Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Linearly χ-bounding (P6, C4)-free graphs*

Given two graphs and , a graph is -free if it contains no induced subgraph isomorphic to or . Let and be the path on vertices and the cycle on vertices, respectively. In this paper we show that for any -free graph it holds that , where and are the chromatic number and clique number of , respectively. Our bound is attained by several graphs, for instance, the 5-cycle, the Petersen graph, the Petersen graph with an additional universal vertex, and all -critical -free graphs other than (see Hell and Huang [Discrete Appl. Math. 216 (2017), pp. 211–232]). The new result unifies previously known results on the existence of linear -binding functions for several graph classes. Our proof is based on a novel structure theorem on -free graphs that do not contain clique cutsets. Using this structure theorem we also design a polynomial time -approximation algorithm for coloring -free graphs. Our algorithm computes a coloring with colors for any -free graph in time.     

QbD approached comparison of reaction mechanism in microwave synthesized gold nanoparticles and their superior catalytic role against hazardous nirto‐dye

Microwave irradiation (MI) process characteristically enables extremely rapid “in‐core” heating of dipoles and ions, in comparison to conventional thermal (conductance) process of heat transfer. During the process of nanoparticles synthesis, MI both modulates functionality behaviors as well as dynamic of reaction in favorable direction. So, MI providing a facile, favorable and alternative approach during nanoparticles synthesis nanoparticles with enhanced catalytic performances. Although, conventionally used reducing and capping reagents of synthetic origin, are usually environmentally hazardous and toxic for living organism. But, in absence of suitable capping agent; stability, shelf life and catalytic activity of metallic nanoparticles adversely affected. However, polymeric templates which emerged as suitable choice of agent for both reducing and capping purposes; bearing additional advantages in terms of catalyst free one step green synthesis process with high degree of biosafety and efficiency. Another aspect of current works was to understand role of process variables in growth mechanism and catalytic performances of microwave processed metallic nanoparticles, as well as comparison of these parameters with conventional heating method. However, due to poor prediction ability with previously published architect OFAT (One factor at a time) design with these nanoparticles as well as random selection of process variables with their different levels, such comparison couldn't be possible. Hence, using gum Ghatti (Anogeissus latifolia) as a model bio‐template and under simulated reaction conditions; architect of QbD design systems were integrated in microwave processed nanoparticles to establish mechanistic role these variables. Furthermore, in comparison to conventional heating; we reported well validated mathematical modeling of process variables on characteristic of nanoparticles as well as synthesized gold nanoparticles of desired and identical dimensions, in both thermal and microwave‐based processes. Interestingly, despite of identical dimension, MI processed gold nanoparticles bearing higher efficiency (kinetic rate) against remediation of hazardous nitro dye (4‐nitrophenol), into safer amino (4‐aminophenol) analogues.     

Size‐Dependence of the Melting Temperature of Individual Au Nanoparticles

Nanoparticles have an immense importance in various fields, such as medicine, catalysis, and various technological applications. Nanoparticles exhibit a significant depression in melting point as their size goes below ≈10 nm. However, nanoparticles are frequently used in high temperature applications such as catalysis where temperatures often exceed several 100 degrees which makes it interesting to study not only the melting temperature depression, but also how the melting progresses through the particle. Using high‐resolution transmission electron microscopy, the melting process of gold nanoparticles in the size range of 2–20 nm Au nanoparticles combined with molecular dynamics studies is investigated. A linear dependence of the melting temperature on the inverse particle size is confirmed; electron microscopy imaging reveals that the particles start melting at the surface and the liquid shell formed then rapidly expands to the particle core.     

In Situ Generated Gold Nanoparticles on Active Carbon as Reusable Highly Efficient Catalysts for a C −C Stille Coupling

Gold nanoparticle catalysts are important in many industrial production processes. Nevertheless, for traditional C ?C cross‐coupling reactions they have been rarely used and Pd catalysts usually give a superior performance. Herein we report that in situ formed gold metal nanoparticles are highly active catalysts for the cross coupling of allylstannanes and activated alkylbromides to form C ?C bonds. Turnover numbers up to 29 000 could be achieved in the presence of active carbon as solid support, which allowed for convenient catalyst recovery and reuse. The present study is a rare case where a gold metal catalyst is superior to Pd catalysts in a cross‐coupling reaction of an organic halide and an organometallic reagent.     

Fe3O4 – Glutathione stabilized Ag nanoparticles: A new magnetically separable robust and facile catalyst for aqueous phase reduction of nitroarenes

The heterostructured Ag nanoparticles decorated Fe₃O₄ Glutathione (Fe₃O₄‐Glu‐Ag) nanoparticles (NPs) were synthesized by sonicating glutathione (Glu) with magnetite and further surface immobilization of silver NPs on it. The ensuing magnetic nano catalyst is well characterized by Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), high resolution transmission electron microscopy (HRTEM), powder X‐ray diffraction (PXRD), thermogravimetric analysis (TGA). The prepared Fe₃O₄‐Glu‐Ag nanoparticles have proved to be an efficient and recyclable nanocatalyst with low catalyst loading for the reduction of nitroarenes and heteronitroarenes to respective amines in the presence of NaBH₄ using water as a green solvent which could be easily separated at the end of a reaction using an external magnet and can be recycled up to 5 runs without any significant loss in catalytic activity. Gram scale study for the reduction of 4‐NP has also being carried out successfully and it has been observed that this method can serve as an efficient protocol for reduction of nitroarenes on industrial level.     

Self‐emulsion polymerization of amphiphilic monomers—a green route to synthesis of polymeric nanoscaffolds

Self‐emulsion polymerization (SEP), a green route developed by us for the polymerization of amphiphilic monomers, does not require any emulsifier or an organic solvent except that the water‐soluble initiators such as 2,2′‐azobis[2‐(2‐imidazolin‐2‐yl)propane]dihydrochloride (VA‐044) and potassium persulfate (KPS) are only used. We report here the polymer nanoscaffolds from a number of amphiphilic monomers, which can be used for in situ encapsulation of a variety of nanoparticles. As a demonstration of the efficacy of these nanoscaffolds, the synthesis of a biocompatible hybrid nanoparticle (nanohybrid), prepared by encapsulating Fe₃O₄ magnetic nanoparticle (Fe₃O₄ MNPs) in poly(2‐hydroxyethyl methacrylate) in water, for MRI application is presented. The nanohybrid prepared following the SEP in the form of an emulsion does not involve the use of any stabilizing agent, crosslinker, polymeric emulsifier, or surfactant. This water‐soluble, spherical, and stable nanohybrid containing Fe₃O₄ MNPs of average size 10 ± 2 nm has a zeta potential value of ?41.89 mV under physiological conditions. Magnetic measurement confirmed that the nanohybrid shows typical magnetic behavior having a saturation magnetization (Ms) value of 32.3 emu/g and a transverse relaxivity (r2) value of 29.97 mM^?1 s^?1, which signifies that it can be used as a T2 contrast agent in MRI. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019     

Starch nanoparticles as a bio-nanocatalyst in synthesis of diheteroaryl thioethers

Nanostarch is shown to be a highly efficient, eco-friendly and heterogenous organocatalyst for the synthesis of the diheteroaryl thioethers via one-pot reaction of methylcarbonyls, thiourea and iodine in DMSO. This method offers significant advantages such as available starting materials, higher purity and excellent yield of products, very easy reaction conditions and absence of any tedious purification. Furthermore, because of employing eco-friendly catalyst without using transition metal catalysts, this novel method emerges as a green-approach leading to less harmful residues. Moreover, a mechanism was proposed to rationalize the reaction and the role of starch nanoparticles was also investigated in these transformations.