Synthesis and heterocyclizations of 3‐alkynyl‐6,8‐dimethylpyrimido‐[4,5‐c]pyridazine‐5,7(6H,8H)‐diones and their lumazine analogues

Synthesis of some condensed pyrrolo‐, thieno‐, furo‐, pyrido‐ and pyranopteridines as well as isomeric pyrrolo‐ and thienopyrimido[4,5‐c]pyridazines from alkynyl derivatives of 6,8‐dimethylpyrimido[4,5‐c]pyridazine‐5,7(6H,8H)‐dione and 1,3‐dimethyllumazine is represented.     

Purines, pyrimidines, and related fused systems. 20. Heterocyclizations of 6-alkynyl-1,3-dimethyllumazines. Synthesis of pyrrole and thiophene analogs of some natural pteridines

Sonogashira cross-coupling of 6-chloro-1,3-dimethyllumazine with terminal alkynes gave 6-alkynyl derivatives in good yields. Oxidative amination of the latter with primary alkylamines was accompanied by the pyrrole-ring closure to form 1-R"-2-R-6,8-dimethylpyrrolo[3,2-g]pteridine-5,7(6H,8H)-diones. The addition of bromine to 6-alkynyllumazines afforded the corresponding dibromoalkenes whose treatment with sodium trithiocarbonate gave rise to 2-R-6,8-dimethylthieno[3,2-g]pteridine-5,7(6H,8H)-diones. The latter compounds are close analogs of the metabolite of molybdenum cofactor (molybdopterine).     

Comprehensive and High-throughput Electrolysis of Water and Urea by 3–5 nm Nickel and Copper Coordination Polymers

Metal-organic coordination polymers (CP) have attracted the scientific attention for electrochemical water oxidation as it has the similar coordination structure like natural photosynthetic coordinated complex. However, the harsh synthesis conditions and bulky nature pose a major challenge in the field of catalysis. Herein, 3–5 nm CP particles synthesized at room temperature using aqueous solutions of Ni²⁺/Cu²⁺ and 2,5-dihydroxyterepthalic acid as precursor were applied for alkaline water and urea electrolysis. The overpotential required is only 300 mV at 10 mA cm⁻² by Nano-Ni CP for water oxidation, with turnover frequency (TOF) of 21.4 s⁻¹ which is around 8 times higher than its bulk-counterpart. Overall water and urea splitting were achieved with Nano-Cu (−) ∥ Nano-Ni (+) couple on Ni foam at 1.69 and 1.52 V to achieve 10 mA cm⁻², respectively. High electrochemical surface area (ECSA), high TOF, and enhanced mass diffusion are found to be the key parameters responsible for the state-of-the-art water and urea splitting performances of nano-CPs as compared to their bulk counterparts.     

H-extension of graphs

We consider the problem of constructing a graphG* from a collection of isomorphic copies of a graphG in such a way that for every two copies ofG, either no vertices or a section graph isomorphic to a graphH is identified. It is shown that ifG can be partitioned into vertex-disjoint copies ofH, thenG* can be made to have at most |H| orbits. A condition onG so thatG* can be vertextransitive is also included.     

Bending of Light and Gravitational Signals in Certain On-Brane and Bulk Geometries

In this article, we first investigate the bending of light rays in 4D line elements representing spherically symmetric, static on–brane geometries. The amount of bending in these four dimensional, strong and weak field solutions is derived. Signatures, which appear in the bending formulae, due to the presence of extra dimensions are discussed. Subsequently, as a separate exercise, we calculate the bending of null geodesic trajectories in a bulk five dimensional spacetime with a Schwarzschild line element on the 3-brane section. We interpret the deviation of null trajectories as that of gravitational signals or five dimensional photons, which are, unlike light rays confined to four dimensions, allowed to propagate along the fifth (extra) dimension. Features of the presence of extra dimensions in the effective potentials and the bending formula are analysed in this context.     

Threshold reduction of stimulated Brillouin scattering in photonic crystal fiber

A simple configuration for the reduction of stimulated Brillouin scattering threshold in photonic crystal fiber is presented. The threshold reduction is contributed by the bidirectional pumping scheme through the reflection of transmitted Brillouin pump back to the gain medium. The pump recycling scheme has greatly reduced the Brillouin threshold of a 200-m long of photonic crystal fiber from 50 to 30 mW of Brillouin pump power.     

A novel tandem cyclization of condensed 2,3-dialkynylpyrazines into [1,2,3]triazolo[1′,5′;1,2]pyrido[3,4-b]pyrazines promoted by sodium azide

6,7-Dialkynyl-1,3-dimethylpteridine-2,4(1H,3H)-diones and 2,3-dialkynylquinoxalines have been shown to react with sodium azide in DMF at room temperature giving rise 9,11-dimethyl-[1,2,3]triazolo[1′,5′;1,2]pyrido[4,3-g]pteridine-8,10(9H,11H)-diones and [1,2,3]triazolo[1′,5′;1,2]pyrido[3,4-b]quinoxalines. A novel tandem cyclization involves 1,3-dipolar cycloaddition of an azide ion to the carbon-carbon triple bond followed by intramolecular nucleophilic addition of the intermediate 1,2,3-triazole N-anion to another CC bond.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.