The paper is essentially a continuation of [PZ], whose main notion is that of logic-geometrical equivalence of algebras (LG-equivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate it to LG-equivalence. We show that these notions coincide. The idea of the type is one of the central ideas ...

An irreducible algebraic Z d-action on a compact abelian group X is a Z d-action by automorphisms of X such that every closed,-invariant subgroup Y (X is nite. We prove the following result: if d 2, then every measurable conjugacy between irreducible and mixing algebraic Z d-actions on compact zero-dimensional abelian groups is aane. For irreducible, expansive and mixing algebraic Z d-actions o...

Abstract The literature on the metaphysics of gender is partially marked by a tension between conceptions that understand categories as importantly at least partly self-determined identities and those them social or cultural imposed upon others tool oppression. I argue this can be mediated understanding essentially contested. then draw “radical functionalism” to that, while, divorced context, c...

This is a survey of essentially normal operators and related developments. There is an overview of Weyl–von Neumann theorems about expressing normal operators as diagonal plus compact operators. Then we consider the Brown–Douglas–Fillmore theorem classifying essentially normal operators. Finally we discuss almost commuting matrices, and how they were used to obtain two other proofs of the BDF t...

The Perron-Frobenius Theorem for irreducible higher order tensors does not guarantee simplicity of the unique positive eigenvalue nor does it guarantee the unique positive eigenvalue is strictly larger than the modulus of any other eigenvalue. Irreducibility of a tensor in relation to a graph is studied. A higher order tensor is essentially positive if it takes the positive cone to its interior...

For an essentially small triangulated category $\mathcal{T}$, we introduce the notion of prime thick subcategories and define spectrum which shares basic properties with a tensor introduced by Balmer. We mainly focus on categories that appear in algebraic geometry such as derived singularity noetherian scheme $X$. prove certain classes are these categories. Furthermore, use this result to show ...

The following case of the Determinantal Conjecture of Marcus and de Oliveira is established. Let A and C be hermitian n × n matrices with prescribed eigenvalues a1, . . . , an and c1, . . . , cn, respectively. Let κ be a non-real unimodular complex number, B = κC, bj = κcj for j = 1, . . . , n. Then det(A− B) ∈ co 8< : n Y j=1 (aj − bσ(j)); σ ∈ Sn 9= ; , where Sn denotes the group of all permut...

The notion of an essentially slant Toeplitz operator on the space L is introduced and some of the properties of the set ESTO(L), the set of all essentially slant Toeplitz operators on L, are investigated. In particular the conditions under which the product of two operators in ESTO(L) is in ESTO(L) are discussed. The notion is generalized to kth-order essentially slant Toeplitz operators. The n...