Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Principal hierarchies of infinite-dimensional Frobenius manifolds: The extended 2D Toda lattice

We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞$0/\infty$ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold _M0$M_0$ introduced by Carlet, Dubrovin and Mertens (2011) [3] and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of _M0$M_0$.     

Comprehensive Characterization of Shredded Lithium-Ion Battery Recycling Material

Herein we report on an analytical study of dry-shredded lithium-ion battery (LIB) materials with unknown composition. Samples from an industrial recycling process were analyzed concerning the elemental composition and (organic) compound speciation. Deep understanding of the base material for LIB recycling was obtained by identification and analysis of transition metal stoichiometry, current collector metals, base electrolyte and electrolyte additive residues, aging marker molecules and polymer binder fingerprints. For reversed engineering purposes, the main electrode and electrolyte chemistries were traced back to pristine materials. Furthermore, possible lifetime application and accompanied aging was evaluated based on target analysis on characteristic molecules described in literature. With this, the reported analytics provided precious information for value estimation of the undefined spent batteries and enabled tailored recycling process deliberations. The comprehensive feedstock characterization shown in this work paves the way for targeted process control in LIB recycling processes.     

TEAD–YAP Interaction Inhibitors and MDM2 Binders from DNA-Encoded Indole-Focused Ugi Peptidomimetics

DNA-encoded combinatorial synthesis provides efficient and dense coverage of chemical space around privileged molecular structures. The indole side chain of tryptophan plays a prominent role in key, or “hot spot”, regions of protein–protein interactions. A DNA-encoded combinatorial peptoid library was designed based on the Ugi four-component reaction by employing tryptophan-mimetic indole side chains to probe the surface of target proteins. Several peptoids were synthesized on a chemically stable hexathymidine adapter oligonucleotide “hexT”, encoded by DNA sequences, and substituted by azide-alkyne cycloaddition to yield a library of 8112 molecules. Selection experiments for the tumor-relevant proteins MDM2 and TEAD4 yielded MDM2 binders and a novel class of TEAD-YAP interaction inhibitors that perturbed the expression of a gene under the control of these Hippo pathway effectors.