Modularity of logarithmic parafermion vertex algebras

The parafermionic cosets \(\mathsf {C}_{k} = {\text {Com}} ( \mathsf {H} , \mathsf {L}_{k}(\mathfrak {sl}_{2}) )\) are studied for negative admissible levels k, as are certain infinite-order simple current extensions \(\mathsf {B}_{k}\) of \(\mathsf {C}_{k}\). Under the assumption that the tensor theory considerations of Huang, Lepowsky and Zhang apply to \(\mathsf {C}_{k}\), irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-modules are obtained from those of \(\mathsf {L}_{k}(\mathfrak {sl}_{2})\). Assuming the validity of a certain Verlinde-type formula likewise gives the Grothendieck fusion rules of these irreducible modules. Notably, there are only finitely many irreducible \(\mathsf {B}_{k}\)-modules. The irreducible \(\mathsf {C}_{k}\)- and \(\mathsf {B}_{k}\)-characters are computed and the latter are shown, when supplemented by pseudotraces, to carry a finite-dimensional representation of the modular group. The natural conjecture then is that the \(\mathsf {B}_{k}\) are \(C_2\)-cofinite vertex operator algebras.     

DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization

Computational Optimization and Applications - The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available...     

Analytic extension of non quasi-analytic Whitney jets of Roumieu type

Let (M_r)_{r∈? 0} be a logarithmically convex sequence of positive numbers which verifies M₀ = 1 as well as M_r ≥ 1 for every r ∈ ? and defines a non quasi-analytic class. Let moreover F be a closed proper subset of ?ⁿ. Then for every function ? on ?ⁿ belonging to the non quasi-analytic (M_r)-class of Roumieu type, there is an element g of the same class which is analytic on ?ⁿ F and such that D^α ?(x) = D^αg(x) for every σ ∈ ?₀ ⁿ SBAP and x ∈ F.     

Homogeneous and facially homogeneous self-dual cones

We show that any self-dual come in a real finite dimensional Hilbert space is homogeneous iff it is facially homogeneous in the sense of A. Connes. We develop a spectral decomposition theory for these cones which is the analogue of the usual one for self-adjoint operators on a finite-dimensional Hilbert space.     

From Slavnov-Taylor identities to the ZJ equation

In their work devoted to the proof of the renormalizability of non-Abelian gauge theories in the broken phase, Lee and Zinn-Justin have directly benefited from Slavnov’s important contributions. Later generalized in the form of the BRST symmetry, the Slavnov-Taylor identities eventually have led to a remarkable quadratic equation for the renormalized gauge action (sometimes called the Zinn-Justin (ZJ) equation), allowing a completely general proof of renormalizability of non-Abelian gauge theories.     

Chemical modification of poly(lactic acid) induced by thermal decomposition of N‐acetoxy‐phthalimide during extrusion

Chemical modification of poly(lactic acid) (PLA) with N‐acetoxy‐phthalimide (NAPI) was performed in the melt by reactive extrusion, without using any peroxide initiator. The aminyl and nitroxide radicals produced from the NAPI thermal degradation, were, respectively, used (a) to create PLA macroradicals, and (b) to functionalize the PLA samples through nitroxide radical coupling. Depending on the extrusion temperature and the initial NAPI concentration, grafting rates up to 0.24 mol % were measured, modifying the PLA optical properties. This study represents an original new way of modification of PLA without the use of conventional peroxide initiators. Indeed, the undesirable side reactions (PLA branching or crosslinking) usually observed when using peroxides to initiate the radical grafting of PLA were avoided when using NAPI. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 120–129