Chemical profiling of bioactive constituents in hop cones and pellets extracts by online comprehensive two‐dimensional liquid chromatography with tandem mass spectrometry and direct infusion Fourier transform ion cyclotron resonance mass spectrometry

Humulus lupulus L. (hop) is highly interesting from a nutraceutical perspective. The hop phytocomplex contains a wide range of bioactive metabolites, and its characterization is challenging. To tackle such a task, for the first time we applied and compared a combined approach consisting of online comprehensive two‐dimensional liquid chromatography with tandem mass spectrometry and direct infusion Fourier transform ion cyclotron mass spectrometry. A reversed phase × reversed phase approach with a shifted gradient in the second dimension ensured selectivity and two‐dimensional space coverage. Hyphenation with an ion trap time‐of‐flight analyzer led to the identification of 83 compounds in 70 min, comprising a novel quercetin derivative and six unknown bitter acids. On the other hand, the direct infusion method was able to identify 40 analytes (except isomers) with high mass accuracy (≤ 0.1 ppm) in less than 1 min analysis time. The developed approach can be used in a complementary way, combining the separation capability and high informative spectra of two‐dimensional liquid chromatography tandem mass spectrometry with the ultra‐high mass accuracy of direct infusion, for potential compound discovery or the accurate profiling of bioactive compounds in different hop cultivars as well as for monitoring processing and storage of hop‐based products.     

Formation of intermediate coupling optical polarons and bipolarons in two-dimensional systems

The formation of the optical polaron and bipolaron in two-dimensional (2D) systems is studied in the intermediate electron–phonon coupling regime. The total energies of the 2D polaron and bipolaron are calculated by using the Buimistrov–Pekar method of canonical transformations. The obtained results are compared with other existing results obtained by using the Feynman path integral method and the modified Lee–Low–Pines unitary transformation method. It is shown that the electron–phonon correlation significantly reduces the total energy of the 2D polaron in comparison with the energy of the strong coupling (adiabatic) polaron. It is found that the polaron formation in 2D systems is possible when the electron–phonon coupling constant α is greater than the critical value ${\alpha }_c?2.94$, which is much lower than a critical value of the electron–phonon coupling constant α in three-dimensional (3D) systems. The critical values of the Fröhlich coupling constant α and the ratio $\eta ={\epsilon }_{\infty }/{\epsilon }_0$ (where ${\epsilon }_{\infty }$ and ${\epsilon }_0$ are the high frequency and static dielectric constants, respectively), which determine the bipolaron stability region in 2D systems, are calculated numerically. It is interesting for application to the layered cuprate superconductors that the (bi)polarons are formed more easily in quasi-2D regions than in the bulk. It is argued that the high-$T_c$ cuprate superconductivity can exist above the bulk superconducting transition temperature $T_c$ as the persisting superfluidity of polaronic (bosonic) Cooper pairs and large bipolarons at quasi-2D grain boundaries or in the CuO₂ layers above $T_c$.     

Multilayered 2D Cesium-Based Hybrid Perovskite with Strong Polarization Sensitivity: Dimensional Reduction of CsPbBr3

3D perovskite CsPbBr₃ has recently taken a blooming position for optoelectronic applications. However, due to the lack of natural anisotropy of optical attributes, it is a great challenge to fulfil polarization-sensitive photodetection. Here, for the first time, we exploited dimensionality reduction of CsPbBr₃ to tailor a 2D-multilayered hybrid perovskite, (TRA)₂CsPb₂Br₇ ( 1 , in which TRA is (carboxy)cyclohexylmethylammonium), serving as a potential polarized-light detecting candidate. Its unique quantum-confined 2D structure results in intrinsic anisotropy of electrical conductivity, optical absorbance, and polarization-dependent responses. Particularly, it exhibits remarkable dichroism with the photocurrent ratio (I_pc/I_pa) of ≈2.1, being much higher than that of the isotropic CsPbBr₃ crystal and reported CH₃NH₃PbI₃ nanowire (≈1.3), which reveals its great potentials for polarization-sensitive photodetection. Further, crystal-based detectors of 1 show fascinating responses to the polarized light, including high detectivity (>10¹⁰ Jones), fast responding time (≈300 μs), and sizeable on/off current ratios (>10⁴). To our best knowledge, this is the first study on 2D Cs-based hybrid perovskite exhibiting strong polarization-sensitivity. The work highlights an effective pathway to explore new polarization sensitive candidates for hybrid perovskites and promotes their future electronic applications.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Lower bound for the ratios of eigenvalues of Schrödinger with nonpositive single‐barrier potentials

Horváth and Kiss (Proc. Amer. Math. Soc., 2005) proved the upper bound estimate for Dirichlet eigenvalue ratios of the Schrödinger problem ?y^′′ + q(x)y = λy with nonnegative and single‐well potential q. In this paper, we prove that if q(x) is a nonpositive, continuous, and single‐barrier potential, then for λ_n > λ_m≥ ? 2q^?, where . In particular, if q(x) satisfies the additional condition , then λ₁ > 0 and for n > m ≥ 1. For this result, we develop a new approach to study the monotonicity of the modified Prüfer angle function.     

Concentration on curves for a nonlinear Schrödinger problem with electromagnetic potential

We prove the existence of solutions to the nonlinear Schrödinger equation ${\epsilon }^2{(i\mathrm{?}+\mathit{A})}^{2}u+V(y)u?|u{|}^{p?1}u=0$ in ${\mathbb{R}}^2$ with a magnetic potential $\mathit{A}=(A_1,A_2)$. Here V represents the electric potential, the index p is greater than 1. Along some sequence $\{{\epsilon }_n\}$ tending to zero we exhibit complex-value solutions that concentrate along some closed curves.