and Applied Analysis 3 we describe a behavior of solutions of the following problem the delay differential inequality with an initial condition ε1 ≤ y′ t − λy t − τ ≤ ε2, t ≥ 0, 1.5 ξ1 t ≤ y t − y 0 ≤ ξ2 t , −τ ≤ t ≤ 0, 1.6 and compare them with solutions of the delay equation 1.4 that are constant on the interval −τ, 0 and therefore have quite simple forms . Functions satisfying those two ineq...

Exact numerical schemes have previously been obtained for some linear retarded delay differential equations and systems. Those were derived from explicit expressions of the exact solutions, expressed in form perturbed difference systems, involving values at previous intervals. In this work, we propose to directly obtain same type fundamental solutions equations, by considering vector with compo...

the performance of nanoscale field effect diodes as a function of the spacer length between two gates is investigated. our numerical results show that the ion/ioff ratio which is a significant parameter in digital application can be varied from 101 to 104 for s-fed as the spacer length between two gates increases whereas this ratio is approximately constant for m-fed. the high-frequency perform...

Transistor designs based on using mixed -L valleys for electron transport are proposed to overcome the density of states bottleneck while maintaining high injection velocities. Using a self-consistent top-of-the-barrier transport model, improved current density over Si is demonstrated in GaAs/AlAsSb, GaSb/AlAsSb, and Ge-on-insulator-based singlegate thin-body n-channel metal–oxide–semiconductor...

Effect of time delay (τ) on intracellular calcium dynamics with non-Gaussian noises in transmission processes of intracellular Ca(2+) is studied by means of second-order stochastic Runge-Kutta type algorithm. By simulating and analyzing time series, normalized autocorrelation function, and characteristic correlation time of cytosolic and calcium store's Ca(2+) concentration, the results exhibit...

Abstract: In this paper, we consider the stabilization problem of 1-d wave equation with input delay. Suppose that the wave system is fixed at one end whereas a control force is applied at other end. Here we consider the control force of the form αu(t) + βu(t − τ) where τ is the time delay. In this paper we find a feedback control law that stabilizes exponentially the system for any |α| ̸= |β| a...

This paper is concerned with the oscillatory behavior of first-order delay differential equations of the form x′(t) + p(t)x(τ(t)) = 0, t ≥ t0, (1) where p, τ ∈ C([t0,∞),R),R = [0,∞), τ(t) is non-decreasing, τ(t) < t for t ≥ t0 and limt→∞ τ(t) =∞. Let the numbers k and L be defined by

The quality of attractor reconstruction using the method of delays is known to be sensitive to the delay parameter, τ . Here we develop a new, computationally efficient approach to choosing τ that quantifies reconstruction expansion from the identity line of the embedding space. We show that reconstruction expansion is related to the concept of reconstruction signal strength and that increased ...

In this article, stability and asymptotic properties of solutions of a real two-dimensional system x′(t) = A(t)x(t)+B(t)x(τ(t))+h(t, x(t), x(τ(t))) are studied, where A, B are matrix functions, h is a vector function and τ(t) ≤ t is a nonconstant delay which is absolutely continuous and satisfies lim t→∞ τ(t) = ∞. Generalization of results on stability of a two-dimensional differential system w...

We establish criteria for the existence of positive solutions to the three-point boundary-value problems expressed by second-order functional delay differential equations of the form −x′′(t) = f(t, x(t), x(t− τ), xt), 0 < t < 1, x0 = φ, x(1) = x(η), where φ ∈ C[−τ, 0], 0 < τ < 1/4, and τ < η < 1.