Taking theophylline and (1R,2S)‐(−)‐ephedrine as template molecules, two imprinted photonic‐hydrogel films are prepared by a combination of colloidal‐crystal and molecular‐imprinting techniques. This paper shows a new approach for rapid and handy stimulant detection with high sensitivity and specificity. One film is proposed for analogous molecule assay, another one for chiral recognition. The key point of this approach is that the imprinted photonic polymer (IPP) consists of a three‐dimensional (3D), highly‐ordered and interconnected macroporous array with a thin hydrogel wall, where nanocavities complementary to analytes in shape and binding sites are distributed. This special, bicontinuous, hierarchical structure enables this polymer to report quickly, easily, sensitively and directly a molecular recognition event without any transducers and treatments for analytes (label‐free). The inherent affinity of the nanocavities, deriving from molecular imprinting, makes these sensors highly specific to analytes, even if in a competitive environment. Their sensitive and specific responses to stimulants in buffer are determined by Bragg diffractive shifts due to the lattice change of their 3D ordered macroporous arrays resulting from their preferential rebinding to the target molecules. The measurements show that the prepared hydrogel films exhibit high sensitivity in such a 0.1 fM concentration of analytes and specificity even in a competitive urinous buffer. The reported method provides a rapid and handy approach for stimulant assay and drug analysis in athletic sports.
In this paper, we study Mabuchi's K-energy on a compactification M of a reductive Lie group G, which is a complexification of its maximal compact subgroup K. We give a criterion for the properness of K-energy on the space of K × K-invariant Kähler potentials. In particular, it turns to give an alternative proof of Delcroix's theorem for the existence of Kähler-Einstein metrics in case of Fano manifolds M . We also study the existence of minimizers of K-energy for general Kähler classes of M .2000 Mathematics Subject Classification. Primary: 53C25; Secondary: 53C55, 58J05, 19L10.
Hollow nanostructured hosts are important scaffolds to achieve high sulfur loading, fast charge transfer, and conspicuous restraint of lithium polysulfides (LiPSs) shuttling in lithium‐sulfur (Li‐S) batteries. However, developing high‐efficiency hollow hosts for improving utilization and conversion of aggregated sulfur in the hollow chamber remains a longstanding challenge. Herein, hollow N‐doped carbon nanocubes confined petal‐like ZnS/SnS2 heterostructures (ZnS/SnS2@NC) as a conceptually novel host for Li‐S batteries are reported. Specifically, compared to consubstantial hollow double‐shelled hosts, the ZnS/SnS2@NC with higher effective active surface area brings dense contact with sulfur and enhances efficient adsorption sites for binding LiPSs and accelerating their conversion. Benefiting from the unique structure and sophisticated composition, the resulting S@ZnS/SnS2@NC cathodes exhibit 1294 mAh g−1 at 0.2 C, an ultralow capacity decay of 0.016% per cycle over 500 cycles at 1.0 C, and a high area capacity of 4.77 mAh cm−2 at 0.5 C (5.9 mg cm−2). Meanwhile, the performance evolution of S@ZnS/SnS2@NC cathodes under various sulfur loadings is further investigated by using EIS, which provides the beneficial guidance to explore viable strategies further optimizing their performance. This work sheds new insights into the design of hollow nanostructured hosts with a distinguished ability to regulate LiPSs in Li‐S batteries.
In this paper, we develop a direct blowing-up and rescaling argument for a nonlinear equation involving the fractional Laplacian operator. Instead of using the conventional extension method introduced by Caffarelli and Silvestre, we work directly on the nonlocal operator. Using the integral defining the nonlocal elliptic operator, by an elementary approach, we carry on a blowing-up and rescaling argument directly on nonlocal equations and thus obtain a priori estimates on the positive solutions for a semi-linear equation involving the fractional Laplacian.We believe that the ideas introduced here can be applied to problems involving more general nonlocal operators.
In this note, we give explicit expressions of Gauss sums for general (resp. special) linear groups over finite fields, which involve classical Gauss sums (resp. Kloosterman sums). The key ingredient is averaging such sums over Borel subgroups, i.e., the groups of upper triangular matrices. As applications, we count the number of invertible matrices of zero-trace over finite fields and we also improve two bounds of Ferguson, Hoffman, Luca, Ostafe and Shparlinski in [R. Ferguson, C. Hoffman, F. Luca, A. Ostafe, I.E. Shparlinski, Some additive combinatorics problems in matrix rings, Rev. Mat. Complut. 23 (2010) 501-513].
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