We study the arithmetic codings of hyperbolic automorphisms of the 2torus, i.e. the continuous mappings acting from a certain symbolic space of sequences with a finite alphabet endowed with an appropriate structure of additive group onto the torus which preserve this structure and turn the two-sided shift into a given automorphism of the torus. This group is uniquely defined by an automorphism,...

let $mathcal {a} $ and $mathcal {b} $ be c$^*$-algebras. assume that $mathcal {a}$ is of real rank zero and unital with unit $i$ and $k>0$ is a real number. it is shown that if $phi:mathcal{a} tomathcal{b}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $phi(|a|^k)=|phi(a)|^k $ for all normal elements $ainmathcal a$, $phi(i)$ is a projection, and there exists a posit...

Using a result of Orlov on Fourier-Mukai transforms we construct a homomorphism from the automorphism group of the derived category to the automorphism group of the Mukai lattice on a K3 surface. Applying Mukai's moduli space construction we show that this homomorphism is surjective up to index 2. Let X be a projective K3 surface over the eld C. Its singular cohomology H∗(X,Z) is free of rank 2...

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

Abstract This paper provides a systematic matrix description for finite Boolean- type algebras (BTAs). A BTA is decomposed into Boolean-type lattice (BTL) and complementation algebra (CA). When the object set finite, expressions of BTL CA (and then BTA) are presented. Via their expression, construction certain properties BTAs investigated, including homomorphism isomorphism, as well decompositi...

Based on a completely distributive lattice M , we propose new fuzzification approach to module, which leads the concept of an id="M2"> -hazy module. Different from traditional that defines fuzzy algebra as subset classical algebra, introduce id="M3"> module by fuzzifications algebraic operations. Then, investigate fundam...

A [semi-]continuous real function of a frame (locale) L has up to now been understood as a frame homomorphism from the frame L(R) of reals into L [as a frame homomorphism (modulo some conditions) from certain subframes of L(R) into L]. Thus, these continuities involve different domains. It would be desirable if all these continuities were to have L(R) as a common domain. This paper demonstrates...

Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

Encoding and indexing of lattice codes is generalized from self-similar lattice codes to a broader class of lattices. If coding lattice Λc and shaping lattice Λs satisfy Λs Ď Λc, then Λc{Λs is a quotient group that can be used to form a (nested) lattice code C. Conway and Sloane’s method of encoding and indexing does not apply when the lattices are not self-similar. Results are provided for two...