This book provides a synopsis of spacetime calculus with applications to classical electrodynamics, quantum theory and gravitation. The calculus is a coordinate-free mathematical language enabling a unified treatment of all these topics and bringing new insights and methods to each of them.

In this paper, fractal calculus, which is called Fα-calculus, reviewed. Fractal calculus implemented on interpolation functions and Weierstrass functions, may be non-differentiable non-integrable in the sense of ordinary calculus. Graphical representations are presented.

In this tutorial we present the system SUBSEXPL that is used for simulating and comparing explicit substitutions calculi. This framework was developed in Ocaml, a language of the ML family, and it allows the manipulation of expressions of the λ-calculus and of several styles of explicit substitutions calculi. Applications of this framework include: the visualisation of the contractions of the λ...

This paper studies a new classical natural deduction system, presented as a typed calculus named λμlet. It is designed to be isomorphic to Curien-Herbelin’s λμμ̃-calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is ...

By analogy with complex K–theory and reality, there are theories of unitary functor calculus both which generalisations Weiss' orthogonal calculus. In this paper we show that can be completely recovered from the in to how topological is reality via forgetting C2–action.

This paper presents the first systematic treatment of tableau calculi for modal logic K with global counting operators. Using a recently introduced tableau synthesis framework we establish two terminating tableau calculi for the logic. Whereas the first calculus is a prefix tableau calculus, the second is a refinement that internalises the semantics of the logic without using nominals. We prove...

the computational method based on using the operational matrix of anorthogonal function for solving variational problems is computeroriented. in this approach, a truncated hartley series together withthe operational matrix of integration and integration of the crossproduct of two cas vectors are used for finding the solution ofvariational problems. two illustrative examples are included todemon...

OBJECTIVES The aim of the present study was to compare the effectiveness of subgingival calculus removal from periodontally involved root surfaces with an Er:YAG laser compared to hand instrumentation in situ. METHODS The mesial and distal surfaces of 30 single-rooted teeth with untreated periodontitis were treated either by hand instrumentation (scaling and root planing (SRP)) or by Er:YAG l...