The global convergence of the BFGS method with a modified WWP line search for nonconvex functions

Numerical Algorithms - The BFGS method, which has great numerical stability, is one of the quasi-Newton line search methods. However, the global convergence of the BFGS method with a Wolfe line...     

Nickel (II) tetrapyridyl complexes as electrocatalysts and precatalysts for water oxidation

Two nickel complexes, [Ni(tpen)](ClO₄)₂.0.5CH₃COCH₃ ( 1 ) and [Ni(tpbn)](ClO₄)₂ ( 2 ), of tetrapyridyl ligands N,N,N′,N′-tetrakis(2-pyridyl-methyl)-1,2-ethanediamine (tpen) and N,N,N′,N′-tetrakis(2-pyridyl-methyl)-1,4-butanediamine (tpbn) were prepared and their catalysis for water oxidation reaction (WOR) studied. In 0.1 M phosphate buffer solution (PBS) of pH 8.0, complex 1 is a homogeneous molecular catalyst with an overpotential of ~440 mV and a Faradaic efficiency of 89%. At pH ≥ 9.0, complex 1 degraded gradually during the catalytic process and formed NiO_x composite (nickel oxide with general formula Ni_xO_yH_z) active for WOR. In contrast, complex 2 deteriorated under measured conditions (pH 8.0–12.0) and formed NiO_x composite active for WOR. The NiO_x composite derived from 1 in 0.1 M PBS at pH 11.0 showed an activity with an overpotential of ~500 mV, a Tafel slope of ~90 mV/decade and a Faradaic efficiency of 97%. Mechanisms were proposed for water oxidation catalyzed by 1 and 2 . This work revealed that the catalytic activity of the nickel complexes was related to the flexibility of the tetrapyridyl ligands and the adaptability of the coordination sphere of the nickel(II) center.     

How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

The extremal irregularity of connected graphs with given number of pendant vertices

Czechoslovak Mathematical Journal - The irregularity of a graph G = (V, E) is defined as the sum of imbalances ∣du ? dv∣ over all edges uv ∈ E, where du denotes the degree...     

Effect of enrichment functions on GFEM solutions of time-dependent conduction heat transfer problems

This article investigates the effect of the selection of enrichment functions on the formulation of the Generalized Finite Element Method (GFEM) for the solutions of transient heat conduction problems. We present the study of an a-posteriori error estimate with the aim to show it as a reliable tool for the selection of enrichment functions to efficiently capture the sharp thermal gradients of the solutions. Problems in two- and three-dimensional domains are considered to demonstrate the robustness of the proposed error estimate. Numerical experiments consider two different types of enrichment functions that mimic the solution behaviour and capture the time-varying thermal gradients. The presented study shows that the error estimate is independent of the heuristically selected enrichment functions and can be used for any type of enrichment functions. It is concluded that the proposed error estimate efficiently reflects the errors in the GFEM solutions for both types of enrichment functions and can be used as an effective tool for the selection of more suitable enrichment functions that produce lower errors under the considered thermal conditions.     

System-size effect on the friction at liquid-solid interfaces

The friction at the liquid-solid interfaces is widely involved in various phenomena ranging from nanometer to micrometer scales. By the molecular dynamic(MD)simulation, the friction properties of liquid-solid interfaces at the molecular level are calculated via the Green-Kubo relation. It is found that the system size will influence the value of the friction coefficient, especially for the solid surfaces with the larger polar charge. The value of the friction coefficient decreases with the increase in the system size and converges at large system sizes. The large polar charge will lead to a significant friction coefficient. However, the diffusion of water molecules on this surface is almost a constant, indicating that the diffusion coefficient seems to be independent of the system size and polar charge. This work provides insights for the selection of the system size in modeling the frictional properties of hydrophobic/hydrophilic surfaces.     

CuFe2O4 magnetic heterogeneous nanocatalyst: Low power sonochemical-coprecipitation preparation and applications in synthesis of 4H-chromene-3-carbonitrile scaffolds

The paper presents the synthesis and catalytic activity of CuFe₂O₄ nanoparticles. The CuFe₂O₄ nanoparticles have been prepared by sonochemical route under low power ultrasonic irradiation (UI) and using silent stirring at room temperature only (ST) along with co-precipitation method, without using any additive/capping agent. The synthesized magnetic nanoparticles were successfully used and compared for the synthesis of 4H-chromene-3-carbonitrile derivatives. The CuFe₂O₄ nanoparticles obtained by sonochemical route exhibit higher catalytic activity because of small size (0.5–5 nm), high surface area (214.55 m²/g), high thermal stability up to 700 °C, recyclability and reusability due to its magnetic characteristics than CuFe₂O₄ nanoparticles obtained by room temperature silent stirring. The synthesized CuFe₂O₄ nanoparticles were characterized by FT-IR, SEM–EDX, HR-TEM, XRD, TGA/DTA/DTG, BET, VSM techniques. The present method is of great interest due to its salient features such as environmentally compatible, efficient, short reaction time, chemoselectivity, high yield, cheap, moisture insensitive, green and recyclable catalyst which make it sustainable protocol.     

Morphology and properties of super-toughened bio-based poly(lactic acid)/poly(ethylene-co-vinyl acetate) blends by peroxide-induced dynamic vulcanization and interfacial compatibilization

Super-toughened poly(lactic acid) (PLA)/poly(ethylene-co-vinyl acetate) (EVA) blends were prepared via 2,5-dimethyl-2,5-di(tert-butylperoxy)hexane (AD) induced dynamic vulcanization and in situ interfacial compatibilization. The effects of AD on the morphology and properties of PLA/EVA blends were studied using a Brabender torque rheometer, gel content test, scanning electron microscopy (SEM), differential scanning calorimetry (DSC) thermogravimetric analysis (TGA) and mechanical properties test. The torque and gel content demonstrated that EVA and PLA was successfully vulcanized in the presence of free radicals obtained by the decomposition of the 2,5-dimethyl-2,5-di(tert-butylperoxy)hexane (AD). Additionally, the gel content results indicated that, compared with PLA, EVA is more aggressive with free radicals. The SEM revealed that a relatively uniform phase morphology and good interfacial compatibilization were achieved in the dynamically vulcanized PLA/EVA/AD blends. The interfacial reaction and compatibilization between the component polymers resulted in the formation of super-toughened PLA/EVA blended materials.     

From Glucose to Polymers: A Continuous Chemoenzymatic Process

Efforts to synthesize degradable polymers from renewable resources are deterred by technical and economic challenges; especially, the conversion of natural building blocks into polymerizable monomers is inefficient, requiring multistep synthesis and chromatographic purification. Herein we report a chemoenzymatic process to address these challenges. An enzymatic reaction system was designed that allows for regioselective functional group transformation, efficiently converting glucose into a polymerizable monomer in quantitative yield, thus removing the need for chromatographic purification. With this key success, we further designed a continuous, three-step process, which enabled the synthesis of a sugar polymer, sugar poly(orthoester), directly from glucose in high yield (73 % from glucose). This work may provide a proof-of-concept in developing technically and economically viable approaches to address the many issues associated with current petroleum-based polymers.