Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory, called BNA (Basic Network Algebra), is presented. BNA, which is essentially a part of the algebra of flownomials, captures the basic algebraic properties of networks. For synchronous and asynchronous dataflow networks, additional constants and axioms for conn...

A theorem of V. L. Klee, Jr. [9] asserts that any homeomorphism between two compact sets in a separable, infinite-dimensional Hilbert space can be extended to a homeomorphism of the entire space onto itself. Since it has recently been shown ( [ l ] , [5] and [6]) that all separable, infinite-dimensional Frechet spaces are homeomorphic (a Frechet space being a metrizable, complete, locally conve...

2,3-Dihydroxybenzylic esters with Frechet-type dendritic branches as the alcohol component form, in a hierarchical self-assembly process, disk shaped dendrimers when titanium(IV) and lithium ions are added.

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to r...

Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

A long-standing problem that arises when constructing the mathematical apparatus of quantum mechanics is need to work with unbounded operators. Since space nuclear operators preconjugate for algebra all bounded operators, we can consider states a system as and observables. In this case, taking trace product operator (a state) observable) gives average value observable in fixed state. The existe...

We consider two versions of the uniform Roe algebra for uniformly discrete spaces without bounded geometry and discuss some their properties.

Let Φ be a root system and let Φ(Zp) be the standard Chevalley Zp-Lie algebra associated to Φ. For any integer t > 1, let G be the uniform pro-p group corresponding to the powerful Lie algebra pΦ(Zp) and suppose that p > 5. Then the Iwasawa algebra ΩG has no nontrivial reflexive ideals. This was previously proved by authors for the root system A1.

The minimal twist map introduced by Abdesselam et al [1] for the nonstandard (Jordanian) quantum sl(2,R) algebra is used to construct the twist maps for two different non-standard quantum deformations of the (1+1) Schrödinger algebra. Such deformations are, respectively, the symmetry algebras of a space and a time uniform lattice discretization of the (1 + 1) free Schrödinger equation. It is sh...

in the present paper, the concepts of module (uniform) approximate amenability and contractibility of banach algebras that are modules over another banach algebra, are introduced. the general theory is developed and some hereditary properties are given. in analogy with the banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...