Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

On the simplicity of induced modules for reductive Lie algebras II

An open problem proposed by Friedlander and Parshall is considered. A sufficient condition is given for the simplicity of induced modules of reductive Lie algebras.     

Free boundary problem for a fully nonlinear and degenerate parabolic equation in an angular domain

This paper concerns with the problem of how to running an insurance company to maximize his total discounted expected dividends. In our model, the dividend rate is limited in $[0,M]$ and the company is allowed to transfer any proportion of risk by reinsuring. So there are two strategies which we call dividend strategy and reinsurance strategy. The objective function and the corresponding optimal two strategies are the solution and the two free boundaries of the following Barenblatt parabolic equation

$v_t?\underset{0\le a\le 1}{\max }?(\frac{1}{2}{a}^2{\sigma }^2{v}_{xx}+a\mu v_x)+cv?\underset{0\le l\le M}{\max }?[(1?v_x)l]=0$

under certain boundary conditions on an angular domain

$Q_T=\{(x,t)|0<x<Mt,0<t\le T\}.$

The main effort is to analyze the properties of the solution and the free boundaries to show the optimal decision for the insurance company.     

Liquid-Repellent Metal Oxide Photocatalysts

Metal oxide photocatalysts (MOPCs) decompose organic molecules under illumination. However, the application of MOPCs in industry and research is currently limited by their intrinsic hydrophilicity because MOPCs can be wetted by most liquids. To achieve liquid repellency, the surface needs to possess a low surface energy, but most organic molecules with low surface energy are degraded by photocatalytic activity. Herein, current methods to achieve liquid repellency on MOPCs, while preventing degradation of hydrophobic coatings, are reviewed. Classically, composite materials containing MOPCs and hydrophobic organic compounds possess good liquid repellency. However, composites normally form irregular coatings and are hard to prepare on surfaces such as those that are mesoporous or nanostructured. In addition, the adhesion of composites to substrates is often weak, resulting in delamination. Recent studies have shown that the direct grafting reaction of polydimethylsiloxane (PDMS) from silicone oil (methyl-terminated PDMS) under illumination results in a stable polymer brush. This easy and simple grafting method allows us to create stable liquid-repellent surfaces on MOPCs of various types, structures, and sizes. In particular, super-liquid-repellent drops with an underlying air layer can be created on PDMS-grafted nano-/microstructured MOPCs. Potential applications of surfaces combining liquid repellency and photocatalytic activity are also discussed; thus offering new ways of using MOPCs in a wider range of applications.     

Optimization of cadmium adsorption from aqueous solutions by functionalized graphene and the reversible magnetic recovery of the adsorbent using response surface methodology

Novel functionalized graphene adsorbent was prepared and characterized using different techniques. The prepared adsorbent was applied for the removal of cadmium ions from aqueous solution. A response surface methodology was used to evaluate the simple and combined effects of the various parameters, including adsorbent dosage, pH, and initial concentration. Under the optimal conditions, the cadmium removal performance of 70% was achieved. A good agreement between experimental and predicted data in this study was observed. The experimental results revealed of cadmium adsorption with high linearity follow Langmuir isotherm model with maximum adsorption capacity of 502 mg g^?1, and the adsorption data fitted well into pseudo‐second order model. Thermodynamic studies showed that adsorption process has exothermic and spontaneous nature. The recommended optimum conditions are: cadmium concentration of 970 mg L^?1, adsorbent dosage of 1 g L^?1, pH of 6.18, and T = 25 °C. The magnetic recovery of the adsorbent was performed using a magnetic surfactant to form a noncovalent magnetic functionalized graphene. After magnetic recovery of the adsorbent both components (adsorbent and magnetic surfactant) were recycled by tuning the surface charges through changing the pH of the solution. Desorption behavior studied using HNO₃ solution indicated that the adsorbent had the potential for reusability.     

Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

An insight into the potent antioxidant activity of a dithiocarbohydrazone appended cis-dioxidomolybdenum (VI) complexes

In search of antioxidants with enriched potency, the present study focus on the design and synthesis of a dithiocarbohydrazone, H₃TCL derived from thiocarbohydrazide and 3-ethoxysalicylaldehyde and its coordination complexes with molybdenum, viz, [MoO₂(HTCL)D] ( 1 – 2 ) (where D = methanol ( 1 ), DMSO ( 2 )) and [MoO₂(HTCL)D]·DMF (where D = H₂O ( 3 )). The synthesized compounds were characterised by elemental analysis, spectroscopic techniques (FT-IR, UV–vis and ¹H-NMR), conductivity measurements and cyclic voltammetry. Moreover the solid state structures of all the three complexes were established by single crystal X-ray diffraction analysis as mononuclear neutral species in which the molybdenum centre assumes a distorted octahedral geometry. The dithiocarbohydrazone binds to the molybdenum centre through its phenolate oxygen, O(1), azomethine nitrogen, N(1) and thioenolate sulfur, S(1) in a dianionic tridentate mode. The assessment of intermolecular contacts in the crystal arrangement was quantified using Hirshfeld surface analysis. Further the antioxidant potential of the dithiocarbohydrazone, H₃TCL and its molybdenum complexes 1 – 3 were evaluated using 1,1-diphenyl-2-picrylhydrazyl(DPPH), 2,2′-azinobis-3-ethylbenzothiazoline-6-sulfonic acid (ABTS) and total antioxidant assays. The antioxidant activities were then compared with standard antioxidant, L-ascorbic acid. The antioxidant potential of the synthesized compounds were then validated by molecular docking studies. Molecular modelling study was achieved to evaluate the recognition of target compound at the binding pocket of the human antioxidant enzyme, 3MNG. The docking results showed that the complexes selectively bond to the vital amino acids present in the binding pocket of the target enzyme, 3MNG.     

On the use of surfaces of section in the N-body ring problem

In the N-body ring problem, we investigate the motion of a massless body interacting with N bodies of equal masses at the vertices of a regular polygon that rotates around a central mass. In this paper, we analyze the use of different surfaces of section in the numerical exploration of the escape in the N-body ring problem in order to get some conclusions about the geometry of the basins of escape in the corresponding configuration spaces.