Mathematical modelling of steady-state concentration in immobilized glucose isomerase of packed-bed reactors

The theoretical model of the steady-state immobilized enzyme electrodes is discussed. This model is based on diffusion equation containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. Homotopy perturbation method (HPM) is employed to solve the non-linear diffusion equation for the steady-state condition. Simple and approximate polynomial expression of concentration and flux are derived for all small values of parameters ${\phi_p}$ (Theiele modulus) and β (kinetic parameter). Furthermore, in this work the numerical solution of the problem is also reported using SCILAB/MATLAB program. The analytical results are compared with the numerical results and found to be in good agreement.     

Branch-and-bound algorithms for scheduling in permutation flowshops to minimize the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted flowtime,weighted tardiness and weighted earliness of jobs

The problem of scheduling in permutation flowshops is considered in this paper with the objectives of minimizing the sum of weighted flowtime/sum of weighted tardiness/sum of weighted flowtime and weighted tardiness/sum of weighted flowtime, weighted tardiness and weighted earliness of jobs, with each objective considered separately. Lower bounds on the given objective (corresponding to a node generated in the scheduling tree) are developed by solving an assignment problem. Branch-and-bound algorithms are developed to obtain the best permutation sequence in each case. Our algorithm incorporates a job-based lower bound (integrated with machine-based bounds) with respect to the weighted flowtime/weighted tardiness/weighted flowtime and weighted tardiness, and a machine-based lower bound with respect to the weighted earliness of jobs. The proposed algorithms are evaluated by solving many randomly generated problems of different problem sizes. The results of an extensive computational investigation for various problem sizes are presented. In addition, one of the proposed branch-and-bound algorithms is compared with a related existing branch-and-bound algorithm.     

Chimeras in random non-complete networks of phase oscillators

We consider the simplest network of coupled non-identical phase oscillators capable of displaying a "chimera" state (namely, two subnetworks with strong coupling within the subnetworks and weaker coupling between them) and systematically investigate the effects of gradually removing connections within the network, in a random but systematically specified way. We average over ensembles of networks with the same random connectivity but different intrinsic oscillator frequencies and derive ordinary differential equations (ODEs), whose fixed points describe a typical chimera state in a representative network of phase oscillators. Following these fixed points as parameters are varied we find that chimera states are quite sensitive to such random removals of connections, and that oscillations of chimera states can be either created or suppressed in apparent bifurcation points, depending on exactly how the connections are gradually removed.     

Transport, structural and thermal studies on nanocomposite polymer blend electrolytes for Li-ion battery applications

Nanocomposite polymer electrolytes (NCPEs) composed of poly(vinylidenefluoride-co-hexafluoropropylene) (PVdF-co-HFP) as a host polymer, Poly(vinyl acetate) (PVAc) as an additive, Ethylene Carbonate (EC) as a plasticizer, Lithium Perchlorate as dopant salt and Barium Titanate (BaTiO₃) as a filler were prepared for various concentrations of BaTiO₃ using solvent casting technique. Thermal stability of the sample having maximum ionic conductivity was found using TG/DTA analysis. Nano composite polymer electrolytes were subjected to ac impedance analysis spectra for acquiring the ionic conductivity values at different temperature. Surface structure of the sample was analysed using scanning electron microscope and the complexations of samples were analysed using X-ray diffraction analysis. It was noted that the polymer electrolyte contains 8 wt. % of BaTiO₃ showed maximum ionic conductivity than the other ratios of BaTiO₃.     

Search for conditions of compressive fracture of hard brittle ceramics at impact loading

In this paper we discuss three different experimental configurations to diagnosing the modes of inelastic deformation and to evaluating the failure thresholds at shock compression of hard brittle solids. One of the manifestations of brittle material response is the failure wave phenomenon, which has been previously observed in shock-compressed glasses. However, based on the measurements from our “theory critical” experiments, both alumina and boron carbide did not exhibit this phenomenon. In experiments with free and pre-stressed ceramics, while the Hugoniot elastic limit (HEL) in high-density B₄C ceramic was found to be very sensitive to the transverse stress, it was found relatively less sensitive in Al₂O₃, implying brittle response of the boron carbide and ductile behavior of alumina. To further investigate the effects of stress states on the shock response of brittle materials, a “divergent flow or spherical shock wave” based plate impact experimental technique was employed to vary the ratio of longitudinal and transversal stresses and to probe conditions for compressive fracture thresholds. Two different experimental approaches were considered to generate both longitudinal and shear waves in the target through the impact of convex flyer plates. In the ceramic target plates, the shear wave separates a region of highly divergent flow behind the decaying spherical longitudinal shock wave and a region of low-divergent flow. Experiments with divergent shock loading of alumina and boron carbide ceramic plates coupled with computer simulations demonstrated the validity of these experimental approaches to develop a better understanding of fracture phenomena.     

Hyers-Ulam stability of an iterative equation for strictly increasing continuous functions

Aequationes mathematicae - The Hyers-Ulam stability of the iterative equation $$f^n=F$$ for continuous functions F was studied under the assumptions that F is a homeomorphism on its range, and the...     

Crystal Structure of Dimeric Cu(II) Complex {μ,μ'‐acetato O,O bis [N‐salicylidene‐2‐amino‐pyridine‐methanolato N,N,O]} : perchlorate

The crystal structure of the title complex has been solved using X‐ray diffraction data.The compound crystallizes from aqueous ethanol solvent in the triclinic system, space group P‐1, with unit cell parameters: a = 8.9532(1), b = 12.7423(3), c = 14.9012(3) Å, α = 73.767(1), β = 75.322(1), γ = 77.496(1)°, Z = 2, V = 1559.4(5) ų. The trial structure was determined by automated Patterson methods and subsequent difference Fourier techniques using DIRDIF98 and refined to a final R‐factor of 0.064. The copper ion Cu1 adopts a (4+1) square‐pyramidal geometry defined by the tridentate N‐salicylidimine dianions and the neutral monodentate pyridine ligand in the basal plane. The apical position is occupied by a solvent methanol molecule at a distance of 2.341(4) Å. The copper Cu2 adopts a square‐planar geometry.