In this paper, we study the behavior of solutions of second order delay differential equation y′′(t)= p1y′(t)+ p2y′(t − τ )+ q1y(t)+ q2y(t − τ ), where p1, p2, q1, q2 are real numbers, τ is positive real number. A basic theorem on the behavior of solutions is established. As a consequence of this theorem, a stability criterion is obtained. © 2006 Elsevier Inc. All rights reserved.

We study the distribution function P(ω) of the random variable ω=τ(1)/(τ(1)+···+τ(N)), where τ(k)'s are the partial Wigner delay times for chaotic scattering in a disordered system with N independent, statistically equivalent channels. In this case, τ(k)'s are independent and identically distributed random variables with a distribution Ψ(τ) characterized by a "fat" power-law intermediate tail ~...

In [1], the authors study the stability of the delay dynamic equation x (t)+ p (t) x (t − τ (t)) = 0 for all t ∈ T, (1) where T (i.e., a nonempty subset of reals) is a time scale and p ∈ Crd ( T,R ) . The statements of their theorems and representations include some mistakes as follows: τ : T → (0, r] and t ∈ T with t − τ (t) ≥ minT, which implies t − τ (t) ∈ T. The forward jump operator σ (t) ...

We have systematically investigated the low-temperature electron dephasing times τ φ in more than 40 three-dimensional polycrystalline impure metals with distinct material characteristics. In all cases, a saturation of the dephasing time is observed below about a (few) degree(s) Kelvin, depending on samples. The value of the saturated dephasing time τ 0 [≡ τ φ (T → 0 K)] falls basically in the ...

1. Introduction Ultra high-speed data transmission capability will be required in the next generation wireless communication systems in a severe frequency-selective fading channel [1]. In a mobile radio channel, the transmitted signal is reflected and diffracted by many obstacles and is received as a multipath signal with different time delays at a receiver, thus creating the frequency-selectiv...

Compared with a two-dimensional (2D) homogeneous channel, the introduction of 2D/2D homojunction or heterojunction is promising method to improve performance tunnel field-effect transistor (TFET), mainly by controlling tunneling barrier. We simulate 10-nm-Lg double-gated GeSe TFETs and van der Waals (vdW) GeSe/GeTe based on ballistic quasi-static ab initio quantum transport simulation. Two devi...

We use Krasnoselskii’s fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the neutral delay difference equation x(n+ 1) = a(n)x(n) + c∆x(n− τ) + g(n, x(n− τ)). AMS Subject Classifications: 39A10, 39A12.

Autoignition of iso-octane was examined using a rapid compression facility (RCF) with iso-octane, oxygen, nitrogen, and argon mixtures. The effects of typical homogeneous charge compression ignition (HCCI) conditions on the iso-octane ignition characteristics were studied. Experimental results for ignition delay times, τ ign, were obtained from pressure time-histories. The experiments were cond...

Occurrence of bi- and trirhythmicities (coexistence of two or three stable limit cycles, respectively, with distinctly different periods) has been studied experimentally by applying delayed feedback control to the copper-phosphoric acid electrochemical system oscillating close to a Hopf bifurcation point under potentiostatic condition. The oscillating electrode potential is delayed by τ and the...

In this study, we introduce a new method for investigation of the delay difference equation ∆αx(t) + p(t)x(t− τ) = 0 for t ∈ [t0,∞) , where p ∈ C ( [t0,∞) ,R ) , α, τ ∈ R and ∆α denotes the forward difference operator defined as ∆αx(t) = x(t+ α)− x(t). AMS Subject Classifications: 39A10.