Lagrangian Supersymmetries Depending on Derivatives. Global Analysis and Cohomology

Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in a very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic nilpotent contact supersymmetry are computed. In particular, the first variational formula and conservation laws for Lagrangian systems on graded manifolds using contact supersymmetries are obtained.     

Living tert‐butyllithium initiated anionic polymerization of 2‐vinylnaphthalene in toluene‐tetrahydrofuran mixtures

The tert‐butyllithium (t‐BuLi) initiated polymerization of carefully purified 2‐vinylnaphthalene in toluene containing small amounts of tetrahydrofuran with respect to t‐BuLi proceeds on a timescale of several hours without significant deactivation and allows the synthesis of very narrow molecular weight distribution poly‐(2‐vinylnaphthalene) (P2VN) (polydispersities as low as 1.04) and molecular weights between 1000 and 20,000. The absence of P2VN‐Li deactivation at these conditions is also indicated by high degrees of trimethylsilyl end functionalization (>95%) and coupling with dibromoxylene. The respective polymerizations of conventionally purified monomer reveal a complex polymerization profile consistent with deactivation by 2‐acetylnaphthalene during the early stages of the reaction. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3034–3041, 2001     

Two-Grid Solution of Symm's Integral Equation

We propose two-grid iteration methods for Symm's integral equation discretized by quadrature-collocation or quadrature methods. Asymptotically the optimal order of error estimate is achieved already on the first iteration, for some modifications on the second iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O(N²) and O(N log N) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes.     

Multimomentum hamiltonian formalism in quantum field theory

The familiar generating functional in quantum field theory fail to be true measures and make sense only in framework of perturbation theory. In our approach, generating functionals are defined strictly as the Fourier transforms of Gaussian measures in nuclear spaces of multimomentum canonical variables when field momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.     

Inverse Conductivity Problem on Riemann Surfaces

An electrical potential U on a bordered Riemann surface X with conductivity function σ>0 satisfies equation d(σ d ^c U)=0. The problem of effective reconstruction of σ from electrical currents measurements (Dirichlet-to-Neumann mapping) on the boundary: U| _bX ↦ σ d ^c U| _bX is studied. We extend to the case of Riemann surfaces the reconstruction scheme given, firstly, by R. Novikov (Funkc. Anal. Ego Priloz. 22:11–22, 2008) for simply connected X. We apply for this new kernels for on the affine algebraic Riemann surfaces constructed in Henkin (, 2008).      

Fast solvers of integral and pseudodifferential equations on closed curves

On the basis of a fully discrete trigonometric Galerkin method and two grid iterations we propose solvers for integral and pseudodifferential equations on closed curves which solve the problem with an optimal convergence order , (Sobolev norms of periodic functions) in arithmetical operations.