This paper is concerned with oscillation of the second-order halflinear delay dynamic equation (r(t)(x)) + p(t)x(τ(t)) = 0, on a time scale T, where γ ≥ 1 is the quotient of odd positive integers, p(t), and τ : T → T are positive rd-continuous functions on T, r(t) is positive and (delta) differentiable, τ(t) ≤ t, and limt→∞ τ(t) = ∞. We establish some new sufficient conditions which ensure that...

We investigate analytically and numerically the statistical properties of a random walk model with delayed transition probability dependence (delayed random walk). The characteristic feature of such a model is the oscillatory behavior of its correlation function. We investigate a model whose transient and stationary oscillatory behavior is analytically tractable. The correspondence of the model...

We propose a new method for constructing exact solutions to nonlinear delay reaction–diffusion equations of the form ut = kuxx + F (u,w), where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = ∑N n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or fun...

We describe a modification of receptor theory for the estimation of observed affinities (K(obs)) and relative efficacies of orthosteric ligands in functional assays that exhibit constitutive activity. Our theory includes parameters for the fractions of the occupied receptor population in the active (intrinsic efficacy, ε) and inactive (ε(i)) states and analogous parameters for the fractions of ...

In this paper, we introduce an innovative and systematic technique to study delay differential equations via polynomials. First, we review an intrinsic relation between delay differential equations and polynomials. From this relation, we obtain long time behaviors of the solutions to delay differential equations via asymptotic analysis of the corresponding polynomials. Moreover, we derive asymp...

The Photoexcited carrier lifetime (τ) and peak to valley transmission difference (ΔTp-v) in direct and indirect band gap crystals has been investigated by the use of single beam open and closed aperture z-scan technique using frequency doubled Nd:YAG laser. The peak to valley transmission difference (ΔTp-v) is found to be of the order of 10-2 in case of direct band gap crystals and of the order...

In this paper we stochastically perturb the delay Lotka–Volterra model ẋ(t)= diag(x1(t), . . . , xn(t))[A(x(t)− x̄)+B(x(t − τ )− x̄)] into the stochastic delay differential equation (SDDE) dx(t)= diag(x1(t), . . . , xn(t)){[A(x(t)− x̄)+B(x(t − τ )− x̄)]dt + σ (x(t)− x̄)dw(t)}. The main aim is to reveal the effects of environmental noise on the delay Lotka–Volterra model. Our results can essentially ...

We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut = νuxx − uux + u+ h(x), 0 < x < 2π, t > 0, u(0, t) = u(2π, t), u(x,0) = u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady state solution and global stabil...