PURPOSE This study was aimed to experimentally and numerically investigate the feasibility of measuring cerebral white matter perfusion using pseudocontinuous arterial spin labeling (PCASL) 3T magnetic resonance imaging (MRI) at a relatively fine resolution to mitigate partial volume effect from gray matter. MATERIALS AND METHODS The Institutional Research Ethics Committee approved this study...

In this note, we examine the oscillatory nature for the fourth-order nonlinear delay dynamic equation (r(t)x 3 (t)) + p(t)x(τ(t)) = 0 on a time scale T unbounded above. Some oscillation criteria are obtained for the cases when ∫ ∞

By means of the Krasnoselskii fixed piont theorem, periodic solutions are found for a neutral type delay differential system of the form x (t) + cx (t− τ) = A (t, x(t)) x (t) + f (t, x (t− r1 (t)) , . . . , x (t− rk (t))) .

and Applied Analysis 3 the synaptic connection weight of the unit j on the unit i at time t; constant bij denotes the synaptic connection weight of the unit j on the unit i at time t − τ t ; Ii is the input of the unit i; τ t is the transmission delay such that 0 < τ t ≤ τ and τ̇ t ≤ ρ < 1, t ≥ t0; τ , ρ are constants. The initial conditions associated with system 2.1 are of the form x s φ s , s...

and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...

We present and analyze deterministic complex networks of pulse-coupled oscillators that exhibits recurrent events comprised of an increase and a decline in synchrony. Events emerging from the networks may form an oscillatory behavior or may be separated by periods of asynchrony with varying duration. The phenomenon is specific to spatial networks with both shortand longranged connections and re...

and Applied Analysis 3 2. Stability of the Equilibrium and Local Hopf Bifurcations Throughout this paper, we assume that the following condition H1 ce−dτ > d , a2 ce−dτ − d > b2d holds. The hypothesis H1 implies that system 1.1 has a unique positive equilibrium E∗ x∗, y∗ , where x∗ √ d ce−dτ − d , y ∗ a − bx∗ 1 x∗2 cx∗ . 2.1 The linearized system of 1.1 around E∗ x∗, y∗ takes the form dx t dt a...

Huang, Yu and Dai in [4], [5] presented conditions when every solution of discrete difference equation xn−xn−1 = −F (xn)+F (xn−k) is bounded and tends to a constant, where k ∈ N, F is a continuous, increasing real function. Similar problems for differential equation x′(t) = β(t)[x(t)−x(t− τ(t))], where τ and β are positive continuous real functions, was investigated in papers by Atkinson and Ha...