Subgradient projection methods extended to monotone bilevel equilibrium problems in Hilbert spaces

Numerical Algorithms - In this paper, by basing on the inexact subgradient and projection methods presented by Santos et al. (Comput. Appl. Math. 30: 91–107, 2011), we develop subgradient...     

Multichannel vector sum phase shifter

A novel multichannel vector sum phase shifter that is suitable for phased array antenna applications is demonstrated. Each channel is implemented using a distinct optical wavelength. Selective control of each channel is performed using an acousto-optic polarization coupler. The concept is successfully demonstrated for two individually controlled channels. For each channel, a continuously variable frequency linear phase shift is demonstrated between DC and 7 GHz, with the phasing range exceeding 100 degrees.     

Effects of Charged Surfactants on Interfacial Water Structure and Macroscopic Properties of the Air-Water Interface

Surfactants are used to control the macroscopic properties of the air-water interface. However, the link between the surfactant molecular structure and the macroscopic properties remains unclear. Using sum-frequency generation spectroscopy and molecular dynamics simulations, two ionic surfactants (dodecyl trimethylammonium bromide, DTAB, and sodium dodecyl sulphate, SDS) with the same carbon chain lengths and charge magnitude (but different signs) of head groups interact and reorient interfacial water molecules differently. DTAB forms a thicker but sparser interfacial layer than SDS. It is due to the deep penetration into the adsorption zone of Br⁻ counterions compared to smaller Na⁺ ones, and also due to the flip-flop orientation of water molecules. SDS alters two distinctive interfacial water layers into a layer where H⁺ points to the air, forming strong hydrogen bonding with the sulphate headgroup. In contrast, only weaker dipole-dipole interactions with the DTAB headgroup are formed as they reorient water molecules with H⁺ point down to the aqueous phase. Hence, with more molecules adsorbed at the interface, SDS builds up a higher interfacial pressure than DTAB, producing lower surface tension and higher foam stability at a similar bulk concentration. Our findings offer improved knowledge for understanding various processes in the industry and nature.     

Designing liquid-crystalline dendronised hexa-adducts of [60]fullerene via click chemistry

ABSTRACT

Liquid-crystalline [60]fullerodendrimers were constructed via click chemistry based on the reaction between hexa-adducts of [60]fullerene (C₆₀) bearing 12 azide groups and alkyne-terminated cyanobiphenyl dendrons of first- and second-generation. The structure of all the new compounds was confirmed by IR, UV, ¹H and ¹³C NMR spectroscopies and mass spectrometry. The mesomorphic properties were studied by polarised optical microscopy, differential scanning calorimetry and small-angle X-ray scattering. The hexa-adduct of C₆₀ functionalised with the first-generation dendrons gave rise to the formation of a smectic A phase and a rectangular columnar phase (c2mm symmetry) while the hexa-adduct of C₆₀ decorated with the second-generation dendrons displayed only a rectangular columnar phase (c2mm symmetry). Our results show that the hexa-adduct of C₆₀ is a unique synthetic platform for the design of fullerodendrimers and dendronised materials.     

Inverse colloidal crystal membranes for hydrophobic interaction membrane chromatography

Hydrophobic interaction membrane chromatography has gained interest due to its excellent performance in the purification of humanized monoclonal antibodies. The membrane material used in hydrophobic interaction membrane chromatography has typically been commercially available polyvinylidene fluoride. In this contribution, newly developed inverse colloidal crystal membranes that have uniform pores, high porosity and, therefore, high surface area for protein binding are used as hydrophobic interaction membrane chromatography membranes for humanized monoclonal antibody immunoglobulin G purification. The capacity of the inverse colloidal crystal membranes developed here is up to ten times greater than commercially available polyvinylidene fluoride membranes with a similar pore size. This work highlights the importance of developing uniform pore size high porosity membranes in order to maximize the capacity of hydrophobic interaction membrane chromatography.     

Real-time tracking of hydrogen peroxide secreted by live cells using MnO2 nanoparticles intercalated layered doubled hydroxide nanohybrids

We report a facile and green method for the fabrication of new type of electrocatalysts based on MnO₂ nanoparticles incorporated on MgAl LDH P-type semiconductive channel and explore its practical applications as high-performance electrode materials for electrochemical biosensor. A series of MgAl layered doubled hydroxide (LDH) nanohybrids with fixed Mg/Al (M²⁺/M³⁺ atomic ratio of 3) and varied amount of MnCl₂.4H₂O are fabricated by a facile co-precipitation method. This approach demonstrates the combination of distinct properties including excellent intercalation features of LDH for entrapping nanoparticles and high loading of MnO₂ nanoparticles in the host layers of LDH. Among all samples, Mn5–MgAl with 0.04% loaded manganese has a good crystalline morphology. A well-dispersed MnO₂ nanoparticles encapsulated into the host matrix of hydrotalcite exhibit enhanced electrocatalytic activity towards the reduction of H₂O₂ as well as excellent stability, selectivity and reproducibility due to synergistic effect of good catalytic ability of MnO₂ and conductive MgAl LDH. Glass carbon electrode (GCE) modified with Mn5–MgAl possesses a wide linear range of 0.05–78 mM, lowest detection limit 5 μM (S/N = 3) and detection sensitivity of 0.9352 μAmM⁻¹. This outstanding performance enables it to be used for real-time tracking of H₂O₂ secreted by live HeLa cells. This work may provide new insight in clinical diagnosis, on-site environmental analysis and point of care testing devices.     

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.     

VMO Spaces Associated with Operators with Gaussian Upper Bounds on Product Domains

In this paper, we extend the well-known result “the predual of Hardy space \(H^1\) is VMO” to the product setting, associated with differential operators. Let \(L_i\), \(i = 1, 2\), be the infinitesimal generators of the analytic semigroups \(\{e^{-tL_i}\}\) on \(L^2({\mathbb {R}})\). Assume that the kernels of the semigroups \(\{e^{-tL_i}\}\) satisfy the Gaussian upper bounds. We introduce the VMO spaces VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) associated with operators \(L_1\) and \(L_2\) on the product domain \(\mathbb {R}\times \mathbb {R}\), then show that the dual space of VMO\(_{L_1, L_2}(\mathbb {R}\times \mathbb {R})\) is the Hardy space \(H^1_{L_1^*, L_2^*}(\mathbb {R}\times \mathbb {R})\) associated with the adjoint operators \(L^*_1\) and \(L^*_2\).