Homotopy type of neighborhood complexes of Kneser graphs, $$\varvec{KG_{2,k}}$$

Schrijver (Nieuw Archief voor Wiskunde, 26(3) (1978) 454–461) identified a family of vertex critical subgraphs of the Kneser graphs called the stable Kneser graphs \(SG_{n,k}\). Björner and de Longueville (Combinatorica 23(1) (2003) 23–34) proved that the neighborhood complex of the stable Kneser graph \(SG_{n,k}\) is homotopy equivalent to a k-sphere. In this article, we prove that the homotopy type of the neighborhood complex of the Kneser graph \(KG_{2,k}\) is a wedge of \((k+4)(k+1)+1\) spheres of dimension k. We construct a maximal subgraph \(S_{2,k}\) of \(KG_{2,k}\), whose neighborhood complex is homotopy equivalent to the neighborhood complex of \(SG_{2,k}\). Further, we prove that the neighborhood complex of \(S_{2,k}\) deformation retracts onto the neighborhood complex of \(SG_{2,k}\).     

Nanoparticle Size‐Fractionation through Self‐Standing Porous Covalent Organic Framework Films

Covalent organic frameworks (COFs) have attracted attention due to their ordered pores leading to important industrial applications like storage and separation. Combined with their modular synthesis and pore engineering, COFs could become ideal candidates for nanoseparations. However, the fabrication of these microcrystalline powders as continuous, crack‐free, robust films remains a challenge. Herein, we report a simple, slow annealing strategy to construct centimeter‐scale COF films ( Tp‐Azo and Tp‐TTA ) with micrometer thickness. The as‐synthesized films are porous (SA_BET=2033 m² g^?1 for Tp‐Azo ) and chemically stable. These COFs have distinct size cut‐offs (ca. 2.7 and ca. 1.6 nm for Tp‐Azo and Tp‐TTA , respectively), which allow the size‐selective separation of gold nanoparticles. Unlike, other conventional membranes, the durable structure of the COF films allow for excellent recyclability (up to 4 consecutive cycles) and easy recovery of the gold nanoparticles from the solution.     

Synthesis and functionalization study of hierarchical ZnO nanowires for potential nitroaromatic sensing applications

In this work, we synthesize hierarchical ZnO nanowires in a customized atmospheric CVD furnace and investigate their surface modification behavior for prospective nitroaromatic sensing applications. The morphology and crystal structure of pristine nanowires are characterized through FE-SEM, TEM, X-ray diffraction and EDAX studies. Photoluminescence behavior of pristine nanowires is also reported. Surface modification behavior of synthesized nanowires on a ZnO–oleic acid system is studied by utilizing Raman and FT-IR spectroscopy. Based on these findings, 1-pyrenebutyric acid (PBA) has been identified as an appropriate fluorescent receptor for sensing p-nitrophenol. Fluorescence quenching experiments on a PBA–p-nitrophenol system are reported and a detection limit of up to 28 ppb is envisaged for PBA-grafted ZnO nanowire-based optical sensor.     

Nanofibrous polyaniline thin film prepared by plasma‐induced polymerization technique for detection of NO2 gas

A nanofibrous polyaniline (PANI) thin film was fabricated using plasma‐induced polymerization method and explored its application in the fabrication of NO₂ gas sensor. The effects of substrate position, pressure, and the number of plasma pulses on the PANI film growth rate were monitored and an optimum condition for the PANI thin film preparation was established. The resulting PANI film was characterized with UV–visible spectrophotometer, FTIR, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The PANI thin film possessed nanofibers with a diameter ranging from 15 to 20 nm. The NO₂ gas sensing behavior was studied by measuring the change in electrical conductivity of PANI film with respect to NO₂ gas concentration and exposure time. The optimized sensor exhibited a sensitivity factor of 206 with a response time of 23 sec. The NO₂ gas sensor using nanofibrous PANI thin film as sensing probe showed a linear current response to the NO₂ gas concentration in the range of 10–100 ppm. Copyright © 2009 John Wiley & Sons, Ltd.     

Second order symmetric duality in nondifferentiable multiobjective fractional programming with cone convex functions

In the present paper, we consider Mond-Weir type nondifferentiable second order fractional symmetric dual programs over arbitrary cones and derive duality results under second order K?F-convexity/K?F-pseudoconvexity assumptions. Our results generalize several known results in the literature.     

Exponential type vector variational-like inequalities and vector optimization problems with exponential type invexities

A new class of exponential form of vector variational-like inequality problems is introduced, and then the equivalence among (weakly) efficient solutions, vector critical points of vector optimization problem and the solutions of vector variational-like inequalities under the framework of (p,r)-invexity is established. To the best our knowledge, the presented results are new and highly application oriented to other results based on generalized invexities to the context of optimization problems in the literature.     

Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.     

High-throughput capillary electrophoresis analysis of biopharmaceuticals utilizing sequential injections

The complexity of biotherapeutic products implies an ever-increasing list of product quality attributes that need to be monitored and characterized. In addition, the growing interest in implementing process analytical technology in biopharmaceutical production has further increased the testing burden, together with the need for rapid testing that can facilitate real-time or near-real-time decision-making. Capillary electrophoresis (CE) has made a place in biopharmaceutical analysis but is regarded as a low-throughput method, with the instrument dead time constituting more than 80% of the total time of analysis. In this study, the dead time of CE was utilized to analyse 3 mAb samples in a single-CE run. This approach resulted in an up to 77% reduction in the total analysis time and increased the productivity by up to 300%, compared to traditional single CE-ultraviolet runs, without compromising resolution or relative peak areas. Additionally, good method reproducibility was observed. The compatibility of the method has been demonstrated with protein A eluate and cation exchange chromatography fractions. We, thus, propose that sequential injections can be applied for fast and robust CE analysis of biopharmaceuticals.     

Generalizing a two-conformation model for describing salt and temperature effects on protein retention and stability in hydrophobic interaction chromatography

A two-conformation adsorption model that includes the effects of salt concentration and temperature on both stability and adsorption has been developed to describe the effects of secondary protein unfolding on hydrophobic interaction chromatography (HIC). The model has been applied to a biotech protein and to beta-lactoglobulin on Phenyl Sepharose 6FF low sub HIC media. Thermodynamic property models for adsorption and protein stability with parameters obtained from experimental chromatographic data successfully describe observed chromatographic behavior over ranges of temperature and salt concentration, provide predictions of distribution among different conformers, and give a basis for calculating trends in retention strength and stability with changing conditions, that might prove useful in HIC process development.