Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Bright,dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

Nonlinear Dynamics - In this paper, a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave and a long-wave in fluid...     

Bifurcation analysis of the travelling waveform of FitzHugh-Nagumo nerve conduction model equation

The FitzHugh-Nagumo model for travelling wave type neuron excitation is studied in detail. Carrying out a linear stability analysis near the equilibrium point, we bring out various interesting bifurcations which the system admits when a specific Z(2) symmetry is present and when it is not. Based on a center manifold reduction and normal form analysis, the Hopf normal form is deduced. The condition for the onset of limit cycle oscillations is found to agree well with the numerical results. We further demonstrate numerically that the system admits a period doubling route to chaos both in the presence as well as in the absence of constant external stimuli. (c) 1997 American Institute of Physics.     

The crystal structure of a novel product from the acid-catalyzed condensation of 1-benzylindole with acetone

The acid-catalyzed condensation of 1-benzylindole with acetone in the presence of N-phenylmaleimide gave a tetrahydrocarbazole, (4,5,10,10b-tetrahydro-5-methyl-2-phenyl-10-(phenylmethyl)pyrrolo[3,4-a]carbazole-1,3[2H, 3aH]-dione (1), as the major product and a novel spiro compound, 1,3,4,4-tetrahydro-1,1,3,3-tetramethyl-4,4-bis(phenylmethyl)-1,3(2H, 2H)-spiro[cyclopent[b]indole] (2), as the minor product. The structure of the spiro compound was determined by an X-ray crystallographic determination. The acid-catalyzed condensation of 1-benzylindole with acetone in the absence of N-phenylmaleimide gave a bisindole, (1,1-bis(phenylmethyl)-3,3-(1-methylethylidene)diindole (3), as the major product and the spiro-compound as the minor product.     

Theoretical analysis of the enzyme reaction processes within the multiscale porous biocatalytic electrodes

Mathematical model describing the oxidation of glucose in a multiscale porous biocatalytic electrode is discussed. The model considers herein is composed of two nonlinear differential equations accounting for reaction and diffusion within the hydrogel film. In this letter, approximate analytical expressions for the concentration of mediator, substrate and current have been obtained using the Adomian decomposition method (ADM). Furthermore, a comparison confirmed that our analytical result fitted very well with the numerical solution (Matlab). Sensitivity analysis of the parameters is also reported.     

Differential effects of hexaconazole and paclobutrazol on biomass, electrolyte leakage, lipid peroxidation and antioxidant potential of Daucus carota L

The application of triazole fungicides is a common practice in the cultivation of carrot (Daucus carota L.) plants. It is there for seems important to test the changes that are occurring in this food crop under triazoles, the non-traditional plant growth regulators, treatments in order to identify the extent to which it tolerate the fungicide application and thereby make it an economical food crop. A field experiment was conducted to find out the effects of two triazole fungicides (hexaconazole (HEX) and paclobutrazol (PBZ) at 20 mg l⁻¹ plant⁻¹) on the biomass, yield, electrolyte leakage, lipid peroxidation and antioxidant potential of carrot. The treatments were given to plants on 15, 30 and 45 days after sowing (DAS). The plants were uprooted for analyses of growth and biochemical parameters on 60 DAS. It was found that both HEX and PBZ have significant effects on the growth and biochemical parameters of this plant. Among the triazoles used, PBZ performed best in terms of anthocyanin, protein, amino acid, proline, starch and sugar, contents whereas HEX enhanced carotenoids, fresh weight, dry weight and biomass. There was no significant variation in chlorophyll (‘a’ and ‘b’) contents between the two triazole treated plants, but HEX and PBZ proved best when compared to untreated control plants. HEX and PBZ increased - and β-amylases enzymes activities to a significant level. Out of these two triazoles, PBZ performed best in increasing the starch hydrolyzing enzymes activities. The non-enzymatic antioxidant, reduced glutathione (GSH) and antioxidant enzyme ascorbate peroxidase (APX) were increased under fungicide applications. The data suggests that, the application of triazole fungicides may be a useful tool to increase the tuber quality as well as quantity in carrot plants, apart from their fungicidal properties.     

Growth, biochemical modifications and proline metabolism in Helianthus annuus L. as induced by drought stress

In the present investigation, two watering treatments, viz., 100% and 60% field capacity (FC) were used to understand the effects of water deficit on early growth, biomass allocation, pigment and biochemical constituents and proline metabolism of five varieties of Sunflower (Helianthus annuus L.) plants. We found that there was a significant difference in early growth, dry matter accumulation, pigment, biochemical constituents and proline metabolism among the five varieties. The root length, shoot length, total leaf area, fresh and dry weight, chlorophyll a, b, total chlorophyll and carotenoid were significantly reduced under water stress treatments. Water stress increased the proline, free amino acid and glycinebetaine contents along with increased activity of γ-glutamyl kinase but the activity of proline oxidase reduced as a consequence of water stress.     

Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing,defocusing and mixed type nonlinearities

Bright and bright-dark type multisoliton solutions of the integrable N-coupled nonlinear Schrödinger (CNLS) equations with focusing, defocusing and mixed type nonlinearities are obtained by using Hirota’s bilinearization method. Particularly, for the bright soliton case, we present the Gram type determinant form of the n-soliton solution (n:arbitrary) for both focusing and mixed type nonlinearities and explicitly prove that the determinant form indeed satisfies the corresponding bilinear equations. Based on this, we also write down the multisoliton form for the mixed (bright-dark) type solitons. For the focusing and mixed type nonlinearities with vanishing boundary conditions the pure bright solitons exhibit different kinds of nontrivial shape changing/energy sharing collisions characterized by intensity redistribution, amplitude dependent phase-shift and change in relative separation distances. Due to nonvanishing boundary conditions the mixed N-CNLS system can admit coupled bright-dark solitons. Here we show that the bright solitons exhibit nontrivial energy sharing collision only if they are spread up in two or more components, while the dark solitons appearing in the remaining components undergo mere standard elastic collisions. Energy sharing collisions lead to exciting applications such as collision based optical computing and soliton amplification. Finally, we briefly discuss the energy sharing collision properties of the solitons of the (2+1) dimensional long wave-short wave resonance interaction (LSRI) system.     

Spin-transfer torque induced reversal in magnetic domains

Using the complex stereographic variable representation for the macrospin, from a study of the nonlinear dynamics underlying the generalized Landau–Lifshitz (LL) equation with Gilbert damping, we show that the spin-transfer torque is effectively equivalent to an applied magnetic field. We study the macrospin switching on a Stoner particle due to spin-transfer torque on application of a spin-polarized current. We find that the switching due to spin-transfer torque is a more effective alternative to switching by an applied external field in the presence of damping. We demonstrate numerically that a spin-polarized current in the form of a short pulse can be effectively employed to achieve the desired macrospin switching.