For every countable group G, a family of isomorphism invariants for measurepreserving G-actions on probability spaces is defined. In the special case in which G is a countable sofic group, a special class of these invariants are computed exactly for Bernoulli systems over G. This leads to a complete classification of Bernoulli systems for many countable groups including all finitely generated l...

In this paper, we investigate even-order linear difference equations and their criticality. However, restrict our attention only to several special cases of the general Sturm–Liouville equation. We wish on such a possible converse known theorem. This theorem holds for second-order as an equivalence; however, one implication is equations. First, show in sense term Later, upper bound criticality ...

Solving linear system of equations Ax = b enters into many scientific applications. In this paper, we consider a special kind of linear systems, the matrix A is an equivariant matrix with respect to a finite group of permutations. Examples of this kind are special Toeplitz matrices, circulant matrices, and others. The equivariance property of A may be used to reduce the cost of computation for ...