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.     

α-SUBSTITUIERTE PHOSPHONATE 52.1 SYNTHESE UND REAKTIONEN VON 1- ACETOXY-1-METHYLTHIOMETHAN PHOSPHORYLVERBINDUNGEN

Abstract

The 1-acetoxy-1-methylthiomethanephosphoryl compounds (4) are prepared from methylthiomethanephosphoryl derivatives (1) by electrolysis in 0.6 molar sodium acetate/acetic acid solution. The reaction of 1-acetoxy compounds (4) with halogen carriers gives the 1-halogen-1-methylthiomethane-phosphoryl derivatives 5, 7 and 8. The reaction of 4a under PTC-conditions results in cleavage of the P-C-bond.

Die 1-Acetoxy-1-methylthiomethanphosphoryl-Verbindungen (4) wurden aus Methylthiomethanphos-phorylderivaten (1) durch Elektrolyse in 0.6 molarer Na-acetat/Essigsäure-Lösung dargestellt. Die Reaktion der 1-Acetoxyverbindungen mit Halogenüberträgern führt zu den 1-Halogen-1-methyl-thiomethanphosphorylderivaten 5, 7 und 8. Bei Reaktion von 4a unter PTC-Bedingungen beobachtet man eine Spaltung der P-C-Bindung.     

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.     

Nonsequential double recombination in intense laser fields

A second plateau in the harmonic spectra of laser-driven two-electron atoms is observed both in the numerical solution of a low-dimensional model helium atom and using an extended strong field approximation. It is shown that the harmonics well beyond the usual cutoff are due to the simultaneous recombination of the two electrons, which were emitted during different, previous half-cycles. The new cutoff is explained in terms of classical trajectories. Classical predictions and the time-frequency analysis of the ab initio quantum results are in excellent agreement. The mechanism corresponds to the inverse single photon double ionization process in the presence of a (low frequency) laser field.     

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.     

Eu(O2C-C≡C-CO2): An EuII Containing Anhydrous Coordination Polymer with High Stability and Negative Thermal Expansion

Anhydrous Eu^II–acetylenedicarboxylate (EuADC; ADC²⁻ = ⁻O₂C-C≡C-CO₂⁻) was synthesized by reaction of EuBr₂ with K₂ADC or H₂ADC in degassed water under oxygen-free conditions. EuADC crystallizes in the SrADC type structure (I4₁/amd, Z=4) forming a 3D coordination polymer with a diamond-like arrangement of Eu²⁺ nodes (msw topology including the connecting ADC²⁻ linkers). Deep orange coloured EuADC is stable in air and starts decomposing upon heating in an argon atmosphere only at 440 °C. Measurements of the magnetic susceptibilities (μ_eff=7.76 μ_B) and ¹⁵¹Eu Mössbauer spectra (δ=−13.25 mm s⁻¹ at 78 K) confirm the existence of Eu²⁺ cations. Diffuse reflectance spectra indicate a direct optical band gap of E_g=2.64 eV (470 nm), which is in accordance with the orange colour of the material. Surprisingly, EuADC does not show any photoluminescence under irradiation with UV light of different wavelengths. Similar to SrADC, EuADC exhibits a negative thermal volume expansion below room temperature with a volume expansion coefficient α_V=−9.4(12)×10⁻⁶ K⁻¹.