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 $d^{⁎}\in \{5,6,7\}$.     

Morphologically controlled synthesis of 1-dimensional selenium dioxide and study of its application as catalyst for diesel fuel additive

In this research work, selenium dioxide (SeO₂) nanorods have been prepared by a solvothermal method in which a strong reducing agent (NaBH₄) was used to reduce precursor salt into SeO₂ nanorods. X-ray diffraction (XRD) technique was applied to observe the crystal structure which confirmed its tetragonal geometry. Moreover, morphology and particle size were studied by scanning electron microscopy (SEM). SEM fully described the 1-dimensional morphology of SeO₂ nanorods which then arranged themselves to create a 3-dimensional flower-like structure with an average particle size of 50 nm. Also, the catalytic activity of SeO₂ nanorods as diesel-additive was studied by defining different parameters such as fire and flash points, calorific value, cloud and pour points, specific gravity, and kinematic viscosity. Subsequently, SeO₂ nanorods proved to be an excellent diesel additive due to higher total heat content and lower value of kinematic viscosity which enhances the better performance of the diesel engine.     

Experimental and numerical analysis of cylindrical turbulators in a double pipe heat exchanger under turbulent flow conditions

In the present work, the use of cylindrical turbulators in a double pipe heat exchanger has been investigated. Cylindrical fin type of turbulators has been placed circumferentially separated by 90° on the outer side of an inner pipe at a regular pitch. Experimental studies were undertaken for different air flow rates in a turbulent regime whose Reynolds number range between 2500 and 10000. Heat transfer characteristics like Nu and friction factor have been experimentally determined. Parametric studies were conducted by changing the pitch and also the orientation of the turbulators. Nu and friction factor were found to increase as the pitch is reduced. A model with alternatively changed orientation outperformed others by exhibiting highest Nu and reduced friction factor.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Assembling hydrodynamic cloaks to conceal complex objects from drag

Transformation hydrodynamics and the corresponding metamaterials have been proposed as a means to exclude the drag force acting on an object. Here, we report a strategy to deploy the hydrodynamic cloaks in a more practical manner by assembling different-shaped cloaking parts. Our strategy is to first model a square-shaped cloak and a carpet cloak and then combine them to conceal a more complex-shaped space in the three-dimensional hydrodynamic flow. With the derivation of transformation hydrodynamics, the coordinate transformations for each hydrodynamic cloaking are demonstrated with the calculated viscosity tensors. The pressure and velocity fields of the square, triangular (carpet), and exemplary three-dimensional house-shaped cloaks are numerically simulated, thus showing a cloaking effect and reduced drag. This study suggests an efficient way of cloaking complex architectures from fluid-dynamic forces.     

Gravitational wave imprint of new symmetry breaking

It is believed that there are more fundamental gauge symmetries beyond those described by the Standard Model of particle physics. The scales of these new gauge symmetries are usually too high to be reachable by particle colliders. Considering that the phase transition (PT) relating to the spontaneous breaking of new gauge symmetries to the electroweak symmetry might be strongly first order, we propose considering the stochastic gravitational waves (GW) arising from this phase transition as an indirect way of detecting these new fundamental gauge symmetries. As an illustration, we explore the possibility of detecting the stochastic GW generated from the PT of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} in the space-based interferometer detectors. Our study demonstrates that the GW energy spectrum is reachable by the LISA, Tianqin, Taiji, BBO, and DECIGO experiments only for the case where the spontaneous breaking of \begin{document}$ {\bf{B}}-{\bf{L}}$\end{document} is triggered by at least two electroweak singlet scalars.     

基于吸收系数的生脉注射液中聚山梨酯80含量测定新方法

聚山梨酯80又名吐温80，为一种亲水型非离子表面活性剂，是食品、保健品和药品中常用的辅料，作为增溶剂和澄清剂广泛用于中药注射剂。近年来，不良反应的发生使得聚山梨酯80的质量和应用愈加受到重视，有研究认为其加入可能引起注射剂不良反应增加。为避免超量使用，有必要对该辅料的投料加以严格控制。中药注射剂中聚山梨酯80的含量测定是当下研究的热点和难点，可以通过分光光度法、分子排阻-蒸发光散射检测法(SEC-ELSD)、液质联用法(LC-MS)直接测定，也可以水解后法经液相色谱-紫外检测法(HPLC-UV)或气相色谱法(GC)间接测定。但由于聚山梨酯80为聚氧乙烯聚合数目不同的混合物、不同厂家生产的聚山梨酯80化学组分及比例存在较大差异，难以采用统一的转换公式或对照品准确定量。此外，中药注射剂的复杂基质造成的假阳性干扰也对定量提出了挑战。为解决以上问题，以生脉注射液为例，提出基于吸收系数的中药注射剂中聚山梨酯80含量测定新方法。优化检测波长、显色剂种类、液液萃取过程振荡和静置时间，在6个不同品牌仪器上测得聚山梨酯80-硫氰酸钴配合物的吸收系数(E1%_{1 cm})为104.23，相对标准偏差(RSD)为2.08%。生脉注射液稀释10倍后，精密量取供试品溶液1.0 mL，精密加入硫氰酸钴溶液10 mL，二氯甲烷20 mL，涡旋振荡3 min。将混合液移至分液漏斗中，静置30 min，取下层二氯甲烷液，将前1 mL弃去，接收约15 mL，在320 nm处测定吸光度，再根据Lambert-Beer定律，利用获得的吸收系数计算得到聚山梨酯80的含量。方法阴性无干扰，精密度和重复性相对标准偏差均低于3%，平均回收率为98.42%。为进一步验证方法的准确性，分别采用吸收系数法和标准曲线法测定了2个厂家的10批生脉注射液，并与实际投料量比较。配对t检验结果表明，当置信度为95%时，两种方法无显著性差异，吸收系数法测得结果与企业生产中聚山梨酯的实际投料量也无显著性差异。研究采用前人未采用的、灵敏度更高的320 nm为检测波长，显著降低了基质干扰，克服了中药注射剂中聚山梨酯80测定结果与实际投料量难以吻合的问题。吸收系数法无需使用对照品，亦不用制备标准曲线，可为中药注射剂中聚山梨酯80的检查标准提供切实可行的解决方案。所建方法灵敏、准确、快速、简便，为含聚山梨酯80制剂的质量控制提供了关键常数及新的思路。     

为什么要引入溶剂的渗透因子

阐明了引入溶剂渗透因子的必要性,较详细地介绍了两种渗透因子及它们间的关系。     

Pulse radiolysis study of the initial steps of the polymerization of cyclohexyl acrylate and cyclohexyl methacrylate

Pulse radiolysis with kinetic spectroscopic detection was applied to study the kinetics of the first steps of radiation induced polymerization of cyclohexyl acrylate and cyclohexyl methacrylate in cyclohexane solvent. The reactions were initiated by cyclohexyl radicals produced in the radiolysis of the solvent. The transient absorption spectra of the -carboxyalkyl type radicals produced in addition reaction show maxima around 300 nm. This shifts to longer wavelength with time after the pulse. This phenomenon was explained by the oligomerization reaction. From the kinetic curves average rate coefficients of termination for the oligomer radicals (2k_t) were determined as a function of time elapsed after the electron pulse. The values obtained were compared with those calculated for other (acrylate and methacrylate type) monomers.