Theorem proving, or algorithmic proof-search, is an essential enabling technology throughout the computational sciences. We explain the mathematical basis of proof-search as the combination of reductive logic together with a control régime. Then we present a games semantics for reductive logic and show how it may be used to model two important examples of control, namely backtracking and unifor...

Reaction between a β-diketiminato magnesium hydride and carbon monoxide results in the isolation of a dimeric cis-enediolate species through the reductive coupling of two CO molecules. Under catalytic conditions with PhSiH3 , an observable magnesium formyl species may be intercepted for the mild reductive cleavage of the CO triple bond.

The in vivo activity of truncated forms of methylorcinaldehyde synthase shows that the synthase retains a hydrolytic release activity in the absence of reductive chain release and that chain-length is not controlled by the reductive release domain; experiments using a methyltransferase inhibitor suggest that methylation occurs prior to aromatisation.

We extend the methods developed in our earlier work to algorithmically compute the intersection cohomology Betti numbers of reductive varieties. These form a class of highly symmetric varieties that includes equivariant compactifications of reductive groups. Thereby, we extend a well-known algorithm for toric varieties.

This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so called Siegel-Jacobi space that is important arithmetically and geometrically. We present some new results on the Siegel-Jacobi space.

We exploit the classical correspondence between finitely generated abelian groups and abelian complex algebraic reductive groups to study the intersection theory of translated subgroups in an abelian complex algebraic reductive group, with special emphasis on intersections of (torsion) translated subtori in an algebraic torus.

Citation: Tarnawski S-E, Rossi P, Brennerova MV, Stavelova M and Holliger C (2016) Validation of an Integrative Methodology to Assess and Monitor Reductive Dechlorination of Chlorinated Ethenes in Contaminated Aquifers. Front. Environ. Sci. 4:7. doi: 10.3389/fenvs.2016.00007 Validation of an Integrative Methodology to Assess and Monitor Reductive Dechlorination of Chlorinated Ethenes in Contami...

The first total synthesis of (-)-maoecrystal Z is described. The key steps of the synthesis include a diastereoselective Ti(III)-mediated reductive epoxide coupling reaction and a diastereoselective Sm(II)-mediated reductive cascade cyclization reaction. These transformations enabled the preparation of (-)-maoecrystal Z in only 12 steps from (-)-γ-cyclogeraniol.

The theory of Whittaker functions is of crucial importance in the classical study of automorphic forms on adele groups. Motivated by the appearance of Whittaker functions for covers of reductive groups in the theory of multiple Dirichlet series, we provide a study of Whittaker functions on metaplectic covers of reductive groups over local fields. Thesis Supervisor: Benjamin Brubaker Title: Assi...

Let G be a complex reductive algebraic group, g its Lie algebra and h a reductive subalgebra of g, n a positive integer. Consider the diagonal actions G : g, NG(h) : h . We study a relation between the algebra C[h]G and its subalgebra consisting of restrictions to h of elements of C[g].