last result is a refinement of well known Pinsker-type inequalities for information divergence. The refinement readily extends to general distributions, but...