All-derivable points in nest algebras

Suppose that $\mathscr{A}$ is an operator algebra on a Hilbert space $H$. An element $V$ in $\mathscr{A}$ is called an all-derivable point of $\mathscr{A}$ for the strong operator topology if every strong operator topology continuous derivable mapping $\phi$ at $V$ is a derivation. Let $\mathscr{N}$ be a complete nest on a complex and separable Hilbert space $H$. Suppose that $M$ belongs to $\mathscr{N}$ with $\{0\}\neq M\neq\ H$ and write $\hat{M}$ for $M$ or $M^{\bot}$. Our main result is: for any $\Omega\in alg\mathscr{N}$ with $\Omega=P(\hat{M})\Omega P(\hat{M})$, if $\Omega |_{\hat{M}}$ is invertible in $alg\mathscr{N}_{\hat{M}}$, then $\Omega$ is an all-derivable point in $alg\mathscr{N}$ for the strong operator topology.Comment: 12 pages, late

On a Partial Decision Method for Dynamic Proofs

This paper concerns a goal directed proof procedure for the propositional fragment of the adaptive logic ACLuN1. At the propositional level, it forms an algorithm for final derivability. If extended to the predicative level, it provides a criterion for final derivability. This is essential in view of the absence of a positive test. The procedure may be generalized to all flat adaptive logics.Comment: 18 pages. Originally published in proc. PCL 2002, a FLoC workshop; eds. Hendrik Decker, Dina Goldin, Jorgen Villadsen, Toshiharu Waragai (http://floc02.diku.dk/PCL/

Renormalization of a gapless Hartree-Fock approximation to a theory with spontaneously broken O(N)-symmetry

The renormalization of a gapless Phi-derivable Hartree--Fock approximation to the O(N)-symmetric lambda*phi^4 theory is considered in the spontaneously broken phase. This kind of approach was proposed by three of us in a previous paper in order to preserve all the desirable features of Phi-derivable Dyson-Schwinger resummation schemes (i.e., validity of conservation laws and thermodynamic consistency) while simultaneously restoring the Nambu--Goldstone theorem in the broken phase. It is shown that unlike for the conventional Hartree--Fock approximation this approach allows for a scale-independent renormalization in the vacuum. However, the scale dependence still persists at finite temperatures. Various branches of the solution are studied. The occurrence of a limiting temperature inherent in the renormalized Hartree--Fock approximation at fixed renormalization scale mu is discussed.Comment: 11 pages, 14 figures / Version accepted by Phys. Rev. D: title and one reference change

Applied type system

We present a type system that can effectively facilitate the use of types in capturing invariants in stateful programs that may involve (sophisticated) pointer manipulation. With its root in a recently developed framework Applied Type System (ATS), the type system imposes a level of abstraction on program states by introducing a novel notion of recursive stateful views and then relies on a form of linear logic to reason about such views. We consider the design and then the formalization of the type system to constitute the primary contribution of the paper. In addition, we mention a prototype implementation of the type system and then give a variety of examples that attests to the practicality of programming with recursive stateful views.National Science Foundation (CCR-0224244, CCR-0229480