Higher order conservation laws and a higher order Noether's theorem

Gauge Gravity and Conservation Laws in Higher Order Anisotropic Spaces

We propose an approach to the theory of higher order anisotropic field interactions and curved spaces (in brief, ha–field, ha–interactions and ha–spaces). The concept of ha–space generaliSes various types of Lagrange and Finsler spaces and higher dimension (Kaluza–Klein) spaces. This work consists from two parts. In the first we outline the theory of Yang–Mills ha–fields and two gauge models of...

Conservation Laws in Higher-Order Nonlinear Optical Effects

Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the selfsteepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schrödinger equation. The first few currents and charges are...

Higher-Order Automated Theorem Provers

Higher-Order Automated Theorem Proving

The history of building automated theorem provers for higher-order logic is almost as old as the field of deduction systems itself. The first successful attempts to mechanize and implement higher-order logic were those of Huet [13] and Jensen and Pietrzykowski [17]. They combine the resolution principle for higher-order logic (first studied in [1]) with higher-order unification. The unification...

First-Order Proof Tactics in Higher-Order Logic Theorem Provers

In this paper we evaluate the effectiveness of first-order proof procedures when used as tactics for proving subgoals in a higher-order logic interactive theorem prover. We first motivate why such first-order proof tactics are useful, and then describe the core integrating technology: an ‘LCFstyle’ logical kernel for clausal first-order logic. This allows the choice of different logical mapping...