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.     

Three component tandem reactions involving protected 2-amino indoles, disubstituted propargyl alcohols, and I2/ICl: iodo-reactant controlled synthesis of dihydro-α-carbolines and α-carbolines via iodo-cyclization/iodo-cycloelimination

Two simple, highly efficient three component tandem reactions for the synthesis of diversified N^aN^b di-carbamate-4,9-dihydro-3-iodo-α-carbolines and N^a-carbamate-3-iodo-α-carbolines have been described. The strategy involves one-pot condensation of bis-carbamate protected 2-amino indoles with disubstituted propargyl alcohols and I₂/ICl. The salient feature of the reaction involves iodocyclo-elimination of N^b-linked carbamate under mild condition in the final step.     

Facile synthesis of substituted pyrrole-fused isocoumarins from ninhydrin

A simple and efficient procedure has been developed for the synthesis of substituted pyrrole-fused isocoumarins from easily available ninhydrin. The cyclic hemiaminal dihydroxy-indenopyrroles, the adducts of ninhydrin with enamines of acetylacetone, give pyrrole-fused isocoumarins upon heating in acidic medium. The process constitutes an interesting acid-catalyzed rearrangement to eight-membered lactams followed by intramolecular cyclization involving the amino and keto groups.     

Cellulose-based liquid crystalline photoresponsive films with tunable surface wettability

We report on a new type of liquid crystalline cellulosic films with light controllable reversible wettability. The films are prepared from a thermotropic cellulose derivative functionalized with azo-containing groups. These groups exhibit dynamic changes in interfacial properties in response to UV irradiation. The UV irradiation induces trans-to-cis isomerization in the azobenzene moiety, which causes a conformational change in the upper molecular layers of the thin films. These changes originate a hydrophobic to comparatively hydrophilic transformation of the surface. The reversible wettability of the surface results from the cis/trans photo and thermal isomerization. The UV-vis absorption spectra, as well as contact angle measurements with UV irradiation, clearly support the understanding of the phenomenon. This type of surface design enables the amplification of molecular level conformational transitions to macroscopic changes in interface properties using the means of isomerism. This opens new opportunities in surface engineering using eco-friendly cellulose manipulation.     

Layer-by-layer assembly of thiol-capped au nanoparticles on a water surface and their deposition on H-terminated Si(001) by the Langmuir-Blodgett method

A monolayer of dodecanethiol-encapsulated Au nanoparticles when compressed laterally transforms into layer-by-layer assemblies on water surface. These layer-by-layer assemblies of Au nanoparticles have been deposited on H-terminated Si(001) substrates by using one down-up cycle (two strokes) in the Langmuir-Blodgett (LB) method. The transformation from monolayer to layer-by-layer assembly on a water surface is irreversible; i.e., if the compressed film is decompressed the layer-by-layer structure cannot regenerate the monolayer structure. Unlike layer-by-layer growth, only odd numbers of layers grow from the monolayer on the H-terminated Si(001) substrates by using different numbers of down-up cycles. Z-type LB deposition occurs only in the first down-up cycle of the hydrophobic substrate, whereas Y-type LB deposition takes place in the successive cycles. Such layer-by-layer assemblies of Au nanoparticles, which are made on bare silicon surfaces and where thickness can be controlled at the nanoscale level, are very promising for their novel applications in the field of nanoscience.     

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.     

Comparison of two repairable systems

Any repairable system improves (deteriorates) with time if the interarrival times of failure tend to get larger (smaller) in some sense. In this paper we consider two such repairable systems, and their performance in terms of several partial orderings of their respective interarrival times of failure are compared. The comparison of two systems’ improvement/deterioration under minimal repair policy has been characterized in terms of s-FR orders and also in terms of their shifted and dispersive versions. These results generalize some of the existing results in the literature and also provide some new results in this direction.     

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).