Roll cutting in the curtain industry,or: A well-solvable allocation problem

We study the problem of cutting a number of pieces of the same length from n rolls of different lengths so that the remaining part of each utilized roll is either sufficiently short or sufficiently long. A piece is ‘sufficiently short’, if it is shorter than a pre-specified threshold value δ_min, so that it can be thrown away as it cannot be used again for cutting future orders. And a piece is ‘sufficiently long’, if it is longer than a pre-specified threshold value δ_max (with δ_max > δ_min), so that it can reasonably be expected to be usable for cutting future orders of almost any length. We show that this problem, faced by a curtaining wholesaler, is solvable in O(nlogn) time by analyzing a non-trivial class of allocation problems.     

Light within small particles

We calculate the energy density distribution in the ultraviolet within small spheres containing concentric cavities, aimed at simulating interstellar dust grains. We explore the dependence on chemical composition by progressively changing, in an arbitrary way, the refractive index of the sphere material. We conclude that a significant fraction of the energy of the impinging radiation is trapped throughout the particle interior.     

N-Acylation of 4-alkylidene-β-lactams: unexpected results

This paper describes the different reactivity of E- and Z-4-alkylidene-β-lactams in acylation reactions under basic conditions. The E isomer is readily acylated, whereas the Z reacted sluggishly rearranging to the corresponding oxazin-6-one. The N-acylation of Z isomers was successfully obtained with oxalyl- or malonyl chlorides in benzene at reflux.     

Green’s function for elliptic systems: existence and Delmotte–Deuschel bounds

This paper is divided into two parts: In the main deterministic part, we prove that for an open domain \(D \subset \mathbb {R}^d\) with \(d \ge 2\), for every (measurable) uniformly elliptic tensor field a and for almost every point \(y \in D\), there exists a unique Green’s function centred in y associated to the vectorial operator \(-\nabla \cdot a\nabla \) in D. This result implies the existence of the fundamental solution for elliptic systems when \(d>2\), i.e. the Green function for \(-\nabla \cdot a\nabla \) in \(\mathbb {R}^d\). In the second part, we introduce a shift-invariant ensemble \(\langle \cdot \rangle \) over the set of uniformly elliptic tensor fields, and infer for the fundamental solution G some pointwise bounds for \(\langle |G(\cdot ; x,y)|\rangle \), \(\langle |\nabla _x G(\cdot ; x,y)|\rangle \) and \(\langle |\nabla _x\nabla _y G(\cdot ; x,y)|\rangle \). These estimates scale optimally in space and provide a generalisation to systems of the bounds obtained by Delmotte and Deuschel for the scalar case.     

Radical defects modulate the photocatalytic response in 2D-graphitic carbon nitride

Graphitic carbon nitride (gCN) is an important heterogeneous metal-free catalytic material. Thermally induced post-synthetic modifications, such as amorphization and/or reduction, were recently used to enhance the photocatalytic response of these materials for certain classes of organic transformations, with structural defects possibly playing an important role. The knowledge of how these surface modifications modulate the photocatalytic response of gCN is therefore not only interesting from a fundamental point of view, but also necessary for the development and/or tuning of metal-free gCN systems with superior photo-catalytic properties. Herein, employing density functional theory calculations and combining both the periodic and molecular approaches, in conjunction with experimental EPR measurements, we demonstrate that different structural defects on the gCN surface generate distinctive radical defect states localized within the electronic bandgap, with only those correlated with amorphous and reduced gCN structures being photo-active. To this end, we (i) model defective gCN surfaces containing radical defect states; (ii) assess the interactions of these defects with the radical precursors involved in the photo-driven alkylation of electron-rich aromatic compounds (namely perfluoroalkyl iodides); and (iii) describe the photo-chemical processes triggering the initial step of that reaction at the gCN surface. We provide a coherent structure/photo-catalytic property relationship on defective gCN surfaces, elaborating how only specific defect types act as binding sites for the perfluoroalkyl iodide reagent and can favor a photo-induced charge transfer from the gCN surface to the molecule, thus triggering the perfluoroalkylation reaction.

The nature of radical defects governs the photocatalytic activity of graphitic carbon nitride.     

Conjugates of Cryptophycin and RGD or isoDGR Peptidomimetics for Targeted Drug Delivery

RGD-cryptophycin and isoDGR-cryptophycin conjugates were synthetized by combining peptidomimetic integrin ligands and cryptophycin, a highly potent tubulin-binding antimitotic agent across lysosomally cleavable Val-Ala or uncleavable linkers. The conjugates were able to effectively inhibit binding of biotinylated vitronectin to integrin α_vβ₃, showing a binding affinity in the same range as that of the free ligands. The antiproliferative activity of the novel conjugates was evaluated on human melanoma cells M21 and M21-L with different expression levels of integrin α_vβ₃, showing nanomolar potency of all four compounds against both cell lines. Conjugates containing uncleavable linker show reduced activity compared to the corresponding cleavable conjugates, indicating efficient intracellular drug release in the case of cryptophycin-based SMDCs. However, no significant correlation between the in vitro biological activity of the conjugates and the integrin α_vβ₃ expression level was observed, which is presumably due to a non-integrin-mediated uptake. This reveals the complexity of effective and selective α_vβ₃ integrin-mediated drug delivery.     

Synthesis of chiral non-racemic intermediates and Arg-Gly-Asp mimetics by CaLB-catalyzed resolution

The reactivity of both the ester and amine functions present in β-amino esters was tested in order to obtain the synthesis of enantiopure αvβ3 and α5β1 integrin ligands. CaLB successfully catalyzed both the enantioselective transesterification and the N-acylation of racemic β-amino esters, allowing the isolation of intermediates for the preparation of Arg-Gly-Asp (RGD) mimetic compounds. In particular, a CaLB-catalyzed amidation reaction with unprotected p-aminobenzylamine reduced the number of synthetic steps, thus avoiding protection and deprotection of the intermediate compounds. Following this procedure, RGD mimetics were isolated with high yields and enantiomeric purities.     

Efficient Electrochemical Reduction of CO2 to Formate in Methanol Solutions by Mn-Functionalized Electrodes in the Presence of Amines**

Carbon cloth electrode modified by covalently attaching a manganese organometallic catalyst is used as cathode for the electrochemical reduction of CO₂ in methanol solutions. Six different industrial amines are employed as co-catalyst in millimolar concentrations to deliver a series of new reactive system. While such absorbents were so far believed to provide a CO₂ reservoir and act as sacrificial proton source, we herein demonstrate that this role can be played by methanol, and that the adduct formed between CO₂ and the amine can act as an effector or inhibitor toward the catalyst, thereby enhancing or reducing the production of formate. Pentamethyldiethylentriamine ( PMDETA) , identified as the best effector in our series, converts CO₂ in wet methanolic solution into bisammonium bicarbonate. Computational studies revealed that this adduct is responsible for a barrierless transformation of CO₂ to formate by the reduced form of the Mn catalyst covalently bonded to the electrode surface. As a consequence, selectivity can be switched on demand from CO to formate anion, and in the case of ( PMDETA ) an impressive TON_HCOO− of 2.8×10⁴ can be reached. This new valuable knowledge on an integrated capture and utilization system paves the way toward more efficient transformation of CO₂ into liquid fuel.     

Anagostic Interactions under Pressure: Attractive or Repulsive?

Square‐planar d⁸‐ML₄ complexes might display subtle but noticeable local Lewis acidic sites in axial direction in the valence shell of the metal atom. These sites of local charge depletion provide the electronic prerequisites to establish weakly attractive 3c–2e M⋅⋅⋅H C agostic interactions, in contrast to earlier assumptions. Furthermore, we show that the use of the sign of the ¹H NMR shifts as major criterion to classify M⋅⋅⋅H C interactions as attractive (agostic) or repulsive (anagostic) can be dubious. We therefore suggest a new characterization method to probe the response of these M⋅⋅⋅H C interactions under pressure by combined high pressure IR and diffraction studies.