Two valued measure and summability of double sequences

In this paper, following the methods of Connor [2], we extend the idea of statistical convergence of a double sequence (studied by Muresaleen and Edely [12]) to μ-statistical convergence and convergence in μ-density using a two valued measure μ. We also apply the same methods to extend the ideas of divergence and Cauchy criteria for double sequences. We then introduce a property of the measure μ called the (APO₂) condition, inspired by the (APO) condition of Connor [3]. We mainly investigate the interrelationships between the two types of convergence, divergence and Cauchy criteria and ultimately show that they become equivalent if and only if the measure μ has the condition (APO₂).     

Copper catalyzed atom transfer radical copolymerization of glycidyl methacrylate and 2‐ethylhexyl acrylate

This investigation reports the atom transfer radical copolymerization (ATRcP) of glycidyl methacrylate (GMA) and 2‐ethylhexyl acrylate (EHA). Poly(glycidyl methacrylate) (PGMA) has easily transformable pendant oxirane group and poly(2‐ethylhexyl acrylate) (PEHA) has very low T_g. They are the important components of coating and adhesive materials. Copolymerization of GMA and EHA was carried out in bulk and in toluene at 70 °C at different molar feed ratios using CuCl as catalyst in combination with 2,2′‐bypyridine (bpy) as well as N,N,N′,N″,N″‐pentamethyl diethylenetriamine (PMDETA) as ligand. The molecular weight (M_n) and the polydispersity index (PDI) of the polymers were determined by GPC analysis. The molar composition of the copolymers was determined by ¹H NMR analysis. The reactivity ratios of GMA (r₁) and EHA (r₂) were determined using Finemann‐Ross and Kelen‐Tudos linearization methods and those had been compared with the literature values for conventional free radical copolymerization. The thermal properties of the copolymers were studied by DSC and TGA analysis. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 6526–6533, 2009     

Imprinted ZnO nanostructure-based electrochemical sensing of calcitonin: A clinical marker for medullary thyroid carcinoma

The present work describes an exciting method for the selective and sensitive determination of calcitonin in human blood serum samples. Adopting the surface molecular imprinting technique, a calcitonin-imprinted polymer was prepared on the surface of the zinc oxide nanostructure. Firstly, a biocompatible tyrosine derivative as a monomer was grafted onto the surface of zinc oxide nanostructure followed by their polymerization on vinyl functionalized electrode surface by activator regenerated by electron transfer–atom transfer radical polymerization (ARGET–ATRP) technique. Such sensor can predict the small change in the concentration of calcitonin in the human body and it may also consider to be as cost-effective, renewable, disposable, and reliable for clinical studies having no such cross-reactivity and matrix effect from real samples. The morphologies and properties of the proposed sensor were characterized by scanning electron microscopy, cyclic voltammetry, difference pulse voltammetry and chronocoulometry. The linear working range was found to be 9.99 ng L⁻¹ to 7.919 mg L⁻¹ and the detection limit as low as 3.09 ± 0.01 ng L⁻¹ (standard deviation for three replicate measurements) (S/N = 3).     

Bounding the gap between the McCormick relaxation and the convex hull for bilinear functions

We investigate how well the graph of a bilinear function \(b{:}\;[0,1]^n\rightarrow \mathbb {R}\) can be approximated by its McCormick relaxation. In particular, we are interested in the smallest number c such that the difference between the concave upper bounding and convex lower bounding functions obtained from the McCormick relaxation approach is at most c times the difference between the concave and convex envelopes. Answering a question of Luedtke, Namazifar and Linderoth, we show that this factor c cannot be bounded by a constant independent of n. More precisely, we show that for a random bilinear function b we have asymptotically almost surely \(c\geqslant \sqrt{n}/4\). On the other hand, we prove that \(c\leqslant 600\sqrt{n}\), which improves the linear upper bound proved by Luedtke, Namazifar and Linderoth. In addition, we present an alternative proof for a result of Misener, Smadbeck and Floudas characterizing functions b for which the McCormick relaxation is equal to the convex hull.     

The transport dynamics in complex systems governing by anomalous diffusion modelled with Riesz fractional partial differential equations

In this paper, numerical solutions of fractional Fokker–Planck equations with Riesz space fractional derivatives have been developed. Here, the fractional Fokker–Planck equations have been considered in a finite domain. In order to deal with the Riesz fractional derivative operator, shifted Grünwald approximation and fractional centred difference approaches have been used. The explicit finite difference method and Crank–Nicolson implicit method have been applied to obtain the numerical solutions of fractional diffusion equation and fractional Fokker–Planck equations, respectively. Numerical results are presented to demonstrate the accuracy and effectiveness of the proposed numerical solution techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Adhesion of nonplanar wrinkled surfaces

Topological patterns on polymer surfaces can significantly alter and control adhesion. In this study, the effect of surface wrinkles on a spherical surface on adhesion has been studied. Surface wrinkling induced by swelling of a crosslinked polydimethylsiloxane elastomer constrained by a stiff, thin surface layer (silicate) is used to produce topographic features of various length scales over a large curved area. By controlling the properties of the stiff layer and the applied strain conditions, surface wrinkles of varying amplitude and wavelength are obtained. The effect of wrinkle morphology on adhesion is quantified, and the results display a transition from enhancement of adhesion to decrease depending upon wrinkle dimensions. A simple phenomenological model is proposed that describes the change of adhesion behavior as a function of wrinkle morphology. Our results provide a critical understanding toward tuning the adhesion behavior of nonplanar surfaces consisting of periodic topographic structures. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Syntheses, transfection efficacy and cell toxicity properties of novel cholesterol-based gemini lipids having hydroxyethyl head group

We have synthesized five new cholesterol based gemini cationic lipids possessing hydroxyethyl (-CH(2)CH(2)OH) function on each head group, which differ in the length of the polymethylene spacer chain. These gemini lipids are important for gene delivery processes as they possess pre-optimized molecular features, e.g., cholesterol backbone, ether linkage and a variable spacer chain between both the headgroups of the gemini lipids. Cationic liposomes were prepared from each of these lipids individually and as a mixture of individual cationic gemini lipid and 1,2-dioleoyl phosphatidylethanolamine (DOPE). Each gemini lipid based formulation induced better transfection activity than that of their monomeric counterpart. One such gemini lipid with a -(CH(2))(12)- spacer, HG-12, showed dramatic increase in the mean fluorescence intensity due to the expression of green-fluorescence protein (GFP) in the presence of 10% FBS compared to the conditions where there was no serum. Other gemini lipids retained their gene transfection efficiency without any marked decrease in the presence of serum. The only exception was seen with the gemini with a -(CH(2))(3)- spacer, HG-3, which on gene transfection in the presence of 10% FBS lost ~70% of its transfection efficiency. Overall the gemini lipid with a -(CH(2))(5)- spacer, HG-5, showed the highest transfection activity at N/P (lipid/DNA) ratio of 0.5 and lipid : DOPE molar ratio of 2. Upon comparison of the relevant parameters, e.g., %-transfected cells, the amount of DNA transfected to each cell and %-cell viability all together against Lipofectamine 2000, one of the best commercial transfecting agents, the optimized lipid formulation based on DOPE/HG-5 was found to be comparable. In terms of its ability to induce gene-transfer in the presence of serum and shelf-life DOPE/HG-5 liposome was found to be superior to its commercial counterpart. Confocal imaging analysis confirmed that in the presence of 10% serum using a Lipid : DOPE of 1 : 4 and N/P charge ratio of 0.75 with 1.2 μg DNA per well, HG-5 is better than Lipofectamine 2000.     

Two valued measure and summability of double sequences in asymmetric context

We extend the ideas of convergence and Cauchy condition of double sequences extended by a two valued measure (called ??-statistical convergence/Cauchy condition and convergence/Cauchy condition in ??-density, studied for real numbers in our recent paper [7]) to a very general structure like an asymmetric (quasi) metric space. In this context it should be noted that the above convergence ideas naturally extend the idea of statistical convergence of double sequences studied by Móricz [15] and Mursaleen and Edely [17]. We also apply the same methods to introduce, for the first time, certain ideas of divergence of double sequences in these abstract spaces. The asymmetry (or rather, absence of symmetry) of asymmetric metric spaces not only makes the whole treatment different from the real case [7] but at the same time, like [3], shows that symmetry is not essential for any result of [7] and in certain cases to get the results, we can replace symmetry by a genuinely asymmetric condition called (AMA).     

Continuous flow enzyme-catalyzed polymerization in a microreactor

Enzymes immobilized on solid supports are increasingly used for greener, more sustainable chemical transformation processes. Here, we used microreactors to study enzyme-catalyzed ring-opening polymerization of ε-caprolactone to polycaprolactone. A novel microreactor design enabled us to perform these heterogeneous reactions in continuous mode, in organic media, and at elevated temperatures. Using microreactors, we achieved faster polymerization and higher molecular mass compared to using batch reactors. While this study focused on polymerization reactions, it is evident that similar microreactor based platforms can readily be extended to other enzyme-based systems, for example, high-throughput screening of new enzymes and to precision measurements of new processes where continuous flow mode is preferred. This is the first reported demonstration of a solid supported enzyme-catalyzed polymerization reaction in continuous mode.     

A new numerical approach for single rational soliton solution of Chen‐Lee‐Liu equation with Riesz fractional derivative in optical fibers

In this paper, time‐splitting spectral approximation technique has been proposed for Chen‐Lee‐Liu (CLL) equation involving Riesz fractional derivative. The proposed numerical technique is efficient, unconditionally stable, and of second‐order accuracy in time and of spectral accuracy in space. Moreover, it conserves the total density in the discretized level. In order to examine the results, with the aid of weighted shifted Grünwald‐Letnikov formula for approximating Riesz fractional derivative, Crank‐Nicolson weighted and shifted Grünwald difference (CN‐WSGD) method has been applied for Riesz fractional CLL equation. The comparison of results reveals that the proposed time‐splitting spectral method is very effective and simple for obtaining single soliton numerical solution of Riesz fractional CLL equation.