In our repertoire studies of varicella zoster virus-specific T cells, we used very stringent computational criteria to keep contamination with T cell receptor sequences from bystander-activated T cells to a minimum.

We develop eigenvalue criteria under which the solutions of a “slowly” time varying linear dynamic system of the form x (t)=A(t)x(t) are unstable. © 2006 Elsevier Inc. All rights reserved.

Some new criteria for the oscillation of solutions of the second-order half-linear dynamic equation ( a ( xΔ )α)Δ (t)+q(t)xα (t) = 0 are established when ∫ ∞ a−1/α(s)Δs = ∞ .

Our aim in this paper is to present criteria for oscillation of the nonlinear differential equation u′′(t) + p(t)f `

Some oscillation criteria are established for the second order nonlinear neutral differential equations of the form ((x(t) + ax(t− τ1)− bx(t+ τ2)) ) ′′ = q(t)x(t− σ1) + p(t)x (t+ σ2), and (x(t) − ax(t− τ1) + bx(t+ τ2) )′′ = q(t)x(t− σ1) + p(t)x (t+ σ2) where α and β are the ratios of odd positive integers with β ≥ 1. Examples are provided to illustrate the main results.

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.

New oscillation criteria for the second order nonlinear neutral delay differential equation [y(t) + p(t)y(t− τ)]′′ + q(t) f(y(g(t))) = 0, t ≥ t0 are given. The relevance of our theorems becomes clear due to a carefully selected example.

Some new criteria for the oscillation of advanced functional differential equations of the form d dt ([ 1 an−1(t) d dt 1 an−2(t) d dt · · · 1 a1(t) d dt x(t) ]α) + δ q(t)f(x[g(t)]) = 0 are presented in this paper. A discussion of neutral equations will also be included.

Some new criteria for the oscillation of the fourth order functional differential equation d dt ( 1 a3(t) ( d dt 1 a2(t) ( d dt 1 a1(t) ( d dt x(t) )α1)α2)α3) + δq(t) f (x[g(t)]) = 0, where δ = ±1 are established. c © 2006 Elsevier Ltd. All rights reserved.

This paper is concerned with the oscillation of second-order nonlinear neutral differential equations of the form [ r(t)[(x(t) + p(t)x(σ(t)))′]γ ]′ + f(t, x(τ(t))) = 0, by using a generalized Riccati’s technique and integral averaging technique, we establish new oscillation results which handle some cases not covered by known criteria.