Introduction 2 1. Lie algebras: recollections 3 1.1. The basics 3 1.2. Scaling the structure 3 1.3. Filtrations 4 1.4. The Chevalley complex 4 1.5. The functor of primitives 6 1.6. The enhanced adjunction 6 1.7. The symmetric Hopf algebra 8 2. Looping Lie algebras 9 2.1. Group-Lie algebras 10 2.2. Forgetting to group structure 10 2.3. Chevalley complex of group-Lie algebras 11 2.4. Chevalley co...

In the framework of one dimensional potential scattering we prove that, modulo a compact term, the wave operators can be written in terms of a universal operator and of the scattering operator. The universal operator is related to the one dimensional Hilbert transform and can be expressed as a function of the generator of dilations. As a consequence, we show how Levinson’s theorem can be rewrit...

Existing theorem prover tools do not adequately support reasoning about general recursive datatypes. Better support for such datatypes would facilitate reasoning about a wide variety of real-world programs, including those written in continuation-passing style, that are beyond the scope of current tools. This paper introduces a new formalization of a universal domain that is suitable for modeli...

We present a method based on extended linear real quantifier elimination for multiple object semilinear motion planning, i.e. finding collision-free trajectories for several robots in a time dependent environment. For practical applicability the method is limited to polygonal objects and linear trajectories. It can, however, deal with situations involving even non-convex objects. c © 2007 Elsev...

A proof of Poincaré-Birkhoff-Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal enveloping algebras of type An and Mp,q,ǫ(n, K), which is a nonstandard quantum deformation of GL(n). In particular, we get, for both algebras, a unified proof of the...

We point out that the matter profile effect — the effect of matter density fluctuation on the baseline — is very important to estimate the parameters in a neutrino factory with a very long baseline. To make it clear, we propose the method of the Fourier series expansion of the matter profile. By using this method, we can take account of both the matter profile effect and its ambiguity. For very...

We point out that the matter profile effect—the effect of matter density fluctuation on the baseline—is very important to estimate the parameters in a neutrino factory with a very long baseline. To make it clear, we propose the method of Fourier series expansion of the matter profile. By using this method, we can take account of both the matter profile effect and its ambiguity. For very long ba...

In the framework of one dimensional potential scattering we prove that, modulo a compact term, the wave operators can be written in terms of a universal operator and of the scattering operator. The universal operator is related to the one dimensional Hilbert transform and can be expressed as a function of the generator of dilations. As a consequence, we show how Levinson’s theorem can be rewrit...

Isabelle [2] is a theorem prover for a large class of logics. The object-logics are formalized within Isabelle’s meta-logic, which is intuitionistic higher-order logic with implication, universal quantifiers, and equality. The implication φ =⇒ ψ means ‘φ implies ψ’, and expresses logical entailment. The quantification ∧ x.φ means ‘φ is true for all x’, and expresses generality in rules and axio...

In this paper we establish a link between satisfiability of universal sentences with respect to varieties of distributive lattices with operators and satisfiability with respect to certain classes of relational structures. We use these results for giving a method for translation to clause form of universal sentences in such varieties, and then use results from automated theorem proving to obtai...