Asymptotic Behavior of Least Energy Solutions for a Fractional Laplacian Eigenvalue Problem on ℝN

Acta Mathematica Sinica, English Series - We are interested in the existence and asymptotic behavior for the least energy solutions of the following fractional eigenvalue problem $$\left({\rm{P}}...     

Fourier transforms on finite group actions and bent functions

Journal of Algebraic Combinatorics - Highly nonlinear functions (bent functions, perfect nonlinear functions, etc.) on finite fields and finite (abelian or nonabelian) groups have been studied in...     

n-APR tilting and $$\tau $$ τ -mutations

Journal of Algebraic Combinatorics - APR tilts for path algebra kQ can be realized as the mutation of the quiver Q in $${\mathbb Z}Q$$ with respect to the translation. In this paper, we show that...     

现代分析仪器在高中化学教学中的应用*——以“防晒霜的防晒效果实验探究”为例

从高中化学原子、分子等抽象性的知识教学出发,以防晒霜的防晒效果实验探究为例,探讨了现代分析仪器在高中化学教学中的应用。通过利用现代分析仪器紫外可见分光光度计,结合紫外线变色球实验探究防晒霜的防晒效果,分析并认识防晒霜中化学防晒的机理。结果表明,防晒霜的厚度越大、SPF越高,防晒霜的防晒效果越好,并且防晒霜的防晒效果可以持续一段时间,但是不同类型的防晒产品存在一定差异。在化学教学中渗透现代分析仪器的应用,为学生进一步了解化学学科在改变学习方式、拓宽学科知识领域、推动自身全面与可持续发展方面打下坚实的基础。     

Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis

In this paper, we present a method of higher-order analysis on bifurcation of small limit cycles around an elementary center of integrable systems under perturbations. This method is equivalent to higher-order Melinikov function approach used for studying bifurcation of limit cycles around a center but simpler. Attention is focused on planar cubic polynomial systems and particularly it is shown that the system studied by ?o?a?dek (1995) [24] can indeed have eleven limit cycles under perturbations at least up to 7th order. Moreover, the pattern of numbers of limit cycles produced near the center is discussed up to 39th-order perturbations, and no more than eleven limit cycles are found.     

Self-supported metal sulphide nanocrystals-assembled nanosheets on carbon paper as efficient counter electrodes for quantum-dot-sensitized solar cells

Developing efficient counter electrodes (CEs) and quantum dots made of earth-abundant and non-toxic elements is essential but still challenging for quantum dot-sensitized solar cells (QDSSCs). Here, we report a facile strategy to prepare self-supported and robust CoS₂ and NiS nanocrystals-assembled nanosheets directly grown on carbon paper (MSx NS@CP) as efficient counter electrodes for QDSSCs. Such CEs integrate the merits of fast electron transfer from interconnected conductive scaffold, efficient mass transfer from hierarchically vertical nanosheet on 3D open substrate, as well as abundant highly active catalytic sites from metal sulphide nanocrystal units. As a result, QDDSCs based on such CoS₂ NS@CP and NiS NS@CP CEs achieve a PCE of 8.88% and 7.53%, respectively. The detailed analyses suggest that CoS₂ NS@CP has the highest catalytic activity and shows the lowest charger transfer resistance, leading to the highest PCE. These findings may inspire the design and exploration of other self-supported efficient CEs by integrating highly active catalysts onto 3D conductive networks for efficient QDSSCs.     

Spectrum–effect relationship of antioxidant and anti-inflammatory activities of Laportea bulbifera based on multivariate statistical analysis

Laportea bulbifera, named Hong He Ma in Chinese, is a Chinese herbal medicine commonly used by the Miao nationality of China. In this study, 43 batches of L. bulbifera were collected from different origins in China. Ethanol, ethyl acetate and petroleum ether were used to prepare different extracts of the plant. UHPLC technique was used to establish the fingerprints, whereas DPPH assay and RAW264.7 inflammatory cell models were used to evaluate the antioxidant and anti-inflammatory activities, respectively. Moreover, the spectrum–effect relationship between relative peak area of common peaks and efficacy value was set up by multivariate statistical analysis. Furthermore, 10 batches were selected randomly for validation of those models. The results showed that ethyl acetate and petroleum ether extracts possess excellent antioxidant and anti-inflammatory activities, respectively. Peaks A₆ and A₇ demonstrated the greatest antioxidant activity, while peak A₁₇ showed the strongest anti-inflammatory activity. After a verified experiment, the result was obtained and illustrated that the spectrum–effect relationship which we established could reliably infer antioxidant and anti-inflammatory compounds of the Chinese herbal medicine.     

Solid‐phase microextraction Arrow for the volatile organic compounds in soy sauce

A novel solid‐phase microextraction Arrow was used to separate volatile organic compounds from soy sauce, and the results were verified by using gas chromatography with mass spectrometry. Solid‐phase microextraction Arrow was optimized in terms of three extraction conditions: type of fiber used (polydimethylsiloxane, polyacrylate, carbon wide range/polydimethylsiloxane, and divinylbenzene/polydimethylsiloxane), extraction temperature (40, 50, and 60°C), and extraction time (10, 30, and 60 min). The optimal solid‐phase microextraction Arrow conditions were as follows: type of fiber = polyacrylate, extraction time = 60 min, and extraction temperature = 50°C. Under the optimized conditions, the solid‐phase microextraction Arrow was compared with conventional solid‐phase microextraction to determine extraction yields. The solid‐phase microextraction Arrow yielded 6–42‐fold higher levels than in solid‐phase microextraction for all 21 volatile organic compounds detected in soy sauce due to the larger sorption phase volume. The findings of this study can provide practical guidelines for solid‐phase microextraction Arrow applications in food matrixes by providing analytical methods for volatile organic compounds.     

Thorium adsorption on graphene oxide nanoribbons/manganese dioxide composite material

A functional graphene oxide nanoribbons/manganese dioxide composite material (MnO₂-GONRs) was synthesized by hydrothermal method using graphene oxide nanoribbons (GONRs) as raw material which were formed by longitudinal unzipping of multi-walled carbon nanotubes with KMnO₄ and H₂SO₄. The microstructure of MnO₂-GONRs was characterized by SEM and FT-IR. The various factors affecting the adsorption of Th(IV) in aqueous solution such as pH, solid–liquid ratio, contact time, initial concentration and temperature were investigated by batch static adsorption experiments, and the adsorption mechanism is also discussed. The results showed that MnO₂-GONRs had a good adsorption effect on Th(IV) with a maximum adsorption of 166.11 mg/g.

     

Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays

A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.