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.     

Effects induced by 𝛄-irradiation on intraband transitions in Sr2+-doped ammonium zinc chloride crystals

Considerable changes were observed in the X-ray diffraction pattern of ammonium zinc chloride after doping with Sr²⁺ in different concentrations and after irradiating with γ rays at different doses. The effect of γ-radiation and Sr²⁺ content on optical parameters of (NH₄)₂ZnCl₄: x Sr²⁺ single crystals (x?=?0.00, 0.020, 0.039, 0.087 or 0.144?wt.%) has been investigated. The transmittance near the absorption edge of unirradiated crystals and crystals irradiated with different γ-doses has been measured, hence the absorption coefficient (α) was calculated. The values of α at room temperature increased under the influence of γ-irradiation. The rate by which α increases with photon energy just before the absorption edge is strongly inhibited by higher γ-doses. The type of intraband transition in (NH₄)₂ZnCl₄: x Sr²⁺ single crystals was found to be of the allowed indirect transition, and γ-irradiation had no effect on the type of transition. The values of the optical energy gap (E _g ) were calculated as a function of γ-dose. The effect of γ-irradiation was found to be more pronounced on samples doped with x?=?0.087 or 0.144?wt.% Sr²⁺. The results can be discussed on the basis of γ-irradiation-induced defects and Sr²⁺ concentration. A diagram representing probable transitions to the created bands due to irradiation could be constructed.     

Influence of gamma radiation on morphology structure,electrochemical corrosion behavior and hardness of Ni–Cr based alloys

This study evaluates the effects of gamma radiation on structure, electrochemical corrosion behavior and Vickers hardness of commercial dental Nikkeli–Kromi–Polttosekoitus [Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn)] alloy. The corrosion rate of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) alloy with 0.5 M HCl is increased with increasing the exposure rate of gamma radiation. The corrosion resistance of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) is varied and reaches a minimum value at 30 KGy. The corrosion potential value also is varied and reaches its highest value at 30 KGy. The Vickers hardness value of Ni_65.2Cr_22.5Mo_9.5X_2.8 (X=Nb, Si, Fe and Mn) alloy is decreased by increasing the gamma radiation dose. Also it is obvious from our results that the effects of gamma radiation at the surface are much higher as compared with deeper parts and the structure of the alloy is changed due to its exposure to gamma radiation.     

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.     

Approximating the relationship among the degree of the reaction forces and the nodes on footprint during a stance phase

This study examined the foot biomechanics that are utilized when foot is in contact with the ground during a stance phase. The purpose of the study was to investigate the normalized ground reaction forces that impacted certain sections and points on the footprint, and to identify patterns in the degrees to which these forces occurred. Foot was modeled in such a manner that a vertex represented a bone and an edge represented a joint, and a graph that depicted the foot was created. Twelve nodes were marked on the footprint and these were linked together to create a gait path. By fusing the graph and the gait path and by manipulating the mathematical models, a profile for an ideal bipedal walking locomotion was developed. A male subject performed bipedal walking through a force plate system in order to obtain the profile that reflected actual bipedal walking. The actual and the proposed profiles were compared and there were significant similarities between the two profiles, with both exhibiting an double-bump pattern. It is therefore viable that the approximation techniques proposed in this work may provide an alternative means over the application of a force plate system to generate a profile for bipedal walking. However, the accuracy and reliability of the results yielded from this technique need further investigation.     

Direct Amination and Synthesis of Fused N‐Substituted Isothiochromene Derivatives

Isothiochromene[3,4‐d] pyrimidine derivatives 2 , 3 , and 4a , b were synthesized from the reaction of 3‐amino‐1‐(pyridin‐4‐yl)‐5‐(pyridin‐4‐ylmethylene)‐5,6,7,8‐tetrahydro‐1H‐isothiochromene‐4‐carbonitrile 1 with acetic anhydride, formamide, urea, or thiourea in appropriate experimental conditions. Combination of 1 with carbon acid derivatives afforded isothiochromene [3,4‐b]pyridine 6 – 8 in good yield. A simple approach for N‐substituted fused isothiochromene derivatives has been explored. A POCl₃‐mediated direct amination of isothiochromene amide 2 with NH₂‐heterocycles, secondary amines, and carbohydrazides is described and compared with classical method, yielding 10 – 14 . The structures of the newly synthesized compounds were elucidated on the basis of elemental analysis, and spectral data.     

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.     

Evaluation of solvents’ effect on solubility,intermolecular interaction energies and habit of ascorbic acid crystals

Solubility of active pharmaceutical ingredient (API) in solvents is very important for drug development and manufacturing. Solubility data may provide further information such as thermochemical properties and intermolecular interactions that may lead to a better understanding of the formation of API crystals. In this study, solubility of ascorbic acid was determined by gravimetric method in four different commonly used polar protic solvents: water, methanol, ethanol and 2-propanol. The solubility of ascorbic acid crystal was also predicted using Conductor-like Screening Model – Realistic Solvent (COSMO-RS) approach. In this computational analysis, the generated ΔG values are based on the solubilities that were experimentally obtained to simulate the intermolecular forces. The intermolecular interaction data from COSMO-RS provide an insight into the relationship between the intermolecular interactions and its crystal habit across four different polar protic solvents. The habit of the crystals was then determined using light microscopy and scanning electron microscopy techniques, while the polymorphic form of the crystals was identified by X-ray powder diffraction and single X-ray diffraction techniques. The solubility and characterization data showed that the solvents with high polarity increased the solubility of ascorbic acid. The data also showed that different solvent polarity influenced the crystal habit, but did not change the crystal structure to form a new polymorph.