Common tripled fixed point results in cone metric type spaces

In this paper, we prove some common tripled fixed point and tripled coincidence point results for contractive conditions in a cone metric type space. Our results extend, unify and generalize well-known results in the literature, in particular the recent results of Aydi et al. (Fixed Point Theory Appl 2012:134, 2012). Some examples are also presented to validate our obtained results and new concepts.     

Weak and cyclic amenability for Fourier algebras of connected Lie groups

Using techniques of non-abelian harmonic analysis, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the real ax+b$ax+b$ group. In particular this provides the first proof that this algebra is not weakly amenable. Using the structure theory of Lie groups, we deduce that the Fourier algebras of connected, semisimple Lie groups also support non-zero, cyclic derivations and are likewise not weakly amenable. Our results complement earlier work of Johnson (1994) [15], Plymen (2001) [18] and Forrest, Samei, and Spronk (2009) [9]. As an additional illustration of our techniques, we construct an explicit, non-zero cyclic derivation on the Fourier algebra of the reduced Heisenberg group, providing the first example of a connected nilpotent group whose Fourier algebra is not weakly amenable.     

Sensitivity Analysis of Merit Function in Solving Nonlinear Equations by Optimization

To solve nonlinear equations by an optimization method, scaling is very important. Two types of poor scaling where: (a) the variables differ greatly in magnitude; (b) the merit function of system is highly sensitive to small changes in certain variables and relatively insensitive to changes in other variables. If poor scaling is ignored, the algorithm may produce solutions with poor quality. To solve (a), we can change units of variables. A numerical solution of the nonlinear equations produced by the finite volume method in the forced convective heat transfer of a nanofluid, as a case study, indicates that the poor scaling (b) is solved by using the Euclidean norm of columns of the Jacobian matrix as scaling data, while some researchers proposed diagonal elements of the Hessian matrix as scaling data.     

Synthesis and characterization of new optically active copoly(amid-imide)s based on N-phthalimido-L-aspartic acid and aromatic diamines

<正>In this article,six new optically active copoly(amide-imide)s(10a-f) were synthesized through the direct polycondensation reaction of N-phthalimido-L-aspartic acid(4) with 1,5-diamino naphthalene(8),3,4-diamino benzophenone(9) in the presence of therphthahc acid(7),fumaric acid(6) and adipic acid(5) as a second diacid in a medium consisting of N-methyl-2-pyrrolidone,triphenyl phosphite, calcium chloride and pyridine.The resulting copolymers were fully characterized by means of FT-IR spectroscopy,elemental analyses, inherent viscosity,solubility tests and UV-vis spectroscopy.Thermal properties of resulting copolymers(10a-c) containing three different second diacid in the main chain were compared by using TGA and DTG thermograms.     

A novel acrylonitrile–butadiene–styrene/poly(ethylene glycol) membrane: preparation,characterization, and gas permeation study

Polymeric membranes were prepared by blending different grades of poly(ethylene glycol) (PEG) as the added polymer with acrylonitrile–butadiene–styrene as the backbone structure. The membranes were characterized by Fourier transform infrared, X‐ray diffractometry, dynamic mechanical thermal analysis, differential scanning calorimetry, and scanning electron microscopy. Furthermore, the gas permeation and separation properties of CO₂/CH₄ were studied. In addition, the effect of pressure (1–8 bar) and the effect of PEG content (0–40 wt%) on CO₂ and CH₄ permeability/selectivity were investigated. The results showed that, in more cases, with the introduction of PEG molecules, CO₂/CH₄ selectivity increases without significant changes in CH₄ permeability, indicating that the incorporation of intermolecular interaction is suitable for the separation of gas pairs with no molecular size domination but the solution–diffusion. From the viewpoint of gas separation applications, the resultant data are in the commercially attractive region. Copyright © 2011 John Wiley & Sons, Ltd.     

PT-Symmetric Talbot Effects

We show that complex PT-symmetric photonic lattices can lead to a new class of self-imaging Talbot effects. For this to occur, we find that the input field pattern has to respect specific periodicities dictated by the symmetries of the system. While at the spontaneous PT-symmetry breaking point the image revivals occur at Talbot lengths governed by the characteristics of the passive lattice, at the exact phase it depends on the gain and loss parameter, thus allowing one to control the imaging process.     

First Report of a Lipopeptide Biosurfactant from Thermophilic Bacterium Aneurinibacillus thermoaerophilus MK01 Newly Isolated from Municipal Landfill Site

A biosurfactant-producing thermophile was isolated from the Kahrizak landfill of Tehran and identified as a bacterium belonging to the genus Aneurinibacillus. A thermostable lipopeptide-type biosurfactant was purified from the culture medium of this bacterium and showed stability in the temperature range of 20–90 °C and pH range of 5–10. The produced biosurfactant could reduce the surface tension of water from 72 to 43 mN/m with a CMC of 1.21 mg/mL. The strain growing at a temperature of 45 °C produces a substantial amount of 5 g/L of biosurfactant in the medium supplemented with sunflower oil as the sole carbon source. Response surface methodology was employed to optimize the biosurfactant production using sunflower oil, sodium nitrate, and yeast extract as variables. The optimization resulted in 6.75 g/L biosurfactant production, i.e., 35 % improved as compared to the unoptimized condition. Thin-layer chromatography, FTIR spectroscopy, ¹H-NMR spectroscopy, and biochemical composition analysis confirmed the lipopeptide structure of the biosurfactant.     

Removal of heavy metals from industrial wastewaters using amine-functionalized nanoporous carbon as a novel sorbent

Nano-porous carbon (NPC) was synthesized by hydrothermal condensation of fructose and characterized by X-ray powder diffraction and also nitrogen adsorption analysis. It was then modified with amino groups and used as a sorbent for the removal of heavy metal ions. The formation of amino-modified NPC was confirmed by X-ray powder diffraction, infrared spectroscopy, thermogravimetric and elemental analysis. NPC was applied for removal of Pb(II), Cd(II), Ni(II) and Cu(II) ions. The effects of sample pH and the adsorption kinetics were studied, and the adsorption capacity was determined. The sorbent was applied to the removal of heavy metal ions in industrial waste water samples.

Fabrication of Stiffness Gradients of GelMA Hydrogels Using a 3D Printed Micromixer

Many properties in both healthy and pathological tissues are highly influenced by the mechanical properties of the extracellular matrix. Stiffness gradient hydrogels are frequently used for exploring these complex relationships in mechanobiology. In this study, the fabrication of a simple, cost‐efficient, and versatile system is reported for creation of stiffness gradients from photoactive hydrogels like gelatin‐methacryloyl (GelMA). The setup includes syringe pumps for gradient generation and a 3D printed microfluidic device for homogenous mixing of GelMA precursors with different crosslinker concentration. The stiffness gradient is investigated by using rheology. A co‐culture consisting of human adipose tissue‐derived mesenchymal stem cells (hAD‐MSCs) and human umbilical cord vein endothelial cells (HUVECs) is encapsulated in the gradient construct. It is possible to locate the stiffness ranges at which the studied cells displayed specific spreading morphology and migration rates. With the help of the described system, variable mechanical gradient constructs can be created and optimal 3D cell culture conditions can be experientially identified.