Counterexamples to countable-section Π21 uniformization and Π31 separation

The 1-Section of a Countable Functional

Synthesis and Optimization of Separation Section of MTBE Process

Methyl tertiary butyl ether (MTBE) is known as a promising substitute for tetra ethyl lead (TEL) in order to increase the octane number of gasoline. MTBE process, as many other processes, has two distinguished section, namely reaction section and separation section. In this paper we focus only on synthesis and optimization of separation section of this process. In order to achieve this obje...

Counterexamples to Isosystolic Inequalities

We explore M. Gromov's counterexamples to systolic inequalities. Does the manifold S 2 × S 2 admit metrics of arbitrarily small volume such that every noncontractible surface inside it has at least unit area? This question is still open, but the answer is affirmative for its analogue in the case of S '~ × S n, n > 3. Our point of departure is M. Gromov's metric on S 1 x S 3, and more general ex...

Counterexamples to witness conjectures

Consider the class of exp-log constants, which is constructed from the integers using the field operations, exponentiation and logarithm. Let z be such an exp-log constant and let n be its size as an expression. Witness conjectures attempt to give bounds $(n) for the number of decimal digits which need to be evaluated in order to test whether z equals zero. For this purpose, it is convenient to...

Uniformization and Anti-uniformization Properties of Ladder Systems

Let S denote a stationary subset of limit ordinals of ω1. A ladder system on S is a sequence {Lα : α ∈ S} such that each Lα is an unbounded subset of α of order type ω. A ladder system is uniformizable if for each sequence 〈fα : α ∈ S〉 of functions fα : Lα → ω there is an F : ω1 → ω such that F Lα =∗ fα for each α ∈ S. I.e., for each α ∈ S, {β ∈ Lα : F (β) 6= fα(β)} is finite. We now formulate ...