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 $d^{⁎}\in \{5,6,7\}$.     

Dynamics of laser-induced cavitation bubble during expansion over sharp-edge geometry submerged in liquid – an inside view by diffuse illumination

Laser ablation in liquids is growing in popularity for various applications including nanoparticle production, breakdown spectroscopy, and surface functionalization. When laser pulse ablates the solid target submerged in liquid, a cavitation bubble develops. In case of “finite” geometries of ablated solids, liquid dynamical phenomena can occur inside the bubble when the bubble overflows the surface edge. To observe this dynamics, we use diffuse illumination of a flashlamp in combination with a high-speed videography by exposure times down to 250 ns. The developed theoretical modelling and its comparison with the experimental observations clearly prove that this approach widens the observable area inside the bubble. We thereby use it to study the dynamics of laser-induced cavitation bubble during its expansion over a sharp-edge (“cliff-like” 90°) geometry submerged in water, ethanol, and polyethylene glycol 300. The samples are 17 mm wide stainless steel plates with thickness in the range of 0.025–2 mm. Bubbles are induced on the samples by 1064-nm laser pulses with pulse durations of 7–60 ns and pulse energies of 10–55 mJ. We observe formation of a fixed-type secondary cavity behind the edge where low-pressure area develops due to bubble-driven flow of the liquid. This occurs when the velocity of liquid overflow exceeds ~20 m s⁻¹. A re-entrant liquid injection with up to ~40 m s⁻¹ velocity may occur inside the bubble when the bubble overflows the edge of the sample. Formation and characteristics of the jet evidently depend on the relation between the breakdown-edge offset and the bubble energy, as well as the properties of the surrounding liquid. Higher viscosity of the liquid prevents the generation of the jet.     

Novel synthesis of sensor for selective detection of Fe+3 ions under various solvents

Naked-eye colored chemo dosimeter based on vanilline based conjugated sensor was synthesized and characterized. The main point of this paper is that the solvent also affects on selectivity of metals. Vanilline based conjugate sensor exhibited high selectivity and sensitivity for detection of Ferric ions (Fe⁺³) in all (both polar and nonpolar) solvents according to absorbance which can be observed by naked eye. The selectivity was more prominent in nonpolar or less polar solvent due to solubility factor of ions and sensor but not for polar. The detection of limit of the synthesized probes was shown up to 0.84 ppm. The dielectric constant of solvents affected on the complex formation of ligand with transition metal ions. A filter paper strip system was used for rapid monitoring of detection by color variation.     

从知识传授到育人:高职“生活中的化学”教学实践*

深挖高职院校公选课“生活中的化学”的育人元素,精心设计教学内容,运用课堂主题辩论、趣味生活实验的设计与展示、探秘生活中的化学等理论知识传授与课内外实践相结合的教学方式,实现全过程育人,充分展现了公选课在立德树人方面的价值。     

γ-Valerolactone (GVL) as a green and efficient dipolar aprotic reaction medium

The great challenge for modern research is to define the most efficient tools to make more sustainable the industrial production and manufacturing. Among the different aspects that require attention the replacement of toxic and/or non-renewable solvents it is certainly playing a crucial role. Dealing with widely used dipolar aprotic solvents, among the different alternatives proposed in the literature γ-valerolactone (GVL) plays a pivotal role covering different application area. In this contribution, the benefits derived from the use of GVL as a circular, safe, biomass-derived reaction medium are highlighted covering most recent publications (2021). The presentation has been divided into three major sections: (i) biomass valorization, (ii) materials synthesis, manufacturing and recycle and (iii) new synthetic methodologies.     

原位液相透射电子显微镜及其在 纳米粒子表征方面的应用

近年来,基于透射电子显微技术、微纳加工技术和薄膜制造技术的发展,原位液相透射电子显微技术产生,为构建多种纳米级分辨率尺度下的微实验平台,发展新型纳米表征技术和众多领域的相关研究提供了途径.本文首先介绍了应用于原位液相透射电子显微技术的液体腔设计要求,然后介绍了液体腔的发展和典型的制备工艺,最后综述了近年来液体腔透射电子显微镜在纳米粒子成核和生长方面的应用研究,并探讨了该技术前沿发展面临的机遇和挑战.本文将为提高我国先进纳米表征技术和原子精准构筑技术提供相关讨论和支持.     

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.     

Design,synthesis and evaluation of novel dehydroabietic acid-dithiocarbamate hybrids as potential multi-targeted compounds for tumor cytotoxicity

In the present study, novel representatives of the important group of biologically-active, dehydroabietic acid-bearing dithiocarbamate moiety, were synthesized and characterized by ¹H NMR, ¹³C NMR, HR-MS. The in vitro antiproliferative activity evaluation (MTT) indicated that these compounds exhibited potent inhibitory activities in various cancer cell lines (HepG-2, MCF-7, HeLa, T-24, MGC-803). Particularly, compound III-b possessed extraordinary cytotoxicity with low micromolar IC₅₀ values ranging from 4.07 to 38.84 µM against tested cancer cell lines, while displayed weak cytotoxicity on two normal cell lines (LO-2 and HEK 293 T). Subsequently, the potential mechanisms of representative compound III-b were elementarily investigated by Transwell experiment, which showed III-b can inhibit cancer cells migration. Annexin-V/PI dual staining showed that the compound can induce HepG-2 cells apoptosis in a dose-dependent manner. Meanwhile this apoptosis may be related to the upregulated protein expression of cleaved-caspase 3, cleaved-caspase 9, Bax and downregulated of Bcl-2 indicated by Western Blot. Later study further confirmed that ROS levels in HepG-2 cells increased significantly with the rise of concentrations. In addition, through the network pharmacology data analyzing, the core targets and signaling pathways of compound III-b for treatment of liver neoplasms were forecasted. Molecular docking model showed that compound III-b had high affinity with hub targets (CASP3, EGFR, HSP90AA1, MAPK1, ERBB2, MDM2), suggesting that compound III-b might target the hub protein to modulate signaling activity. Taken together, these data indicated that dehydroabietic acid structural modification following the “Molecular hybridization” principle is a feasible way to discover the potential multi-targeted antitumor compounds.