Existence of positive solution for nonlocal singular fourth order Kirchhoff equation with Hardy potential

This paper is concerned with the existence of positive solution to a class of singular fourth order elliptic equation of Kirchhoff type

$$\begin{aligned} \triangle ^2 u-\lambda M(\Vert \nabla u\Vert ^2)\triangle u-\frac{\mu }{\vert x\vert ^4}u=\frac{h(x)}{u^\gamma }+k(x)u^\alpha , \end{aligned}$$

under Navier boundary conditions, \(u=\triangle u=0\). Here \(\varOmega \subset {\mathbf {R}}^N\), \(N\ge 1\) is a bounded \(C^4\)-domain, \(0\in \varOmega \), h(x) and k(x) are positive continuous functions, \(\gamma \in (0,1)\), \(\alpha \in (0,1)\) and \(M:{\mathbf {R}}^+\rightarrow {\mathbf {R}}^+\) is a continuous function. By using Galerkin method and sharp angle lemma, we will show that this problem has a positive solution for \(\lambda > \frac{\mu }{\mu ^*m_0}\) and \(0<\mu <\mu ^*\). Here \(\mu ^*=\Big (\frac{N(N-4)}{4}\Big )^2\) is the best constant in the Hardy inequality. Besides, if \(\mu =0\), \(\lambda >0\) and h, k are Lipschitz functions, we show that this problem has a positive smooth solution. If \(h,k\in C^{2,\,\theta _0}(\overline{\varOmega })\) for some \(\theta _0\in (0,1)\), then this problem has a positive classical solution.

     

Elucidation of Antioxidant Compounds in Moroccan Chamaerops humilis L. Fruits by GC–MS and HPLC–MS Techniques

The aim of this study was to characterize the phytochemical content as well as the antioxidant ability of the Moroccan species Chamaerops humilis L. Besides crude ethanolic extract, two extracts obtained by sonication using two solvents with increased polarity, namely ethyl acetate (EtOAc) and methanol-water (MeOH-H₂O) 80:20 (v/v), were investigated by both spectroscopy and chromatography methods. Between the two extracts, the MeOH-H₂O one showed the highest total polyphenolic content equal to 32.7 ± 0.1 mg GAE/g DM with respect to the EtOAc extract (3.6 ± 0.5 mg GAE/g DM). Concerning the antioxidant activity of the two extracts, the EtOAc one yielded the highest value (1.9 ± 0.1 mg/mL) with respect to MeOH-H2O (0.4 ± 0.1 mg/mL). The C. humilis n-hexane fraction, analyzed by GC–MS, exhibited 69 compounds belonging to different chemical classes, with n-Hexadecanoic acid as a major compound (21.75%), whereas the polyphenolic profile, elucidated by HPLC–PDA/MS, led to the identification of a total of sixteen and thirteen different compounds in both EtOAc (major component: ferulic acid: 104.7 ± 2.52 µg/g) and MeOH-H₂O extracts (major component: chlorogenic acid: 45.4 ± 1.59 µg/g), respectively. The attained results clearly highlight the potential of C. humilis as an important source of bioactive components, making it a valuable candidate to be advantageously added to the daily diet. Furthermore, this study provides the scientific basis for the exploitation of the Doum in the food, pharmaceutical and nutraceutical industries.     

Highly efficient one-pot synthesis of tetrahydropyridines

The combination of aromatic aldehydes, and 1,3-dicarbonyl compounds in the presence of a catalytic amount of poly(N,N′-dibromo-N-ethyl-benzene-1,3-disulfonamide) [PBBS] and N,N,N′,N′-tetrabromobenzene-1,3-disulfonamide [TBBDA] leads to the formation of highly substituted tetrahydropyridines. In this way, a series of pharmacologically interesting substituted piperidine derivatives were obtained in moderate to high yields at room temperature.     

Bimetallic Lanthanum-Cerium-Loaded HZSM-5 Composite for Catalytic Deoxygenation of Microalgae-Hydrolyzed Oil into Green Hydrocarbon Fuels

Due to their high lipid content, microalgae are one of the most significant sources of green hydrocarbons, which might help lessen the world’s need for fossil fuels. Many zeolite-based catalysts are quickly deactivated by coke production and have a short lifetime. In this study, a bimetallic Lanthanum-Cerium (La-Ce)-modified HZSM-5 zeolite catalyst was synthesized through an impregnation method and was tested for the conversion of hydrolyzed oil into oxygen-free hydrocarbon fuels of high energy content. Initially, hydrolyzed oil (HO), the byproduct of the transesterification process, was obtained by the reaction of crude oil derived from Chlorella vulgaris microalgae and a methanol. Various catalysts were produced, screened, and evaluated for their ability to convert algal HO into hydrocarbons and other valuable compounds in a batch reactor. The performance of HZSM-5 was systematically tested in view of La-Ce loaded on conversion, yield, and selectivity. NH₃-TPD analysis showed that the total acidity of the La-Ce-modified zeolites was lower than that of the pure HZSM-5 catalyst. TGA testing revealed that including the rare earth elements La and Ce in the HZSM-5 catalyst lowered the catalyst propensity for producing coke deposits. The acid sites necessary for algal HO conversion were improved by putting La and Ce into HZSM-5 zeolite at various loading percentages. The maximum hydrocarbon yield (42.963%), the highest HHV (34.362 MJ/Kg), and the highest DOD% (62.191%) were all achieved by the (7.5%La-2.5%Ce)/HZSM-5 catalyst, which was synthesized in this work. For comparison, the hydrocarbon yield for the parent HZSM-5 was 21.838%, the HHV was (33.230 MJ/Kg), and the DOD% was 44.235%. In conclusion, La and Ce-loading on the parent HZSM-5 may be responsible for the observed alterations in textural properties; nevertheless, there is no clear correlation between the physical features and the hydrocarbon yield (%). The principal effect of La and Ce modifying the parent HZSM-5 zeolite was to modify the acidic sites needed to enhance the conversion (%) of the algal HO during the catalytic deoxygenation process, which in turn raised the hydrocarbon yield (%) and increased the HHV and DOD%.     

Catalytic Deoxygenation of Hydrolyzed Oil of Chlorella Vulgaris Microalgae over Lanthanum-Embedded HZSM-5 Zeolite Catalyst to Produce Bio-Fuels

Microalgae is one of the most important sources of green hydrocarbons because it contains a high percentage of lipids and is likely to reduce reliance on fossil fuels. Several zeolite-based catalysts have a short lifetime due to coke-formation deactivation. In this study, a lanthanum-modified HZSM-5 zeolite catalyst for the conversion of crude oil into non-oxygenated compounds (hydrocarbons) and oxygenated compounds has been investigated. The crude oil of Chlorella Vulgaris microalgae was extracted using Soxhlet and converted into hydrolyzed oil (HO) through a transesterification reaction. The experiments were conducted in a batch reactor (300 °C, 1000 rpm, 7 bar of N₂, the catalyst to the algal HO ratio of 15% (wt.%) and 6 h). The results were organized into three groups: product yield, chemical composition, and carbon number distribution. The liquid products were investigated, including their elemental composition, higher heating value (HHV), atomic ratios of O/C and H/C, and degree of deoxygenation (DOD%). The loading of lanthanum into HZSM-5 zeolite with different loading percentages enhanced the acid sites needed for the algal HO conversion. Among all the synthesized catalysts, 10%La/HZSM-5 produced the highest conversion of the algal HO, the highest yield of hydrocarbons, the highest HHV, and the highest DOD%; those were 100%, 36.88%, 34.16 MJ/kg, and 56.11%, respectively. The enhanced catalytic conversion was due to the presence of lanthanum, which alters the active sites for the desired reactions of catalytic deoxygenation. The main effect of the modification of the parent HZSM-5 zeolite with lanthanum led to adjusting the acidic sites needed to increase the conversion (%) of the algal HO in the catalytic deoxygenation process and thus increase the hydrocarbon yield (%), which in turn led to an increase in the HHV and DOD%. The proposed La-based zeolite composite is promising for different energy applications due to its unique benefits compared to other expensive and less-stable catalysts.     

Minimizing Curves in Prox-regular Subsets of Riemannian Manifolds

Set-Valued and Variational Analysis - We obtain a characterization of the proximal normal cone to a prox-regular subset of a Riemannian manifold and some properties of Bouligand tangent cones to...     

Ligandless C‐C bond formation via Suzuki–Miyaura reaction in micelles or water–ethanol solution using PdPtZn and PdZn nanoparticle thin films

PdPtZn and PdZn nanoparticle (NP) thin films were synthesized by the reduction of [PdCl₂(cod)], [PtCl₂(cod)] (cod = cis,cis‐1,5‐cyclooctadiene) and [Zn(acac)₂] (acac = acetylacetonate) complexes at an oil–water interface. The structure and morphology of the as‐prepared NPs were characterized with X‐ray diffraction, transmission electron microscopy and energy dispersive analysis of X‐rays. Catalytic activity of the prepared NPs was investigated in the Suzuki–Miyaura cross‐coupling reaction in H₂O–EtOH and various micellar media systems such as cetyltrimethylammonium bromide (cationic surfactant), sodium dodecylsulfate (anionic surfactant) and Pluronic P123 (non‐ionic surfactant). PdPtZn and PdZn thin films exhibited higher catalytic activity compared to Pd thin film in the Suzuki–Miyaura coupling reaction due to the appropriate interaction between palladium, platinum and zinc metals. Copyright © 2015 John Wiley & Sons, Ltd.     

Crystal structure and density functional theory study on structural properties and energies of a isonicotinohydrazide compound

An X-ray and a theoretical study of the structure of the isoniazid derivative N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate (1) are reported. In this work, we will report a combined experimental and theoretical study on the molecular structure, vibrational spectra and energies of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate. The calculated parameters are in good agreement with the corresponding X-ray diffraction values. The FTIR spectrum in the range of 400-4000 cm-1 of N'-(4-dimethylaminobenzylidene)-isonicotinohydrazide monohydrate has been recorded. The molecular geometry and vibrational frequencies and energies in the ground state are calculated by using the DFT (B3LYP, PBE1PBE) methods with 6-311G** basis sets. The calculated HOMO and LUMO energies also confirm that charge transfer occurs within the molecule. The geometries and normal modes of vibrations obtained from B3LYP/PBE1PBE/6-311G** calculations are in good agreement with the experimentally observed data.     

Applications of Inorganic Polymeric Materials II: Polysilanes

Polysilanes which cover one of the most attractive and challenging fields, are high molecular weight polymers with inorganic elements in their backbone. These materials have silicon atoms in their main chain and exhibit unique properties resulting from the easy delocalization of sigma electrons in the Si─Si bonds. There are many technical uses as well as applications of these materials such as precursors of silicon carbide ceramics; a strengthening agent in porous ceramic; imaging materials in microlithography; photoiniting in radical reactions; and photoconducting, conducting, and semiconducting which are due to the unusual mobility of sigma electrons. In this work, the main structural features, properties, and some other important and recent applications of polysilanes are discussed.