Bifurcation of limit cycles in small perturbations of a hyper-elliptic Hamiltonian system with two nilpotent saddles

In this paper we study the first-order Melnikov function for a planar near-Hamiltonian system near a heteroclinic loop connecting two nilpotent saddles. The asymptotic expansion of this Melnikov function and formulas for the first seven coefficients are given. Next, we consider the bifurcation of limit cycles in a class of hyper-elliptic Hamiltonian systems which has a heteroclinic loop connecting two nilpotent saddles. It is shown that this system can undergo a degenerate Hopf bifurcation and Poincarè bifurcation, which emerges at most four limit cycles in the plane for sufficiently small positive ε. The number of limit cycles which appear near the heteroclinic loop is discussed by using the asymptotic expansion of the first-order Melnikov function. Further more we give all possible distribution of limit cycles bifurcated from the period annulus.     

The uniqueness of the solution of dual equations of an inverse indefinite Sturm-Liouville problem

In this paper we consider a linear second-order equation of Sturm-Liouville type:

(I)     

N‐(2‐Hydroxypropyl)methacrylamide (HPMA) Copolymer‐Linked Nitroxides: Potential Magnetic Resonance Contrast Agents

N‐(2‐Hydroxypropyl)methacrylamide (HPMA) copolymer‐linked nitroxides were synthesized as macromolecular contrast agents for MR imaging. Molar relaxivities of HPMA copolymer‐linked nitroxides increased linearly in proportion to the number of nitroxides attached per gram of copolymer. HPMA copolymer‐linked nitroxides with 15, 20 and 30 mol‐% nitroxide exhibited higher relaxivities than gadolinium diethylenetriaminepentaacetic acid (Gd‐DTPA). These results demonstrate the potential of HPMA copolymer‐linked nitroxides as MR contrast agents for solid tumors.

Structure of HPMA copolymer‐linked nitroxides.     

Nanoclay and Cu Nanoparticles Loaded Polyethylene Nanocomposites for Natural Gas Transfer Applications

High density polyethylene nanocomposites loaded with a reinforcing filler (Cloisite 20A as a modified nanoclay) and an electrically conductive filler (Cu nanoparticles) were prepared by a melt blending method. The morphological, mechanical, thermal, and electrical properties of the prepared nanocomposites were investigated to evaluate their performances as appropriate materials for production of reinforced conductive polymeric pipes to be used in natural gas distribution and transportation pipelines. A random and uniform dispersion of both nanoparticles in the polyethylene matrix, with a nanoclay intercalated morphology, was observed by scanning electron microscopy and X-ray diffraction techniques. The results revealed ca. 117, 13 and 21% increases in the Young’s modulus, tensile strength and yield stress of the polyethylene matrix by adding 3 wt.% of Cloisite 20A into it. For the similar conditions, however, more than a 71% decrease was observed for the elongation at break. Thermal analysis demonstrated that the melting points of the nanocomposites were increased by incorporating both fillers and the crystallinity of polyethylene chains was decreased by incorporating Cloisite 20A and then slightly increased by adding Cu nanoparticles. Moreover, the results revealed the creation of conductivity inside the non-conductive polyethylene matrix due to the presence of the conductive Cu nanoparticles.     

A stochastic local search algorithm with adaptive acceptance for high-school timetabling

Automating high school timetabling is a challenging task. This problem is a well known hard computational problem which has been of interest to practitioners as well as researchers. High schools need to timetable their regular activities once per year, or even more frequently. The exact solvers might fail to find a solution for a given instance of the problem. A selection hyper-heuristic can be defined as an easy-to-implement, easy-to-maintain and effective ‘heuristic to choose heuristics’ to solve such computationally hard problems. This paper describes the approach of the team hyper-heuristic search strategies and timetabling (HySST) to high school timetabling which competed in all three rounds of the third international timetabling competition. HySST generated the best new solutions for three given instances in Round 1 and gained the second place in Rounds 2 and 3. It achieved this by using a fairly standard stochastic search method but significantly enhanced by a selection hyper-heuristic with an adaptive acceptance mechanism.     

Electrochemical Properties of Th(IV)‐Hexacyanoferrate Sol‐Gel Carbon Composite Electrode: Electrocatalytic Oxidation of Dopamine and Ascorbic Acid

A new sol‐gel carbon composite electrode using hexacyanoferrate (HCF)‐Th(IV) ion pair as a suitable modifier is fabricated in the present study. The Th(IV)‐HCF‐sol‐gel carbon composite electrode (THCF‐CCE) has been prepared by mixing methyl trimethoxysilan (MTMOS) sol‐gel precursor and carbon powder with ion pair and then to fix in a plastic tube. Cyclic voltammetry and chronoamperometry were employed to study the electrochemical and electrocatalytic properties of proposed electrode. The apparent charge transfer rate constant, k_s, and transfer coefficient, α, for electron transfer between ion‐pair and sol‐gel CPE were calculated as 3.10 ± 0.10 s^?1 and 0.52, respectively. The THCF‐CCE showed a significant electrocatalytic activity towards oxidation of ascorbic acid (AA) and dopamine (DA) in 0.1 M acidic phosphate buffer solutions (pH 3) containing KCl as a supporting electrolyte. The mean value of the diffusion coefficients for ascorbic acid and dopamine were found 4.12 × 10^?5 and 4.43 × 10^?5 (cm²s^?1), respectively. High stability, good reproducibility, rapid response, easy surface regeneration and fabrication are the important characteristics of the proposed sensor. The resulting peaks from the electrocatalytic oxidation of AA and DA were well resolved with good sensitivity. A linear response was observed for AA and DA in the concentration range of 1 × 10^?5 to 3 × 10^?3 M and 4 × 10^?6 to 2.2 × 10^?4 M, respectively.     

Cold Deposition as a Novel Procedure for the Preparation of Titania Sol‐Gel: A Development of a High Sensitive Electrochemical Method for Determination of Cu(II) in the Presence of Arsenic(III)

Titania sol‐gel modified gold electrode (TSGMGE) was prepared with the usage of a new proposed cold deposition method at ?10 °C. Scanning electron microscope (SEM) operating at 30 kV was used to obtain micrographs of unmodified and modified electrodes. The obtained results showed that this procedure yields a sol‐gel with high porosity in comparison to conventional methods. The modified Au electrode was fabricated by trapping the L‐glutamine in titania sol‐gel at low temperatures to preparation of a new titania sol‐gel glutamine modified gold electrode (TSGGMGE). The possibility determination of traces of Cu(II) in the presence of As(III) was investigated using proposed electrode. Under the optimized conditions, copper was accumulated at ?0.35 V (vs. Ag/AgCl) for 40 s in 0.1 M acetate buffer (pH 4.0) in the presence of different amounts of arsenic. Two dynamic linear responses with good reproducibility were observed for copper ions in the concentration range of 1 × 10^?6 ?4 × 10^?4 M and 4 × 10^?8 ?6 × 10^?7 M.     

Impact of Surface Defects on LaNiO3 Perovskite Electrocatalysts for the Oxygen Evolution Reaction

Perovskite oxides are regarded as promising electrocatalysts for water splitting due to their cost-effectiveness, high efficiency and durability in the oxygen evolution reaction (OER). Despite these advantages, a fundamental understanding of how critical structural parameters of perovskite electrocatalysts influence their activity and stability is lacking. Here, we investigate the impact of structural defects on OER performance for representative LaNiO₃ perovskite electrocatalysts. Hydrogen reduction of 700 °C calcined LaNiO₃ induces a high density of surface oxygen vacancies, and confers significantly enhanced OER activity and stability compared to unreduced LaNiO₃; the former exhibit a low onset overpotential of 380 mV at 10 mA cm⁻² and a small Tafel slope of 70.8 mV dec⁻¹. Oxygen vacancy formation is accompanied by mixed Ni²⁺/Ni³⁺ valence states, which quantum-chemical DFT calculations reveal modify the perovskite electronic structure. Further, it reveals that the formation of oxygen vacancies is thermodynamically more favourable on the surface than in the bulk; it increases the electronic conductivity of reduced LaNiO₃ in accordance with the enhanced OER activity that is observed.     

Common Pitfalls of Reporting Electrocatalysts for Water Splitting

Rigorous assessment of heterogeneous electrocatalysts for electrochemical water splitting has been a critical issue mainly due to insufficient standard protocols to measure and report experimental data. In this perspective, we highlight some common pitfalls when measuring and reporting electrocatalytic data, which should be avoided to ensure the accuracy and reproducibility and to advance the water splitting field. We advocate to prevent the introduction of artefacts from the counter and reference electrodes, as well as the impurities in the electrolyte when conducting electrocatalyst activity measurements. In addition, we encourage the use of the electrochemically active surface area(ECSA)-normalized current densities to represent the intrinsic activity of the reported catalysts for a better comparison with previously known materials. Suitable ECSA measurement methods should be employed based on the nature of catalysts. Recommendations made in this perspective will hopefully assist in identifying advanced catalysts for water splitting research.