Measures of weak noncompactness and fixed point theory for 1-set weakly contractive operators on unbounded domains

The main purpose of this paper is to prove a collection of new fixed point theorems and existence theorems for the nonlinear operator equation F(x) =αx (α ≥ 1) for so-called 1-set weakly contractive operators on unbounded domains in Banach spaces. We also introduce the concept of weakly semi-closed operator at the origin and obtain a series of new fixed point theorems and the existence theorems for the nonlinear operator equation F(x) = αx (α ≥ 1) for such class of operators. As consequences, the main results generalize and improve the relevant results, which are obtained by O’Regan and A. Ben Amar and M. Mnif in 1998 and 2009 respectively. In addition, we get the famous fixed point theorems of Leray-Schauder, Altman, Petryshyn and Rothe type in the case of weakly sequentially continuous, 1-set weakly contractive (μ-nonexpansive) and weakly semi-closed operators at the origin and their generalizations. The main condition in our results is formulated in terms of axiomatic measures of weak compactness.     

On L^{r} hypoellipticity of solutions with compact support of the Cauchy–Riemann equation

In one complex variable, the existence of a compactly supported solution to the Cauchy–Riemann equation is related to the vanishing of certain integrals of the data; trying to generalize this approach, we find an explicit construction, via convolution, for a compactly supported solution in \(\mathbb C ^n\) , which allows us to estimate the \(L^p\) norm of the solution. We also investigate the possible generalizations of this method to domains of the form \(P\setminus Z\) , where \(P\) is a polydisc and \(Z\) is the zero locus of some holomorphic function.     

Dielectric and impedance measurements on (1−x)Ba(Fe1/2Ta1/2)O3-xBa(Zn1/3Ta2/3)O3 ceramics

In this work, ((1−x)Ba(Fe_1/2Ta_1/2)O₃-xBa(Zn_1/3Ta_2/3)O₃), ((1−x)BFT-xBZT) ceramics with x = 0.00–0.12 were synthesized by the solid–state reaction method. X-ray diffraction data revealed that both the powders and ceramics were of a pure-phase cubic perovskite structure. All ceramics showed large dielectric constants. For the x = 0.12 sample, a very high dielectric constant (>20,600) was observed. A lowering in the dielectric loss compared to pure BFT ceramics was observed with the BZT addition. The impedance measurements indicated that BZT has a strong effect on the bulk grain and grain boundary resistance of BFT ceramics. These results are in agreement with the measured dielectric properties. Based on dielectric and impedance results, (1−x)BFT-xBZT ceramics could be of great interest for high performance dielectric materials applications due their giant dielectric constant behavior.     

Co3O4/SiO2 nanocomposites for supercapacitor application

In this study, Co₃O₄/SiO₂ nanocomposites have been successfully synthesized by citrate–gel method by utilizing SiO₂ matrix for Co₃O₄ embedment. Spectroscopy analyses confirm the formation of high crystalline Co₃O₄ nanoparticles; meanwhile, microscopy findings reveal that the Co₃O₄ nanoparticles are embedded in SiO₂ matrix. Electrochemical properties of the Co₃O₄/SiO₂ nanocomposites were carried out using cyclic voltammetry (CV), galvanostatic charge–discharge, and electrochemical impedance spectroscopy (EIS) in 5 M KOH electrolyte. The findings show that the charge storage of Co₃O₄/SiO₂ nanocomposites is mainly due to the reversible redox reaction (pseudocapacitance). The highest specific capacitance of 1,143 F g ^?1 could be achieved at a scan rate of 2.5 mV s^?1 in the potential region between 0 and 0.6 V. Furthermore, high-capacitance retention (>92 %) after 900 continuous charge–discharge tests reveals the excellent stability of the nanocomposites. It is worth noting from the EIS measurements that the nanocomposites have low ESR value of 0.33 Ω. The results manifest that Co₃O₄/SiO₂ nanocomposites are the promising electrode material for supercapacitor application.     

1,3-Diaxially substituted trans-decalins: potential nonsteroidal human progesterone receptor inhibitors

On the basis of molecular modeling and QSAR analysis of the known human progesterone receptor (hPR) inhibitor Mifepristone (RU-486) and other hPR ligands, a new class of potential nonsteroidal hPR inhibitors was designed. The parent racemic compound 1 was synthesized through an efficient 13-step synthetic pathway. The key constructive steps are a stereoselective epoxide ring opening and the reductive Heck cyclization to form the main framework of (+/-)-1. The current established flexible synthetic route allows for further chemical diversification.     

Liquid–liquid equilibria for pseudo-ternary systems: (Sulfolane + 2-ethoxyethanol) + octane + toluene at 293.15 K

Liquid–liquid equilibrium data, both binodal and tie lines are presented for the pseudo-ternary systems: {(sulfolane + 2-ethoxyethano) (1) + octane (2) + toluene (3)} at 293.15 K. The experimental liquid–liquid equilibrium data have been correlated using NRTL and UNIQUAC models, and the binary interaction parameters of these components have been presented. The correlated tie lines have been compared with the experimental data. The comparisons indicate that both NRTL and UNIQUAC models satisfactorily correlated the equilibrium compositions. The tie-line data of the studied systems also were correlated using the Hand method.     

Patchy particles by glancing angle deposition

The application of glancing angle deposition (GLAD) as a means to produce patchy particles is reported. Shadow effects are caused by neighboring particles within the particle monolayer. The patch geometry is determined by the angle of incidence of the vapor rays and the monolayer orientation. A mathematical model is used to study the patch geometry and to calculate the area of the patch. The smallest patch produced with GLAD is 3.7% of the particle surface.     

Lanthanum nitride endohedral fullerenes La3N@C2n (43 <or= n <or= 55): preferential formation of La3N@C96

While the trimetallic nitrides of Sc, Y and the lanthanides between Gd and Lu preferentially template C(80) cages, M(3)N@C(80), and while those of Ce, Pr and Nd preferentially template the C(88) cage, M(3)N@C(88), we show herein that the largest metallic nitride cluster, La(3)N, preferentially leads to the formation of La(3)N@C(96) and to a lesser extent the La(3)N@C(88). This is the first time that La(3)N is successfully encapsulated inside fullerene cages. La(3)N@C(2n) metallofullerenes were synthesized by arcing packed graphite rods in a modified Kr?tschmer-Huffman arc reactor, extracted from the collected soot and identified by mass spectroscopy. They were isolated and purified by high performance liquid chromatography (HPLC). Different arcing conditions were studied to maximize fullerene production, and results showed that yields have a high La(2)O(3)/C dependence. Relatively high yields were obtained when a 1:5 ratio was used. Three main fractions, La(3)N@C(88), La(3)N@C(92), and La(3)N@C(96), were characterized by UV/Vis-NIR and cyclic voltammetry. Unlike other trimetallic nitride metallofullerenes of the same carbon cage size, La(3)N@C(88) exhibits a higher HOMO-LUMO gap and irreversible reduction and oxidation steps.     

Quantification of the π-π interactions that govern tertiary structure in donor-acceptor [2]pseudorotaxanes

Flexibility in pseudorotaxanes and interlocked molecules that rely on interactions between π-donor-acceptor subunits provides access to folded structures reminiscent of the tertiary structure of proteins. While they have been described before, only now have we been able to quantify one such tertiary structure by making use of pseudorotaxanes designed for the purpose. Here, the enhanced stability of a pseudorotaxane inside a folded structure is measured to be ΔG = ca. 0.5 kcal mol(-1). The tertiary structure is stabilized by a charge-transfer interaction between a tetrathiafulvalene-based π-donor that can situate alongside a π-accepting paraquat-based macrocycle by folding of a flexible linker. At room temperature, it was estimated that 70% of the pseudorotaxanes examined here exist in their folded state. This quantitative information is critical for the creation of interlocked molecular machines that have predictable energetics and structures and for revealing a complexity approaching biological molecules.