Abstract We study automatic injectivity of surjective algebra homomorphisms from $\mathscr{B}(X)$, the (bounded, linear) operators on X, to $\mathscr{B}(Y)$, where X is one following long sequence spaces: c0(λ), $\ell_{\infty}^c(\lambda)$, and $\ell_p(\lambda)$ ($1 \leqslant p \lt \infty$) Y arbitrary. En route proof that these spaces do indeed enjoy such a property, we classify two-sided ideal...

A classic ‘reference’ variable provides an indirect way to access a variable or aggregate. packetC, [1] a language for network packet processing, has specialized requirements for references that apply to aggregates, based on domain-specific, extended data types. The primary functional requirement is to defer selecting particular aggregates until runtime. In addition, requirements for high progr...

This paper presents a dynamic strategy for monitoring the depth of program trees evolved by STEPS (Strongly Typed Evolutionary Programming System). STEPS evolves higher-order functional programs in the form of trees, which are allowed to grow or shrink to fit the size of the problem, via specialised genetic operators. Thus, the need for arbitrary cut-off mechanisms is eliminated.

The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

System F ! is an extension of system F ! with subtyping and bounded quantiication. Order-sorted algebra is an extension of many-sorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higher-order typed-calculus with subtyping, bounded quan-tiication and order-sorted inductive types, i.e. data types with built-in subtyping and overloading. Moreover we show t...

The goal of the Mathemagix project is to develop a new and free software for computer algebra and computer analysis, based on a strongly typed and compiled language. In this paper, we focus on the underlying type system of this language, which allows for heavy overloading, including parameterized overloading with parameters in so called “categories”. The exposition is informal and aims at givin...

The Hodge theory of the de Rham complex in the setting of the Sobolev topology is studied. As a result, a new elliptic boundaryvalue problem is obtained. Next, the Hodge theory of the @-Neumann problem in the Sobolev topology is studied. A new @-Neumann boundary condition is obtained, and the corresponding subelliptic estimate derived. The classical Hodge theory on a domain in R N+1 (or, more g...