The equivalence of correct Hamiltonian and naive Lagrangian (Faddeev–Popov) path integral quantization (Matthews’s theorem) is proven for gauge theories with arbitrary effective interaction terms. Effective gauge-boson self-interactions and effective interactions with scalar and fermion fields are considered. This result becomes extended to effective gauge theories with higher derivatives of th...

A new genus and species of leptopodid bug, Grimaldinia pronotalis Popov & Heiss is described and illustrated from Burmese Middle Cretaceous (Albian-Cenomanian) amber originating from the northern Myanmar's Kachin State. This is the second finding of Leptosaldinae (Leptopodidae), after Poinar published on Palaeoleptus burmanicus from Burmese amber in 2009.

1 Department of Mathematical Sciences, University of Durham, South Road, Durham DH1 3LE, United Kingdom [email protected] 2 Institut de Recherche Mathématique, Université de Rennes I and CNRS UMR 6625, 35042 Rennes Cedex, France [email protected] 3 Instituto de Matemática e Estatı́stica, Universidade de São Paulo, Rua do Matão 1010, CEP 05508-090, São Paulo SP, Brasil...

Let Sr be the blow-up of P 2 in r general points, i.e., a smooth Del Pezzo surface of degree 9 − r. For r ≤ 7, we determine the quadratic equations defining its Cox ring explicitly. The ideal of the relations in Cox(S8) is calculated up to radical. As conjectured by Batyrev and Popov, all the generating relations are quadratic.

A simple algorithm for lattice reduction of polynomial matrices is described and analysed. The algorithm is adapted and applied to various tasks, including rank profile and determinant computation, transformation to Hermite and Popov canonical form, polynomial linear system solving and short vector computation. © 2003 Elsevier Science Ltd. All rights reserved.

Node Department(s) People Bath Maths Graham, Spence, Smyshlyaev, Toland Cardiff & Liverpool Engineering, Maths Levitin, McWhirter, Marletta, Maz’ya KCL and UCL Maths Davies, Shargorodsky, Parnovski Lancaster Physics Burton, Tucker Birmingham & Manchester Maths Betcke, Chahlaoui, Higham, Mathias, Mehl, Tisseur Nottingham Engineering Garvey, Popov, Prells Reading Maths Chandler-Wilde, Kondratiev,...

We present conditions for absolute stability of recurrent neural networks with time-varying weights based on the Popov theorem from non-linear feedback system theory. We show how to maximise the stability bounds by deriving a convex optimisation problem subject to linear matrix inequality constraints, which can efficiently be solved by interior point methods with standard software.