A Differentiation Theory for Itô's Calculus

A Nonlinear Creep-damage Constitutive Model of Mudstone Based on the Fractional Calculus Theory

During the flood development in an oil field, the creep characteristic of mudstone is one of the important factors causing casing damage. In this study, based on the theory of fractional order differential and taking into account the creep damage evolution rules, a fractional nonlinear creep-damage model is proposed to reflect the instantaneous deformation in loading processes and the accelerat...

A Sequent Calculus for Type Theory

Based on natural deduction, Pure Type Systems (PTS) can express a wide range of type theories. In order to express proof-search in such theories, we introduce the Pure Type Sequent Calculi (PTSC) by enriching a sequent calculus due to Herbelin, adapted to proof-search and strongly related to natural deduction. PTSC are equipped with a normalisation procedure, adapted from Herbelin’s and defined...

SPACETIME CALCULUS for GRAVITATION THEORY

A new gauge theory of gravitation on flat spacetime has recently been developed by Lasenby, Doran, and Gull in the language of Geometric Calculus. This paper provides a systematic account of the mathematical formalism to facilitate applications and extensions of the theory. It includes formulations of differential geometry, Lie derivatives and integrability theorems which are coordinate-free an...

A Behavioural Theory for a π-calculus with Preorders

We study the behavioural theory of πP, a π-calculus featuring restriction as the only binder. In contrast with calculi such as Fusions and Chi, reduction in πP generates a preorder on names rather than an equivalence relation. We present two characterisations of barbed congruence in πP: the first is based on a compositional LTS, and the second is an axiomatisation. The results in this paper bri...

Calculus, Applications and Theory