In this work, we investigate the oscillation criteria for second order neutral delay differential equations of the form (r(t)[y(t)+ p(t)y(δ (t))]′)′ +q(t)G(y(τ(t))) = 0 and (r(t)[[y(t)+ p(t)y(δ (t))]′]α )′ +q(t)(yβ (τ(t))) = 0, where α and β are the ratio of odd positive integers. Mathematics subject classification (2010): 34C10, 34C15.

We present new oscillation criteria for the second order nonlinear damped delay dynamic equation (r(t)(x(t))) + p(t)(x(t)) + q(t)f (x(τ(t))) = 0. Our results generalize and improve some known results for oscillation of second order nonlinear delay dynamic equation. Our results are illustrated with examples.

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ( φp(x ′(t)) )′′ = g ( t, ∫ 0 −τ x(t+ s) dα(s) ) + e(t), some criteria to guarantee the existence of periodic solutions are obtained. Keywords—p–Laplacian, Distributed delay, Periodic solution, Mawhin’s continuation theorem

In [1], the author studied the oscillation of forced neutral delay differential equations with positive and negative coefficients, having the following form: [x(t)− R(t)x(t − r)] + P(t)x(t − τ)− Q(t)x(t − σ) = f (t), (1) where R, P, Q ∈ C([t0,∞),R) with r > 0, τ ≥ σ ≥ 0. The readers are referred to [1] for further details. The author uses an ill representation which yields a mistake. To avoid t...

Balance control models are used to describe balance behavior in health and disease. We identified the unique contribution and relative importance of each parameter of a commonly used balance control model, the Independent Channel (IC) model, to identify which parameters are crucial to describe balance behavior. The balance behavior was expressed by transfer functions (TFs), representing the rel...

The linear relationship of the original grey prediction model is too single, and does not consider time delay effect current input parameters on output parameters. In order to solve these problems, interval number sequence taken as modelling model, nonlinear parameter γ time-delay τ are introduced into multivariate so construct multivariable for number. view uncertain characteristics smog index...

In the analysis of chaotic time series, a standard technique is to reconstruct an image of the original dynamical system using delay coordinates. If the original dynamical system has an attractor, then the correlation dimension D2 of its image in the reconstruction can be estimated using the Grassberger–Procaccia algorithm. The quality of the reconstruction can be probed by measuring the length...

In the last 35 years the characterization of tumor growth using Gompertizian models has led to new understandings of the spread of tumor cells, and enabled researchers to develop novel therapeutic strategies to eradicate disease in some cases [2, 32, 35, 40]. A long standing assertion is that the Gompertizian framework doesn’t allow characterizations of complex biological and clinical phenomena...

In this report, a parameter extraction procedure and a model presented in [4] are tested using a 280×0.25μm transistor manufactured in a 0.25 μmCMOS process. The extraction procedure is based on two sets of S-parameter measurements. The first transistor measurement is in the linear region, to obtain the extrinsic terminal resistances which are biasindependent . The intrinsic parameters of the t...

In this paper, we are concerned with the following problem  autt(x, t)− duxx(x, t) + βθx(x, t) = 0, in (0, L)× (0,∞) bθt(x, t)− k1θxx(x, t)− ∫ τ 2 τ 1 k2(s)θxx(x, t− s)ds+ βuxt(x, t) = 0, in (0, L)× (0,∞) u(x, 0) = u0(x), ut(x, 0) = u1(x), θ(x, 0) = θ0(x), x ∈ (0, L) θx(x,−t) = f0(x, t), x ∈ (0, L), t ∈ (0, τ 2), (1.1) a thermoelastic system with a distributed delay associated with initi...