The paper has two parts, in the first part, we apply the localisation technique to the Rozansky–Witten theory on compact hyperkähler targets. We do so via first reformulating the theory as some ...supersymmetric sigma-model. We obtain the exact formula for the partition function with Wilson loops on
S
1
×
Σ
g
and the lens spaces, the results match with earlier computations using Feynman diagrams on K3. The second part is motivated by a very curious paper (Gukov in J Geom Phys 168, 104311, 2021), where the equivariant index formula for the dimension of the Hilbert space of the Rozansky–Witten theory is interpreted as a kind of Verlinde formula. In this interpretation, the fixed points of the target hyperkähler geometry correspond to certain ‘states’. We extend the formalism of part one to incorporate equivariance on the target geometry. For certain non-compact hyperkähler geometry, we can apply the tilting theory to the derived category of coherent sheaves, whose objects label the Wilson loops, allowing us to pick a basis for the latter. We can then compute the fusion products in this basis and we show that the objects that have diagonal fusion rules are intimately related to the fixed points of the geometry. Using these objects as basis to compute the dimension of the Hilbert space leads back to the Verlinde formula, thus answering the question that motivated the paper.
Electrochemiluminescence (ECL) plays a key role in analysis and sensing because of its high sensitivity and low background. Its wide applications are however limited by a lack of highly tunable ECL ...luminophores. Here we develop a scalable method to design ECL emitters of covalent organic frameworks (COFs) in aqueous medium by simultaneously restricting the donor and acceptor to the COFs' tight electron configurations and constructing high-speed charge transport networks through olefin linkages. This design allows efficient intramolecular charge transfer for strong ECL, and no exogenous poisonous co-reactants are needed. Olefin-linked donor-acceptor conjugated COFs, systematically synthesized by combining non-ECL active monomers with C
or C
symmetry, exhibit strong ECL signals, which can be boosted by increasing the chain length and conjugation of monomers. The present concept demonstrates that the highly efficient COF-based ECL luminophores can be precisely designed, providing a promising direction toward COF-based ECL phosphors.
Following our previous proposal, we construct a class of good "lattice cross sections" (LCSs), from which we can study the partonic structure of hadrons from ab initio lattice QCD calculations. These ...good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that the proposed functions for lattice QCD calculation of PDFs in the literature are special cases of these good LCSs.
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Uranium is a key resource for the development of the nuclear industry, and extracting uranium from the natural seawater is one of the most promising ways to address the shortage of uranium resources. ...Herein, a semiconducting covalent organic framework (named NDA‐TN‐AO) with excellent photocatalytic and photoelectric activities was synthesized. The excellent photocatalytic effect endowed NDA‐TN‐AO with a high anti‐biofouling activity by generating biotoxic reactive oxygen species and promoting photoelectrons to reduce the adsorbed UVI to insoluble UIV, thereby increasing the uranium extraction capacity. Owing to the photoinduced effect, the adsorption capacity of NDA‐TN‐AO to uranium in seawater reaches 6.07 mg g−1, which is 1.33 times of that in dark. The NDA‐TN‐AO with enhanced adsorption capacity is a promising material for extracting uranium from the natural seawater.
Photoelectric and photocatalytic effects endow the covalent organic framework NDA‐TN‐AO with good anti‐biofouling activity. This occurs by generating biotoxic reactive oxygen species and promoting photoelectrons to reduce the adsorbed UVI to insoluble UIV, thereby improving the uranium adsorption capacity.
The emergence of flexible and wearable electronic devices with shape amenability and high mobility has stimulated the development of flexible power sources to bring revolutionary changes to daily ...lives. The conventional rechargeable batteries with fixed geometries and sizes have limited their functionalities in wearable applications. The first‐ever graphene‐based fibrous rechargeable batteries are reported in this work. Ultralight composite fibers consisting of reduced graphene oxide/carbon nanotube filled with a large amount of sulfur (rGO/CNT/S) are prepared by a facile, one‐pot wet‐spinning method. The liquid crystalline behavior of high concentration GO sheets facilitates the alignment of rGO/CNT/S composites, enabling rational assembly into flexible and conductive fibers as lithium–sulfur battery electrodes. The ultralight fiber electrodes with scalable linear densities ranging from 0.028 to 0.13 mg cm−1 deliver a high initial capacity of 1255 mAh g−1 and an areal capacity of 2.49 mAh cm−2 at C/20. A shape‐conformable cable battery prototype demonstrates a stable discharge characteristic after 30 bending cycles.
A freestanding and ultralight reduced graphene oxide (rGO)/carbon nanotube (CNT)/sulfur composite fibers are prepared by wet‐spinning as the cathode for lithium–sulfur batteries (LSBs). The liquid crystallinity of high concentration GO sheets enables rational assembly of rGO/CNT/S as flexible, conductive fibers. A cable LSB prototype comprising rGO/CNT/S cathode and lithium wire anode demonstrates excellent flexibility and stable static discharge performance.
2D covalent organic frameworks (2D COFs) have been recognized as a novel class of photoactive materials owing to their extended π‐electron conjugation and high chemical stabilities. Herein, a new ...covalent organic framework (Tph‐BDP) is facilely synthesized by using a porphyrin derivative and an organic dye BODIPY derivative (5,5‐difluoro‐2,8‐diformyl‐1,3,7,9‐tetramethyl‐10‐phenyl‐5H‐dipyrrolo1,2‐c:2′,1′‐f1,3,2diazabori‐nin‐4‐ium‐5‐uide) as monomers for the first time, and their unique photosensitive properties endow them excellent simulated oxidase activity under 635 nm laser irradiation that can catalyze the oxidation of 3,3′,5,5′‐tetramethylbenzidine (TMB). Further findings demonstrate that the presence of uranium (UO22+) can coordinate with imines of the oxidation products of TMB, thus modulating the charge transfer process of the colored products accompanied with intensive aggregation and remarkable color fading. This research provides a preparation strategy for COFs with excellent photocatalytic properties and nanozyme activity, and broadens the applications of the simple colorimetric methods for sensitive and selective radionuclide detection.
A new covalent organic framework is facilely synthesized and its unique photosensitive property endows excellent simulated oxidase activity that can catalyze the oxidation of 3,3′,5,5′‐tetramethylbenzidine (TMB). The presence of uranium can coordinate with imines of the oxidation products of TMB, thus modulating the charge transfer process of the colored products accompanied with intensive aggregation and remarkable color fading.
A
bstract
We present the details of a new factorized approach to semi-inclusive deep-inelastic scattering which treats QED and QCD radiation on equal footing, and provides a systematically improvable ...approximation to the extraction of transverse momentum dependent parton distributions. We demonstrate how the QED contributions can be well approximated by collinear factorization, and illustrate the application of the factorized approach to QED radiation in inclusive scattering. For semi-inclusive processes, we show how radiation effects prevent a well-defined “photon-nucleon” frame, forcing one to use a two-step process to account for the radiation. We illustrate the utility of the new method by explicit application to the spin-dependent Sivers and Collins asymmetries.
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