Global dynamics and bifurcation in delayed SIR epidemic model

An SIR epidemic model with time delay, information variable and saturated incidence rate, where the susceptibles are assumed to satisfy the logistic equation and the incidence term, is of saturated form with the susceptibles. This model exhibits two bifurcations, one is transcritical bifurcation and the other is Hopf bifurcation. The local and global stability of endemic equilibrium is also discussed. Finally, numerical simulations are carried out to explain the mathematical conclusions.     

Synthesis and characterization of water-soluble carbon nanotubes from mustard soot

Carbon nanotubes (CNT) has been synthesized by pyrolysing mustard oil using an oil lamp. It was made water-soluble (wsCNT) through oxidative treatment by dilute nitric acid and was characterized by SEM, AFM, XRD, Raman and FTIR spectroscopy. The synthesized wsCNT showed the presence of several junctions and defects in it. The presence of curved graphene structure (sp²) with frequent sp³ hybridized carbon is found to be responsible for the observed defects. These defects along with the presence of di- and tri-podal junctions showed interesting magnetic properties of carbon radicals formed by spin frustration. This trapped carbon radical showed ESR signal in aqueous solution and was very stable even under drastic treatment by strong oxidizing or reducing agents. Oxidative acid treatment of CNT introduced several carboxylic acid group functionalities in wsCNT along with the nicking of the CNT at different lengths with varied molecular weight. To evaluate molecular weights of these wsCNTs, an innovative method like gel electrophoresis using high molecular weight DNA as marker was introduced.     

Two storage inventory model with fuzzy deterioration over a random planning horizon

An inventory model for a deteriorating item with stock dependent demand is developed under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. For crisp deterioration rate, the expected profit is derived and maximized via genetic algorithm (GA). On the other hand, when deterioration rate is imprecise then optimistic/pessimistic equivalent of fuzzy objective function is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to maximize the optimistic/pessimistic return and finally fuzzy simulation-based GA is developed to solve the model. The models are illustrated with some numerical data. Sensitivity analyses on expected profit function with respect to distribution parameter λ and confidence levels α₁ and α₂ are also presented.     

Synthesis of the active sites of molybdoenzymes: MoO2(VI) and MoO(IV)-dithiolene complexes mimicking enzymatic reactions of sulphite oxidase with saturation kinetics

[Mo^VIO₂(S₂C₂(CN)₂)₂]₂₋ (┘1) and [Mo^IVO(S₂C₂(CN)₂)₂]²⁻ (2) mimick oxidoreductase enzymatic activities of sulphite oxidase with biological electron donor, SO ₃ ²⁻ , andin vitro electron acceptor, [Fe(CN)₆]³⁻, demonstrating proton coupled electron transfer reaction in water and inhibition of the oxidation of (2) in the presence of KCN. The sulphite exidizing system is characterized by substrate saturation kinetics indicating the biological significance of the reactions     

Nonlinear Dynamics of a Cantilever Beam Carrying an Attached Mass with 1:3:9 Internal Resonances

In this paper the nonlinear response of a base-excited slender beam carrying an attached mass is investigated with 1:3:9 internal resonances for principal and combinationparametric resonances. Here the method of normal forms is used to reduce the second order nonlinear temporal differential equation of motion of the system to a set offirst order nonlinear differential equations which are used to find the fixed-point, periodic, quasi-periodic and chaotic responses of the system.Stability and bifurcation analysis of the responses are carried out and bifurcation sets are plotted. Many chaotic phenomena are reported in this paper.     

Lanthanide‐Doped Nanocrystals: Strategies for Improving the Efficiency of Upconversion Emission and Their Physical Understanding

The fundamental understanding of lanthanide‐doped upconverted nanocrystals remains a frontier area of research because of potential applications in photonics and biophotonics. Recent studies have revealed that upconversion luminescence dynamics depend on host crystal structure, size of the nanocrystals, dopant concentration, and core–shell structures, which influence site symmetry and the distribution and energy migration of the dopant ions. In this review, we bring to light the influences of doping/co‐doping concentration, crystal phase, crystal size of the host, and core–shell structure on the efficiency of upconversion emission. Furthermore, the lattice strain, due to a change in the crystal phase and by the core–shell structure, strongly influences the upconversion emission intensity. Analysis suggests that the local environment of the ion plays the most significant role in modification of radiative and nonradiative relaxation mechanisms of overall upconversion emission properties. Finally, an outlook on the prospects of this research field is given.     

Influence of Size and Shape on the Photocatalytic Properties of SnO2 Nanocrystals

Tuning the functional properties of nanocrystals is an important issue in nanoscience. Here, we are able to tune the photocatalytic properties of SnO₂ nanocrystals by controlling their size and shape. A structural analysis was carried out by using X‐ray diffraction (XRD)/Rietveld and transmission electron microscopy (TEM). The results reveal that the number of oxygen‐related defects varies upon changing the size and shape of the nanocrystals, which eventually influences their photocatalytic properties. Time‐resolved spectroscopic studies of the carrier relaxation dynamics of the SnO₂ nanocrystals further confirm that the electron–hole recombination process is controlled by oxygen/defect states, which can be tuned by changing the shape and size of the materials. The degradation of dyes (90 %) in the presence of SnO₂ nanoparticles under UV light is comparable to that (88 %) in the presence of standard TiO₂ Degussa P‐25 (P25) powders. The photocatalytic activity of the nanoparticles is significantly higher than those of nanorods and nanospheres because the effective charge separation in the SnO₂ nanoparticles is controlled by defect states leading to enhanced photocatalytic properties. The size‐ and shape‐dependent photocatalytic properties of SnO₂ nanocrystals make these materials interesting candidates for photocatalytic applications.     

Dynamic polarizability of two‐electron ions under Debye screening

The effect of plasma screening on the dynamic dipole polarizability (DPP) of two‐electron ions Be²⁺, B³⁺, and C⁴⁺ has been investigated using highly correlated exponential wave functions within the framework of pseudostate summation technique and Debye screening concept. Plasma‐screening effect on the oscillator strengths (OS) of the ultraviolet and visible series has also been investigated for the systems Li⁺, Be²⁺, B³⁺, C⁴⁺. The DPP are reported as functions of screening parameters. The OS for S‐P transitions are also reported for various screening parameters. The OS and dynamic polarizability show interesting behavior with increasing screening strength and nuclear charge. © 2015 Wiley Periodicals, Inc.