The location of median paths on grid graphs

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case.     

Aromatic-aromatic interactions in crystal structures of helical peptide scaffolds containing projecting phenylalanine residues

Aromatic-aromatic interactions between phenylalanine side chains in peptides have been probed by the structure determination in crystals of three peptides: Boc-Val-Ala-Phe-Aib-Val-Ala-Phe-Aib-OMe, I; Boc-Val-Ala-Phe-Aib-Val-Ala-Phe-Aib-Val-Ala-Phe-Aib-OMe, II; Boc-Aib-Ala-Phe-Aib-Phe-Ala-Val-Aib-OMe, III. X-ray diffraction studies reveal that all three peptides adopt helical conformations in the solid state with the Phe side chains projecting outward. Interhelix association in the crystals is promoted by Phe-Phe interactions. A total of 15 unique aromatic pairs have been characterized in the three independent crystal structures. In peptides I and II, the aromatic side chains lie on the same face of the helix at i/i + 4 positions resulting in both intrahelix and interhelix aromatic interactions. In peptide III, the Phe side chains are placed on the opposite faces of the helix, resulting in exclusive intermolecular aromatic interactions. The distances between the centroids of aromatic pair ranges from 5.11 to 6.86 A, while the distance of closest approach of ring carbon atoms ranges from 3.27 to 4.59 A. Examples of T-shaped and parallel-displaced arrangements of aromatic pairs are observed, in addition to several examples of inclined arrangements. The results support the view that the interaction potential for a pair of aromatic rings is relatively broad and rugged with several minima of similar energies, separated by small activation barriers.     

Polycondensed nitrogen heterocycles. Part 19. Pyrrolo[1,2-f]phenanthridines by pschorr-type cyclization brought about by hypophosphorous acid

Pyrrolo[1,2-f]phenanthridines were prepared in good yields by the diazotization in acetic acid of the amines la,b and subsequent treatment with hypophosphorous acid. The necessity for hypophosphorous acid in the reaction was demonstrated.     

Methylene‐Bridged Metallocenes with 2,2′‐Methylenebis[1H‐inden‐1‐yl] Ligands: Synthesis,Characterization, and Polymerization Catalysis of a Synthetically Simple Class of C2‐ and C2v‐Symmetric ansa‐Metallocenes

The acid‐catalyzed reaction between formaldehyde and 1H‐indene, 3‐alkyl‐ and 3‐aryl‐1H‐indenes, and six‐membered‐ring substituted 1H‐indenes, with the 1H‐indene/CH₂O ratio of 2 : 1, at temperatures above 60° in hydrocarbon solvents, yields 2,2′‐methylenebis[1H‐indenes] 1 – 8 in 50–100% yield. These 2,2′‐methylenebis[1H‐indenes] are easily deprotonated by 2 equiv. of BuLi or MeLi to yield the corresponding dilithium salts, which are efficiently converted into ansa‐metallocenes of Zr and Hf. The unsubstituted dichloro{(1,1′,2,2′,3,3′,3a,3′a,7a,7′a‐η)‐2,2′‐methylenebis[1H‐inden‐1‐yl]}zirconium ([ZrCl₂( 1′ )]) is the least soluble in organic solvents. Substitution of the 1H‐indenyl moieties by hydrocarbyl substituents increases the hydrocarbon solubility of the complexes, and the presence of a substituent larger than a Me group at the 1,1′ positions of the ligand imparts a high diastereoselectivity to the metallation step, since only the racemic isomers are obtained. Methylene‐bridged ‘ansa‐zirconocenes’ show a noticeable open arrangement of the bis[1H‐inden‐1‐yl] moiety, as measured by the angle between the planes defined by the two π‐ligands (the ‘bite angle’). In particular, of the ‘zirconocenes’ structurally characterized so far, the dichloro{(1,1′,2,2′,3,3′,3a,3′a,7a,7′a‐η)‐2,2′‐methylenebis[4,7‐dimethyl‐1H‐inden‐1‐yl]}zirconium ([ZrCl₂( 5′ )] is the most open. The mixture [ZrCl₂( 1′ )]/methylalumoxane (MAO) is inactive in the polymerization of both ethylene and propylene, while the metallocenes with substituted indenyl ligands polymerize propylene to atactic polypropylene of a molecular mass that depends on the size of the alkyl or aryl groups at the 1,1′ positions of the ligand. Ethene is polymerized by rac‐dichloro{(1,1′,2,2′,3,3′,3a,3′a,7a,7′a‐η)‐2,2′‐methylenebis[1‐methyl‐1H‐inden‐1‐yl]}zirconium ([ZrCl₂( 2′ )])/MAO to polyethylene waxes (average degree of polymerization ca. 100), which are terminated almost exclusively by ethenyl end groups. Polyethylene with a high molecular mass could be obtained by increasing the size of the 1‐alkyl substituent.     

Is the A-ring of sparteine essential for high enantioselectivity in the asymmetric lithiation-substitution of N-Boc-pyrrolidine?

The simplest chiral portion of sparteine, N,N'-dimethyl-2-endo-methylbispidine, was prepared and evaluated in the asymmetric lithiation-substitution of N-Boc-pyrrolidine. The results indicate that the complete A-ring of sparteine is essential for high levels of asymmetric induction. DFT-QSSR analyses of the diamine/Li(+) complexes and DFT calculations of the pertinent i-PrLi/diamine/N-Boc-pyrrolidine complexes are predictive and provide complementary pictures of the stereochemical features critical to this transformation.     

Redox site confinement in highly unsymmetric dimanganese complexes

A set of highly preorganized pyrazolate-bridged dimanganese complexes L(Mn)MnX have been prepared and structurally characterized. They can be described as hybrid organometallic/Werner-type systems that consist of a low-spin CpMn(I)(CO)2 subunit (Mn1) and a proximate tripodal tetradentate {N4} binding pocket accommodating a high-spin Mn(II) ion (Mn2), with Mn...Mn distances of approximately 4.3 A and different coligands bound to Mn2. Density functional theory (DFT) calculations (both the hybrid B3LYP and the pure BP86 functionals and the all-electron basis sets 6-311G and 6-311G*) confirm that the valence alpha and beta Kohn-Sham molecular orbitals (MOs) of these mixed-valent Mn(I)Mn(II) compounds have predominant Mn(3d) character and an almost perfectly localized nature: all five unpaired electrons are essentially localized at the Werner-type Mn2, whereas Mn1 possesses an effective closed-shell structure with the MOs of highest energy centered there. One-electron oxidation occurs in a clean process at approximately E(1/2) = -0.6 V (versus ferrocene/ferrocinium), giving the low-spin/high-spin Mn(II)Mn(II) species. UV/vis and IR spectroelectrochemistry as well as a detailed theoretical analysis reveal that the redox process takes place with strict site control at the organometallic subunit, while it does not significantly influence the spin and charge distribution on the Werner-type site. Positions and shifts of the nu(C[triple bond]O) absorptions are largely reproduced by the DFT calculations. These systems thus represent an exceptional example of the effect the unsymmetry of a dinucleating ligand scaffold has on the spin and charge distribution in homobimetallic complexes and might offer interesting prospects for the study of the cooperative effects of bimetallic arrays.     

Design and application of dielectric distributed Bragg back reflector in thin-film silicon solar cells

A dielectric distributed Bragg reflector (DBR) formed by four pairs of hydrogenated amorphous silicon/silicon nitride layers is used as the back reflector in thin-film silicon solar cells. The DBR was designed to perform in a broad wavelength range with the peak reflectance at 600 nm. The DBR was fabricated at low substrate temperature (172 °C) and applied at the rear side of flat and textured amorphous silicon single-junction solar cells in both superstrate (pin) and substrate (nip) configurations. The spectral response and electrical I–V characteristics were measured. Solar cells with optimized DBR exhibit an enhanced external quantum efficiency in the long wavelength range and the electrical performance is comparable to solar cells having conventional Ag back reflector.     

Copper-Mediated Conversion of Complex Ethers to Esters: Enabling Biopolymer Depolymerisation under Mild Conditions

Selective processing of the β-O-4 unit in lignin is essential for the efficient depolymerisation of this biopolymer and therefore its successful integration into a biorefinery set-up. An approach is described in which this unit is modified to incorporate a carboxylic ester with the goal of enabling the use of mild depolymerisation conditions. Inspired by preliminary results using a Cu/TEMPO/O₂ system, a protocol was developed that gave the desired β-O-4-containing ester in high yield using certain dimeric model compounds. The optimised reaction conditions were then applied to an oligomeric lignin model system. Extensive 2D NMR analysis demonstrated that analogous chemistry could be achieved with the oligomeric substrate. Mild depolymerisation of the ester-containing oligomer delivered the expected aryl acid monomer.