It is consistent that there is a partial order (P,≤) of size א1 such that every monotone function f : P → P is first order definable in (P,≤) It is an open problem whether there can be an infinite lattice L such that every monotone function from L to L is a polynomial. Kaiser and Sauer [KS] showed that such a lattice would have to be bounded, and cannot be countable. Sauer then asked the weaker...

In the first two sections, we review the Block-Wilson-PremetStrade classification of restricted simple Lie algebras. In the third section, we compute their infinitesimal deformations. In the last section, we indicate some possible generalizations by formulating some open problems. 1. Restricted Lie algebras We fix a field F of characteristic p > 0 and we denote with Fp the prime field with p el...

The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.

A study was made pertaining to the variations in sensitivity to inhibitors that may be encountered in industrial deterioration problems. The results indicate that at least three types of variations are involved: first, the variation in sensitivity of different strains, secondly, the variation in sensitivity of an individual strain, and finally, the variation produced by the particular environme...