Coexistence of domains of attraction of nonautonomous neural networks with time-varying delays

This paper presents new dynamical behavior, i.e., the coexistence of 2^N domains of attraction of N-dimensional nonautonomous neural networks with time-varying delays. By imposing some new assumptions on activation functions and system parameters, we construct 2^N invariant basins for neural system and derive some criteria on the boundedness and exponential attractivity for each invariant basin. Particularly, when neural system degenerates into periodic case, we not only attain the coexistence of 2^N periodic orbits in bounded invariant basins but also give their domains of attraction. Moreover, our results are suitable for autonomous neural systems. Our new results improve and generalize former ones. Finally, computer simulation is performed to illustrate the feasibility of our results.     

Computational studies on cyclic [n]paraphenyleneacetylenes using homodesmotic reactions

Cyclic [n]paraphenyleneacetylenes ([n]CPPAs) are potentially useful compounds for molecular electronics. In this article, a homodesmotic reaction scheme coupled with density functional theory has been used to estimate theoretically strain energies and heats of formation of [n]CPPAs. Calculations have been done for a series of [n]CPPAs, containing up to ten phenylacetylene units. Strain energies of [n]CPPAs decrease, while heats of formation increase steadily with the increase in the number of phenylacetylene units using homodesmotic reaction schemes. B3LYP and mPW1PW91 functionals have been used with the Pople basis set 6-31G* to analyze the trends. The results are sensitive to the scheme of homodesmotic reaction chosen, thereby necessitating careful chemical consideration before spending considerable computational resources for higher [n]CPPAs not considered here. Computational estimates for the ring diameter of [n]CPPAs and absolute entropy have also been obtained here. The HOMO-LUMO gaps of the belt shaped [n]CPPAs show an odd–even difference. In addition, the HOMOs of the [3]CPPA, [5]CPPA, [7]CPPA and [9]CPPA are doubly degenerate.     

Global Exponential Stability in Discrete-time Analogues of Delayed Cellular Neural Networks

A novel method called semi-discretization is employed in the formulation of discrete-time analogues of nonlinear delayed differential equations modelling cellular neural networks. The dynamical characteristics of the discrete-time analogues are studied. When the network parameters satisfy certain sufficient conditions which are independent of the delays, the discrete-time analogues for any choice on the discretization step-size are shown to be globally exponentially stable. The sufficient conditions are obtained by employing an appropriate form of Lyapunov sequences and these conditions correspond to those which have been obtained in the literature for the global exponential stability of continuous-time delayed cellular neural networks. Several examples and computer simulations are given to support our results and to demonstrate some of the advantages of the discrete-time analogues in numerically simulating their continuous-time counterparts.     

Beyond Zudilin's conjectured q-analogue of Schmidt's problem

Using the methodology of (rigorous) experimental mathematics, we give a simple and motivated solution to Zudilin's question concerning a q-analogue of a problem posed by Asmus Schmidt about a certain binomial coefficients sum. Our method is based on two simple identities that can be automatically proved using the Zeilberger and q-Zeilberger algorithms. We further illustrate our method by proving two further binomial coefficient sums.     

Stochastic optimal multi-modes switching with a viscosity solution approach

We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary (_gij(t,x)≥0$g_{ij}(t,x)\ge 0$). We show existence of the optimal strategy, via a verification theorem. Finally, when the state of the system is a Markov process, we show that the vector of value functions of the optimal problem is the unique viscosity solution to the system of m$m$ variational partial differential inequalities with inter-connected obstacles.     

High-Performance Liquid Chromatographic Method for the Simultaneous Determination of Four Flavonols in Food Supplements and Pharmaceutical Formulations

A method using high-performance liquid chromatography with diode array detection (HPLC-DAD) as a powerful separation technique has been developed for the simultaneous determination of the four flavonols rutin, quercetin, kaempferol and isorhamnetin in food supplements and pharmaceutical formulations. The chromatographic separation was achieved in 36?min using a Symmetry C₁₈ column (250?×?3?mm; 5?µm) as the stationary phase and a mixture of methanol, acetonitrile, and pH 2.5 aqueous acetic acid as the mobile phase in gradient elution mode. The analytical wavelengths were 256?nm for rutin, quercetin and isorhamnetin, and 368?nm for kaempferol. An ultrasound-assisted extraction protocol was performed using methanol as solvent. The detection and quantification limits were lower than 0.03?µg mL^?1 and 0.08?µg mL^?1, respectively. The inter-day and intra-day precisions were less than 4.8 and 5.1%, respectively, and the average recoveries were in the range from 96 to 107%. The method was applied for the determination of the studied flavonols in food supplements and pharmaceutical preparations. The satisfactory recovery values demonstrate the potential of the developed method for the determination of the analytes in these samples. In addition, the method is suitable for routine quality control due its ease of operation.     

HPLC profiling of phenolics and flavonoids of Adonidia merrillii fruits and their antioxidant and cytotoxic properties

In this study the antioxidant and cytotoxicity activity of the Adonidia merrillii fruits were investigated using different solvent polarities (methanol, ethyl acetate and water). The results showed that the total phenolic and flavonoid contents of the methanolic extract was higher compare with other extract with respective values of 17.80 ± 0.45 mg gallic acid equivalents/g dry weight (DW) and 5.43 ± 0.33 mg rutin equivalents/g DW. Beside that The RP-HPLC analyses indicated the presence of gallic acid, pyrogallol, caffeic acid, vanillic acid, syringic acid, naringin and rutin. In the DPPH, NO2 and ABTS scavenging assays, the methanolic extract exhibited higher antioxidant activity as compared to the ethyl acetate and water extracts. The extracts exhibited moderate to weak cytotoxic activity in the assays using human hepatocytes (Chang liver cells) and NIH/3T3 (fibroblasts cell) cell lines. The findings showed the Adonidia merrillii fruit extracts to possess considerable antioxidant and cytotoxicity properties. The fruit, therefore, is a potential candidate for further work to discover antioxidant and cytotoxic drugs from natural sources.     

Conductivity studies of plasticized anhydrous PEO-KOH alkaline solid polymer electrolyte

Polyethylene oxide (PEO)–potassium hydroxide (KOH)-based alkaline solid polymer electrolyte films have been prepared by using methanol as solvent. The highest room temperature ionic conductivity of (2.1 ± 0.5) × 10⁻⁸ S cm⁻¹ was achieved for the composition of 70 wt% PEO:30 wt% KOH. The addition of plasticizer, ethylene carbonate, propylene carbonate, or polyethylene glycol to the highest conductivity of PEO–KOH system helps to increase the ambient ionic conductivity to the order of 10⁻⁶–10⁻⁴ S cm⁻¹. The log σ vs 1/T plot of PEO–KOH showed a small conductivity decrease at 50–60 °C range. The small decrease and the hysteresis that occur during the heating–cooling cycle was overcome by the presence of the plasticizer. X-ray diffraction observation supports the conductivity results.     

Photo-recycling the Sacrificial Electron Donor: Towards Sustainable Hydrogen Evolution in a Biphasic System

H₂ may be evolved biphasically using a polarised liquid|liquid interface, acting as a “proton pump”, in combination with organic soluble metallocenes as electron donors. Sustainable H₂ production requires methodologies to recycle the oxidised donor. Herein, the photo-recycling of decamethylferrocenium cations (DcMFc⁺) using aqueous core-shell semiconductor CdSe@CdS nanoparticles is presented. Negative polarisation of the liquid|liquid interface is required to extract DcMFc⁺ to the aqueous phase. This facilitates the efficient capture of electrons by DcMFc⁺ on the surface of the photo-excited CdSe@CdS nanoparticles, with hydrophobic DcMFc subsequently partitioning back to the organic phase and resetting the system. TiO₂ (P25) and CdSe semiconductor nanoparticles failed to recycle DcMFc⁺ due to their lower conduction band energy levels. During photo-recycling, CdS (on CdSe) may be self-oxidised and photo-corrode, instead of water acting as the hole scavenger.