C−C Bond Formation of Benzyl Alcohols and Alkynes Using a Catalytic Amount of KOtBu: Unusual Regioselectivity through a Radical Mechanism

We report a C?C bond‐forming reaction between benzyl alcohols and alkynes in the presence of a catalytic amount of KO^tBu to form α‐alkylated ketones in which the C=O group is located on the side derived from the alcohol. The reaction proceeds under thermal conditions (125 °C) and produces no waste, making the reaction highly atom efficient, environmentally benign, and sustainable. Based on our mechanistic investigations, we propose that the reaction proceeds through radical pathways.     

Gold nanoparticle induced conformational changes in heme protein

Change of α-helical structure of heme protein (Hb) to a β-sheet and random coil conformation because of the interaction of glycine capped gold nanoparticles (20–60 nm) as observed from attenuation total reflectance, absorption, Fourier transform infra red, and Circular Dichroism spectroscopy has been reported in this article. Upon interaction, protein takes a cylindrical shape of length 12 μm and diameter 0.35 μm as revealed from scanning electron microscopy and transmission electron microscopy. The Selected-Area Electron beam Diffraction pattern shows change of crystalline structure in GNP to amorphous nature with the interaction of Hb.     

An unconditional proof of the Andr���COort conjecture for Hilbert modular surfaces

We give an unconditional proof of the André?COort conjecture for Hilbert modular surfaces asserting that an algebraic curve contained in such a surface and containing an infinite set of special points, is special. The proof relies on a combination of Galois-theoretic techniques and results from the theory of o-minimal structures.     

Every Large Point Set contains Many Collinear Points or an Empty Pentagon

We prove the following generalised empty pentagon theorem for every integer ℓ ≥ 2, every sufficiently large set of points in the plane contains ℓ collinear points or an empty pentagon. As an application, we settle the next open case of the “big line or big clique” conjecture of Kára, Pór, and Wood [Discrete Comput. Geom. 34(3):497–506, 2005].     

Radial variation of pump and signal intensities in EDFA; accurate prediction by a novel approximation of the fundamental modal field

The doped fiber amplifier has already emerged as the indispensable potential candidate for repeaterless transmission of information processed through single mode. Therefore the fundamental modal field in the doped single-mode fiber needs to be accurately prescribed both in the pump as well as the signal to facilitate further study of their variation with distance. Based on the novel approximation of the fundamental modal field in graded-index fiber, we formulate analytical expression as regards the variation of modal intensity with radial distance from the axis of the fiber both for the pump and the signal fields and estimate such variation for step-index fiber of some typical V values as example. We find that our estimation matches excellently with the available exact results in case of both the pump and the signal and is shown to be much superior to one-parameter Gaussian approximation. In addition, our methodology involves less computation compared to the exact analysis involving cumbersome computation.     

Biosynthesis of Streptolidine Involved Two Unexpected Intermediates Produced by a Dihydroxylase and a Cyclase through Unusual Mechanisms

Streptothricin‐F (STT‐F), one of the early‐discovered antibiotics, consists of three components, a β‐lysine homopolymer, an aminosugar D ‐gulosamine, and an unusual bicyclic streptolidine. The biosynthesis of streptolidine is a long‐lasting but unresolved puzzle. Herein, a combination of genetic/biochemical/structural approaches was used to unravel this problem. The STT gene cluster was first sequenced from a Streptomyces variant BCRC 12163, wherein two gene products OrfP and OrfR were characterized in vitro to be a dihydroxylase and a cyclase, respectively. Thirteen high‐resolution crystal structures for both enzymes in different reaction intermediate states were snapshotted to help elucidate their catalytic mechanisms. OrfP catalyzes an Fe^II‐dependent double hydroxylation reaction converting L ‐Arg into (3R,4R)‐(OH)₂‐L ‐Arg via (3S)‐OH‐L ‐Arg, while OrfR catalyzes an unusual PLP‐dependent elimination/addition reaction cyclizing (3R,4R)‐(OH)₂‐L ‐Arg to the six‐membered (4R)‐OH‐capreomycidine. The biosynthetic mystery finally comes to light as the latter product was incorporation into STT‐F by a feeding experiment.     

Synthesis of a novel uracil-2,6-diaminopyridine-lithocholic acid conjugate that self-assembles into a cyclic dimer

Synthesis and self-association studies of a uracil-2,6-diaminopyridine-lithocholic acid conjugate are described. The dimeric supramolecular structure is characterized by NMR spectroscopic, ESI-MS, and size exclusion chromatographic studies.     

Packing two disks into a polygonal environment

We consider the following problem. Given a polygon P, possibly with holes, and having n vertices, compute a pair of equal radius disks that do not intersect each other, are contained in P, and whose radius is maximized. Our main result is a simple randomized algorithm whose expected running time, on any input, is O(nlogn). This is optimal in the algebraic decision tree model of computation.     

Approximating geometric bottleneck shortest paths

In a geometric bottleneck shortest path problem, we are given a set S of n points in the plane, and want to answer queries of the following type: given two points p and q of S and a real number L, compute (or approximate) a shortest path between p and q in the subgraph of the complete graph on S consisting of all edges whose lengths are less than or equal to L. We present efficient algorithms for answering several query problems of this type. Our solutions are based on Euclidean minimum spanning trees, spanners, and the Delaunay triangulation. A result of independent interest is the following. For any two points p and q of S, there is a path between p and q in the Delaunay triangulation, whose length is less than or equal to 2π/(3cos(π/6)) times the Euclidean distance |pq| between p and q, and all of whose edges have length at most |pq|.     

Relation between the common anion rule and the defect model of Schottky barrier formation

We present calculations of the energy levels of anion vacancies near the (110) surface of GaInAs, GaInP and GaAlAs. The results suggest that the defect model of Schottky barrier formation with anion vacancy-like states being responsible for Fermi level pinning is consistent with the common anion rule as observed in GaInAs and GaInP and also with the exception to the rule presented by GaAlAs.