Stiff algebras

Consistent examples of atomic Boolean algebras with restricted types of automorphisms are constructed. In particular, the existence of an atomic Hopfian Boolean algebra of size less than 2 is shown to be consistent.Presented by V. Trnková.     

Quinones and quinone methides—V: Further rearrangements of the dimer from 5-methoxy-2-(4-methoxyphenylmethyl)-1,4-benzoquinone

In strongly acid solutions the dimer 3 dissociates to the quinone 1 and quinone methide 2 which recombine with elimination of p-methoxybenzyl alcohol to form the xanthylium salt 9a. With zinc and acetic acid 3 yields isormeric meso- and dl-ethylenediquinol derivatives 14a. Sodium borohydride reduction of 3 yields an alcoholic quinol 5a which rapidly reoxidizes to the spiro-tetrahydrofuran derivative 24a. Possible mechanisms which may be involved in the formation of these rearranged products are discussed.     

Uncountable autohomeomorphism groups of thin-tall locally compact scattered spaces

Under a hypothesis weaker thanCH, both the free group with ₁ generators and the free Abelian group with ₁ generators are non-trivial autohomeomorphism groups of locally compact thin-tall scattered spaces.Presented by V. Trnkova.     

Finite generation of powers of ideals

Suppose is a maximal ideal of a commutative integral domain and that some power of is finitely generated. We show that is finitely generated in each of the following cases: (i) is of height one, (ii) is integrally closed and , (iii) is a monoid domain over a field , where is a cancellative torsion-free monoid such that , and is the maximal ideal . We extend the above results to ideals of a reduced ring such that is Noetherian. We prove that a reduced ring is Noetherian if each prime ideal of has a power that is finitely generated. For each with , we establish existence of a -dimensional integral domain having a nonfinitely generated maximal ideal of height such that is -generated.

     

Efficiency enhancement of high power vacuum BWO's using nonuniformslow wave structures

The Sinus-6, a high-power relativistic repetitively-pulsed electron beam accelerator, is used to drive various slow wave structures in a BWO configuration in vacuum. Peak output power of about 550 MW at 9.45 GHz was radiated in an 8-ns pulse. We describe experiments which study the relative efficiencies of microwave generation from a two-stage nonuniform amplitude slow wave structure and its variations without an initial stage. Experimental results are compared with 2.5 D particle-in-cell computer simulations. Our results suggest that prebunching the electron beam in the initial section of the nonuniform BWO results in increased microwave generation efficiency, Furthermore, simulations reveal that, in addition to the backward propagating surface harmonic of the TM₀₁ mode, backward and forward propagating volume harmonics with phase velocity twice that of the surface harmonic play an important role in high-power microwave generation and radiation