Bi-Sobolev solutions to the prescribed Jacobian inequality in the plane with Lp data and applications to nonlinear elasticity

We construct planar bi-Sobolev mappings whose local volume distortion is bounded from below by a given function $f\in L^p$ with $p>1$. More precisely, for any $1<q<(p+1)/2$ we construct $W^{1,q}$-bi-Sobolev maps with identity boundary conditions; for $f\in L^{\infty }$, we provide bi-Lipschitz maps. The basic building block of our construction are bi-Lipschitz maps which stretch a given compact subset of the unit square by a given factor while preserving the boundary. The construction of these stretching maps relies on a slight strengthening of the celebrated covering result of Alberti, Csörnyei, and Preiss for measurable planar sets in the case of compact sets. We apply our result to a model functional in nonlinear elasticity, the integrand of which features fast blowup as the Jacobian determinant of the deformation becomes small. For such functionals, the derivation of the equilibrium equations for minimizers requires an additional regularization of test functions, which our maps provide.     

Bridging the Green Gap: Metal–Organic Framework Heteromultilayers Assembled from Porphyrinic Linkers Identified by Using Computational Screening

In organic photovoltaics, porphyrins (PPs) are among the most promising compounds owing to their large absorption cross-section, wide spectral range, and stability. Nevertheless, a precise adjustment of absorption band positions to reach a full coverage of the so-called green gap has not been achieved yet. We demonstrate that a tuning of the PP Q- and Soret bands can be carried out by using a computational approach for which substitution patterns are optimized in silico. The most promising candidate structures were then synthesized. The experimental UV/Vis data for the solvated compounds were in excellent agreement with the theoretical predictions. By attaching further functionalities, which allow the use of PP chromophores as linkers for the assembly of metal-organic frameworks (MOFs), we were able to exploit packing effects resulting in pronounced redshifts, which allowed further optimization of the photophysical properties of PP assemblies. Finally, we use a layer-by-layer method to assemble the PP linkers into surface-mounted MOFs (SURMOFs), thus obtaining high optical quality, homogeneous and crystalline multilayer films. Experimental results are in full accord with the calculations, demonstrating the huge potential of computational screening methods in tailoring MOF and SURMOF photophysical properties.     

Effect of Sulfation Route and Subsequent Oxidation on Derivatization Degree and Biocompatibility of Cellulose Sulfates

Sulfated cellulose (CS) represents an interesting biopolymer due to bioactivity comparable to heparin. However, use of CS for making surface coatings or hydrogels requires the presence of reactive groups for covalent reactions. Here, an approach is presented to oxidize cellulose sulfates for subsequent cross‐linking reactions with amino groups to form imine bonds. Cellulose is sulfated by direct sulfation or acetosulfation, followed by a M alaprade oxidation. The CS obtained is characterized by elemental analysis and ¹³C‐NMR spectroscopy. The resulting oxidized cellulose sulfates (oxCS) have different degrees of sulfation ranging from 0.79 to 1.13 and oxidation degrees from 0.18 to 0.34, but also different mass average molecular mass (M_W). Toxicity studies are carried out with mouse 3T3 fibroblasts exposed to aqueous solutions of oxCS. The results show that all oxCS are non‐toxic at lower concentrations (0.5 mg mL^?1), but with both increasing degree of oxidation and concentrations, toxic effects are observed particularly for acetosulfated and lesser for direct sulfated oxCS, which is related to a decrease in the M_W of the products. It is concluded that oxCS obtained by direct sulfation with M_W above 70 kDa may represent a biocompatible material for the applications suggested above.     

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Imaging of the formerly bonded area of individual fibre to fibre joints with SEM and AFM

Besides the determination of the force and the energy needed to break individual fibre to fibre joints, the investigation of the formerly bonded area (FBA) is of essential importance to learn more about the failure mechanisms of fibre–fibre bonds in general. In this study the surfaces of paper fibres and the FBA of fibre–fibre joints after the determination of the breaking force as well as the bonding energy were analysed by means of low voltage scanning electron microscopy and atomic force microscopy. A comparison between the contact zone of fibres broken at different loading rates as well as under cyclic loading showed that there seems to be no significant difference in the appearance of the FBA in these cases. Only minor delamination of the cell wall could be found in the bonding zone, which indicates no mechanical interlocking of fibrils in the bonding zone. Furthermore, it is shown that some glues used for specimen preparation of fibre–fibre bond strength measurement are forming a glue film on the fiber surface and migrate into the bonding region.     

The structural organization of oligonuclear cobalt(II,III) and cobalt(III) carboxylates

The review deals with the topology of homonuclear carboxylate complexes of cobalt(II, III) and cobalt(III) whose structures are built from the monocarboxylate anions RCOO^– (R is a radical containing no electron-donating substituents), water, and its deprotonated forms.     

Cardinal characteristics at κ in a small u(κ) model

We provide a model where $\mathfrak{u}(\kappa )<2^{\kappa }$ for a supercompact cardinal κ. [10] provides a sketch of how to obtain such a model by modifying the construction in [6]. We provide here a complete proof using a different modification of [6] and further study the values of other natural generalizations of classical cardinal characteristics in our model. For this purpose we generalize some standard facts that hold in the countable case as well as some classical forcing notions and their properties.     

Methane Oxidation over Cu2+/[CuOH]+ Pairs and Site-Specific Kinetics in Copper Mordenite Revealed by Operando Electron Paramagnetic Resonance and UV/Visible Spectroscopy

Cu-exchanged mordenite (MOR) is a promising material for partial CH₄ oxidation. The structural diversity of Cu species within MOR makes it difficult to identify the active Cu sites and to determine their redox and kinetic properties. In this study, the Cu speciation in Cu-MOR materials with different Cu loadings has been determined using operando electron paramagnetic resonance (EPR) and operando ultraviolet-visible (UV/Vis) spectroscopy as well as in situ photoluminescence (PL) and Fourier-transform infrared (FTIR) spectroscopy. A novel pathway for CH₄ oxidation involving paired [CuOH]⁺ and bare Cu²⁺ species has been identified. The reduction of bare Cu²⁺ ions facilitated by adjacent [CuOH]⁺ demonstrates that the frequently reported assumption of redox-inert Cu²⁺ centers does not generally apply. The measured site-specific reaction kinetics show that dimeric Cu species exhibit a faster reaction rate and a higher apparent activation energy than monomeric Cu²⁺ active sites highlighting their difference in the CH₄ oxidation potential.     

Catalytic Alkyne Semihydrogenation with Polyhydride Ni/Ga Clusters

The bimetallic, decanuclear Ni₃Ga₇-cluster of the formula [Ni₃(GaTMP)₃(μ²-GaTMP)₃(μ³-GaTMP)] ( 1 , TMP=2,2,6,6-tetramethylpiperidinyl) reacts reversibly with dihydrogen under the formation of a series of (poly-)hydride clusters 2 . Low-temperature 2D NMR experiments at −80 °C show that 2 consist of a mixture of a di- ( 2_Di ), tetra- ( 2_Tetra ) and hexahydride species ( 2_Hexa ). The structures of 2_Di and 2_Tetra are assessed by a combination of 2D NMR spectroscopy and DFT calculations. The cooperation of both metals is essential for the high hydrogen uptake of the cluster. Polyhydrides 2 are catalytically active in the semihydrogenation of 4-octyne to 4-octene with good selectivity. The example is the first of its kind and conceptually relates properties of molecular, atom-precise transition metal/main group metal clusters to the respective solid-state phase in catalysis.