Irreducibility of the -classes on smooth rational surfaces

We give a characterization for a -divisor on a smooth rational surface to be irreducible under the assumption that an anticanonical divisor of is nef. Here is nef means for every effective divisor on , and a -divisor is a divisor such that the two numerical conditions hold.

As an application we give explicit examples of blowing up the projective plane at nine points infinitely near such that the obtained surface has an infinite number of -curves. A -curve is a smooth rational curve of self-intersection .

     

Allylic oxidation: easy synthesis of alkenones from activated alkenes with TEMPO

Activated alkenes and dienes are converted into the corresponding alkenone in excellent yields (>90%). In aqueous acetonitrile, the transformations are catalyzed by 2,2,6,6-tetramethyl-1-oxopiperidinium (TEMPO⁺) in the presence of water and 2,6-lutidine. TEMPO⁺ cations were regenerated electrochemically from the radical parent (TEMPO) at a vitreous carbon anode.     

Synthesis,structural studies and antituberculosis evaluation of new hydrazone derivatives of quinoline and their Zn(II) complexes

The quinoline hydrazone ligands were synthesized through multi-step reactions. The 2-hydroxy-3-formylquinoline derivatives (1a–1c) were prepared from acetanilide derivatives as starting materials using Vilsmeier–Haack reaction. Then the condensation of 2-hydroxy-3-formylquinoline derivatives with hydrazide derivatives (2a–2c) yielded quinoline hydrazone ligands (3a–3i). The synthesis of a new series of Zn(II) complexes carried out by refluxing with these quinoline hydrazone ligands (3a–3i) is reported. The molecular structures of the ligands (3a–3i) and the Zn complexes were characterized by elemental analysis and spectral studies like FT-IR, ¹H and ¹³C NMR, MS, UV–Visible and fluorescence. The preliminary results of antituberculosis study showed that most of the Zn(II) complexes 4a–4i demonstrated very good antituberculosis activity while the ligands 3a–3i showed moderate activity. Among the tested compounds 4e and 4g were found to be most active with minimum inhibitory concentration (MIC) of 8.00 μM and 7.42 μM respectively against Mycobacterium tuberculosis (H37 RV strain) ATCC No-27294 which is comparable to “first and second line” drugs used to treat tuberculosis.     

Enhancement in the supercapacitive storage performance of MnCO<Subscript>3</Subscript> using SiO<Subscript>x</Subscript> nanofluid-based electrolyte

Generally adopted strategies to improve capacitance of the electrode materials are tuning various properties of the electrode material or increasing the cell voltage. While tuning the properties of the electrode material is tedious, increasing the cell voltage is restricted by the stability of the electrolyte. Herein, we report a facile approach to improve the capacitance of MnCO₃ by the influence of SiO_x nanofluid in the electrolyte. The capacitance properties of MnCO₃ are studied in 0.1 M Mg(ClO₄)₂ electrolyte in the presence and in the absence of SiO_x nanofluid. The presence of small amount of SiO_x nanofluid in the electrolyte provides higher diffusivity and more conductive percolation paths for ions and thus decreases internal resistance and increases ionic conductivity of the electrolyte. As a result, 60% enhancement in the capacitance is witnessed for MnCO₃. Further, nanofluid containing electrolyte is found to be stable over a month.

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Graphical abstract Improvement in the capacitance properties of MnCO by the influence of SiO nanofluid

     

Refining the Hermite-Hadamard inequalities for operator convex maps in multiple operator variables

Intensive studies aiming to extend the Hermite-Hadamard inequalities and to explore some properties and applications of these inequalities have been carried out recently. The contribution of this paper falls within this framework. We investigate here some refinements of the Hermite-Hadamard inequalities for operator convex maps involving multiple operator arguments.

     

The Effect of the Microstructure on Trap‐Assisted Recombination and Light Soaking Phenomenon in Hybrid Perovskite Solar Cells

Despite the rich experience gained in controlling the microstructure of perovskite films over the past several years, little is known about how the microstructure affects the device properties of perovskite solar cells (HPSCs). In this work, the effects of the perovskite film microstructure on the charge recombination and light‐soaking phenomenon in mixed halide HPSCs are investigated. Devices with noncompact perovskite morphology show a severe light soaking effect, with the power conversion efficiency (PCE) improved from 3.7% to 11.6% after light soaking. Devices with compact perovskite morphology show a negligible light soaking effect, with PCE slightly increased from 11.4% to 11.9% after light soaking. From device investigations, photoluminescence, and impedance spectroscopy measurements, it is demonstrated that interface electron traps at the grain boundaries as well as at the crystal surface dominate the light soaking effect. Severe trap‐assisted recombination takes place in HPSCs using noncompact films, while it is effectively eliminated in devices with compact films. Moreover, how the grain size of the perovskite film affects the light soaking phenomenon is investigated. In the case of compact perovskite films, the size of the grains has a limited effect on the light soaking. In these compact films, grains are fused and trap states are effectively reduced.     

Ratios of some domination parameters in trees

We determine upper bounds on the ratios of several domination parameters in trees.