Regularity of optimal sets for some functional involving eigenvalues of an operator in divergence form

In this paper we consider minimizers of the functional$\min \{{\lambda }_1(\mathrm{\Omega })+\cdots +{\lambda }_k(\mathrm{\Omega })+\mathrm{\Lambda }|\mathrm{\Omega }|,:\mathrm{\Omega }\subset D\text{ open}\}$ where $D\subset {\mathbb{R}}^d$ is a bounded open set and where $0<{\lambda }_1(\mathrm{\Omega })\le \cdots \le {\lambda }_k(\mathrm{\Omega })$ are the first k eigenvalues on Ω of an operator in divergence form with Dirichlet boundary condition and with Hölder continuous coefficients. We prove that the optimal sets ${\mathrm{\Omega }}^{⁎}$ have finite perimeter and that their free boundary $\partial {\mathrm{\Omega }}^{⁎}\cap D$ is composed of a regular part, which is locally the graph of a $C^{1,\alpha }$-regular function, and a singular part, which is empty if $d<d^{⁎}$, discrete if $d=d^{⁎}$ and of Hausdorff dimension at most $d-d^{⁎}$ if $d>d^{⁎}$, for some $d^{⁎}\in \{5,6,7\}$.     

The Fifty Percent Machines—A Short History of Influence Machines and an Elementary Theory of Their Efficiency: An Attempt

Presenting the devices invented by Toepler, Holtz, Wimshurst, and Wommelsdorf, the history of the influence machines, the progress made, and the remaining deficits are discussed. The theoretical considerations published in the literature lack generalizable statements on the efficiency. Based on R. W. Pohl's model (1927), an elementary analysis is made, with the result that the upper limit of the theoretically achievable efficiency of influence machines is only 50%.     

游客情感计算的文本大数据挖掘方法比较研究

旅游文本大数据以其方便、快捷和低门槛的特点为游客情感计算提供了极大便利，已经成为旅游大数据的主要来源之一。基于大数据理论和情感理论，以文本大数据为数据源，在全面梳理国内外情感计算相关成果的基础上，利用人工智能中的逻辑/算法编程方法、机器学习方法、深度学习方法对旅游文本大数据进行挖掘，探索最佳的基于文本大数据的游客情感计算方法。研究发现：（1）基于情感词典的游客情感计算模型，其核心是构建情感词典和设计情感计算规则，方法简单，容易实现，适用语料范围广。（2）机器学习，用统计学方法抽取文本中的特征项，具有非线性特征，可靠性较线性特征的情感词典方法高。（3）基于深度学习技术的游客情感计算，效果良好，准确率在85%以上。训练多领域的文本语料易于移植，实用性强，且泛化能力好，较适合大数据时代游客情感计算研究。     

The impact of insecticides containing deltamethrin and cyfluthrin on the composition of surface compounds in the larvae,females and males of Tenebrio molitor

This paper presents the effect of insecticides on the composition of the surface compounds of one of the most harmful insects, Tenebrio molitor, by analysis using GC–MS. As a result of the use of insecticides, the composition of the chemical compounds on the surface of insects changes, depending on the insecticides used. The most numerous groups of the marked compounds were fatty acids, alkanes, esters and sterols. The content of the identified compounds in the larvae increased at both 24 and 48 h after the application of insecticides, in comparison with the control samples. The content of identified compounds in the samples taken from the females increased 24, 48 and 72 h after the application of insecticides in comparison with the control samples. By contrast, in samples prepared from males, the content of identified compounds decreased 24 h after the application of insecticides, compared with the control samples. The highest content of chemical compounds was for fatty acids and alkanes after the use of insecticides. The content of fatty acids after the application of the insecticide with deltamethrin was 62.1 ± 3.3–466.9 ± 5.9 μg/g, and after the application of the insecticide with cyfluthrin was 49.9 ± 1.9–458.3 ± 4.2 μg/g. However, the content of alkanes after the use of deltamethrin was 115.6 ± 4.2–4672.0 ± 32.1 μg/g, and after the use of cyfluthrin was 189.4 ± 3.8–3975.0 ± 10.2 μg/g.     

LC-MS-based multi-omics analysis of brain tissue for the evaluation of the anti-ischemic stroke potential of Tribulus terrestris L. fruit extract in MCAO rats

This study aimed to investigate the chemical composition of Tribulus terrestris L. fruit (TT) extract named TT15 and its protective effect against ischemic stroke (IS) as well as corresponding mechanisms. The chemical composition of TT15 was analyzed by liquid chromatography-mass spectrometry (LC-MS), and the compound identification was conducted via searching the in-house database. The LC-MS-based multi-omics approach was applied to search the differential metabolites and differential proteins in rat brain tissue and to explore the biomarker and molecular mechanism of TT15 against middle cerebral artery occlusion (MCAO). A total of 20 compounds were identified from TT15, mainly including alkaloids, flavonoids, phenols, quinones, and esters. These 20 compounds significantly affected the metabolism of 44 metabolites and the expression of 51 proteins. Joint pathway analysis showed that these metabolites and proteins were mainly involved in the response to elevated platelet cytosolic Ca²⁺ and platelet activation, which inferred that TT15 may exert a protective effect against cerebral ischemic injury via regulating platelet function. This study provides useful information for further exploration of the mechanisms of TT extract against IS.     

Key Role of a-Top CO on Terrace Sites of Metallic Pd Clusters for CO Oxidation

Pd-based catalysts are the most widely used for CO oxidation because of their outstanding catalytic activity and thermal stability. However, fundamental understanding of the detailed catalytic processes occurring on Pd-based catalysts under realistic conditions is still lacking. In this study, we investigated CO oxidation on metallic Pd clusters supported on Al₂O₃ and SiO₂. High-angle annular dark-field scanning transmission electron microscopy revealed the formation of similar-sized Pd clusters on Al₂O₃ and SiO₂. In contrast, CO chemisorption analysis indicated a gradual change in the dispersion of Pd (from 0.79 to 0.2) on Pd/Al₂O₃ and a marginal change in the dispersion (from 0.4 to 0.24) on Pd/SiO₂ as the Pd loading increased from 0.27 to 5.5 wt %; these changes were attributed to differences in the metal-support interactions. Diffuse reflectance infrared Fourier-transform spectroscopy revealed that fewer a-top CO species were present in Pd supported on Al₂O₃ than those in Pd supported on SiO₂, which is related to the morphological differences in the metallic Pd clusters on these two supports. Despite the different dispersion profiles and surface characteristics of Pd, O₂ titration demonstrated that linearly bound CO (with an infrared signal at 2090 cm⁻¹) reacted first with oxygen in the case of CO-saturated Pd on Al₂O₃ and SiO₂, which suggests that a-top CO on the terrace site plays an important role in CO oxidation. The experimental observations were corroborated by periodic density functional calculations, which confirmed that CO oxidation on the (111) terrace sites is most plausible, both kinetically and thermodynamically, compared to that on the edge or corner sites. This study will deepen the fundamental understanding of the effect of Pd clusters on CO oxidation under reaction conditions.     

Versatile Near-Infrared Super-Resolution Imaging of Amyloid Fibrils with the Fluorogenic Probe CRANAD-2

CRANAD-2 is a fluorogenic curcumin derivative used for near-infrared detection and imaging in vivo of amyloid aggregates, which are involved in neurodegenerative diseases. We explore the performance of CRANAD-2 in two super-resolution imaging techniques, namely stimulated emission depletion (STED) and single-molecule localization microscopy (SMLM), with markedly different fluorophore requirements. By conveniently adapting the concentration of CRANAD-2, which transiently binds to amyloid fibrils, we show that it performs well in both techniques, achieving a resolution in the range of 45–55 nm. Correlation of SMLM with atomic force microscopy (AFM) validates the resolution of fine features in the reconstructed super-resolved image. The good performance and versatility of CRANAD-2 provides a powerful tool for near-infrared nanoscopic imaging of amyloids in vitro and in vivo.     

Optimisation of the ultrasound-assisted extraction of betalains and polyphenols from Amaranthus hypochondriacus var. Nutrisol

The present study optimised the ultrasound-assisted extraction (UAE) of bioactive compounds from Amaranthus hypochondriacus var. Nutrisol. Influence of temperature (25.86–54.14 °C) and ultrasonic power densities (UPD) (76.01–273.99 mW/mL) on total betalains (BT), betacyanins (BC), betaxanthins (BX), total polyphenols (TP), antioxidant activity (AA), colour parameters (L*, a*, and b*), amaranthine (A), and isoamaranthine (IA) were evaluated using response surface methodology. Moreover, betalain extraction kinetics and mass transfer coefficients (K_La) were determined for each experimental condition. BT, BC, BX, TP, AA, b*, K_La, and A were significantly affected (p < 0.05) by temperature extraction and UPD, whereas L*, a*, and IA were only affected (p < 0.05) by temperature. All response models were significantly validated with regression coefficients (R²) ranging from 87.46 to 99.29%. BT, A, IA, and K_La in UAE were 1.38, 1.65, 1.50, and 29.93 times higher than determined using conventional extraction, respectively. Optimal UAE conditions were obtained at 41.80 °C and 188.84 mW/mL using the desired function methodology. Under these conditions, the experimental values for BC, BX, BT, TP, AA, L*, a*, b*, K_La, A, and IA were closely related to the predicted values, indicating the suitability of the developed quadratic models. This study proposes a simple and efficient UAE method to obtain betalains and polyphenols with high antioxidant activity, which can be used in several applications within the food industry.     

Classify the Higgs decays with the PFN and ParticleNet at electron–positron colliders

Various Higgs factories are proposed to study the Higgs boson precisely and systematically in a model- independent way. In this study, the Particle Flow Network and ParticleNet techniques are used to classify the Higgs decays into multicategories, and the ultimate goal is to realize an "end-to-end" analysis. A Monte Carlo simulation study is performed to demonstrate the feasibility, and the performance looks rather promising. This result could be the basis of a "one-stop" analysis to measure all the branching fractions of the Higgs decays simultaneously.