On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

Evolutionary neighborhood discovery algorithm for agricultural routing planning in multiple fields

Annals of Operations Research - In recent years, operations research in agriculture has improved the harvested yield, reduced the cost and time required for field operations, and maintained...     

What is the role of acid–acid interactions in asymmetric phosphoric acid organocatalysis? A detailed mechanistic study using interlocked and non-interlocked catalysts

Organocatalysis has revolutionized asymmetric synthesis. However, the supramolecular interactions of organocatalysts in solution are often neglected, although the formation of catalyst aggregates can have a strong impact on the catalytic reaction. For phosphoric acid based organocatalysts, we have now established that catalyst–catalyst interactions can be suppressed by using macrocyclic catalysts, which react predominantly in a monomeric fashion, while they can be favored by integration into a bifunctional catenane, which reacts mainly as phosphoric acid dimers. For acyclic phosphoric acids, we found a strongly concentration dependent behavior, involving both monomeric and dimeric catalytic pathways. Based on a detailed experimental analysis, DFT-calculations and direct NMR-based observation of the catalyst aggregates, we could demonstrate that intermolecular acid–acid interactions have a drastic influence on the reaction rate and stereoselectivity of asymmetric transfer-hydrogenation catalyzed by chiral phosphoric acids.

Supramolecular acid–acid interactions lead to competing monomeric and dimeric pathways in phosphoric acid catalysis – so that stereoselectivities depend on catalyst concentration.     

The Riemann–Hilbert analysis to the Pollaczek–Jacobi type orthogonal polynomials

In this paper, we study polynomials orthogonal with respect to a Pollaczek–Jacobi type weight The uniform asymptotic expansions for the monic orthogonal polynomials on the interval (0,1) and outside this interval are obtained. Moreover, near , the uniform asymptotic expansion involves Airy function as , and Bessel function of order α as in the neighborhood of , the uniform asymptotic expansion is associated with Bessel function of order β as . The recurrence coefficients and leading coefficient of the orthogonal polynomials are expressed in terms of a particular Painlevé III transcendent. We also obtain the limit of the kernel in the bulk of the spectrum. The double scaled logarithmic derivative of the Hankel determinant satisfies a σ‐form Painlevé III equation. The asymptotic analysis is based on the Deift and Zhou's steepest descent method.     

Platinum Oxide Nanoparticles for Electrochemical Hydrogen Evolution: Influence of Platinum Valence State

Electrochemical hydrogen generation is a rising prospect for future renewable energy storage and conversion. Platinum remains a leading choice of catalyst, but because of its high cost and low natural abundance, it is critical to optimize its use. In the present study, platinum oxide nanoparticles of approximately 2 nm in diameter are deposited on carbon nitride (C3N4) nanosheets by thermal refluxing of C3N4 and PtCl₂ or PtCl₄ in water. These nanoparticles exhibit apparent electrocatalytic activity toward the hydrogen evolution reaction (HER) in acid. Interestingly, the HER activity increases with increasing Pt⁴⁺ concentration in the nanoparticles, and the optimized catalyst even outperforms commercial Pt/C, exhibiting an overpotential of only −7.7 mV to reach the current density of 10 mA cm⁻² and a Tafel slope of −26.3 mV dec⁻¹. The results from this study suggest that the future design of platinum oxide catalysts should strive to maximize the Pt⁴⁺ sites and minimize the formation of the less active Pt²⁺ species.     

Electronic Finetuning of 8-Methoxy Psoralens by Palladium-Catalyzed Coupling: Acidochromicity and Solvatochromicity

Differently 5-substituted 8-methoxypsoralens can be synthesized by an efficient synthetic route with various cross-coupling methodologies, such as Suzuki, Sonogashira and Heck reaction. Compared to previously synthesized psoralens, thereby promising daylight absorbing compounds as potentially active agents against certain skin diseases can be readily accessed. Extensive investigations of all synthesized psoralen derivatives reveal fluorescence in the solid state as well as several distinctly emissive derivatives in solution. Donor-substituted psoralens exhibit remarkable photophysical properties, such as high fluorescence quantum yields and pronounced emission solvatochromicity and acidochromicity, which were scrutinized by Lippert–Mataga and Stern–Volmer plots. The results indicate that the compounds exceed the limit of visible light, a significant factor for potential applications as an active agent. In addition, (TD)DFT calculations were performed to elucidate the underlying electronic structure and to assign experimentally obtained data.