Dense Banach subalgebras of the null sequence algebra which do not satisfy a differential seminorm condition

Physical Variational Principles Which Satisfy the Palais-smale Condition

1. Using variational techniques we have found conditions which insure the existence of trajectories to conservative dynamical systems which wind around singularities of the potential and are of the following four types: (la) periodic trajectories cutting arbitrary small neighborhoods of the singularities; (lb) periodic trajectories having arbitrary given period; (2a) trajectories joining two fi...

A Model in Which Every Boolean Algebra Has Many Subalgebras

We show that it is consistent with ZFC (relative to large cardinals) that every infinite Boolean algebra B has an irredundant subsetA such that 2|A| = 2|B|. This implies in particular that B has 2|B| subalgebras. We also discuss some more general problems about subalgebras and free subsets of an algebra. The result on the number of subalgebras in a Boolean algebra solves a question of Monk from...

On subalgebras of an evolution algebra of a "chicken" population

We consider an evolution algebra which corresponds to a bisexual population with a set of females partitioned into finitely many different types and the males having only one type. For such algebras in terms of its structure constants we calculate right and plenary periods of generator elements. Some results on subalgebras of EACP and ideals on low-dimensional EACP are obtained.

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

A New Class of Banach Sequence Spaces