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 ∫ ∞

UNLABELLED The Catalan Agency for Health Technology Assessment and Research (AETIM) proposed, in 2001, criteria for performing a bone densitometry (BD) for use in the consultations of the public health system. OBJECTIVE To determine the sensitivity, specificity, positive predictive value and negative predictive value of the criteria to indicate BD. MATERIAL AND METHODS Five groups of volunt...

This paper concerns the oscillation of solutions to the differential equation ` r(t)x′(t) ́′ + p(t)x′(t) + q(t)g(x(t)) = 0, where xg(x) > 0 for all x 6= 0, r(t) > 0 for t ≥ t0 > 0. No sign conditions are imposed on p(t) and q(t). Our results solve the open problem posed by Rogovchenko [27], complement the results in Sun [29], and improve a number of existing oscillation criteria. Our main resul...

kand t-optimality algorithms [9, 6] provide solutions to DCOPs that are optimal in regions characterized by its size and distance respectively. Moreover, they provide quality guarantees on their solutions. Here we generalise the kand t-optimal framework to introduce C-optimality, a flexible framework that provides reward-independent quality guarantees for optima in regions characterised by any ...

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.

In this paper, interval oscillation criteria are established for second order forced impulsive differential equations with mixed nonlinearities of the form ⎧⎪⎨ ⎪⎩ ( r(t)Φα(x′(t)) )′ + p(t)Φα(x′(t))+q(t)Φα(x(t))+ n ∑ i=1 qi(t)Φβi (x(t)) = e(t), t = τk, x(τk) = akx(τk), x′(τk+) = bkx′(τk), k = 1,2, . . . . The results obtained in this paper extend some of the existing results and are illustrated ...

BACKGROUND Colorectal cancers (CRCs) with microsatellite instability (MSI) are associated with a good prognosis and a high density of tumor-infiltrating lymphocytes (TILs). We have undertaken to determine the link between TIL densities and MSI CRC histologic features. PATIENTS AND METHODS Using tissue microarrays, T-cell sub-population infiltration, including T cells (CD3), cytotoxic T cells ...

We offer criteria for the existence of positive solutions for two-point right focal eigenvalue problems (−1) n−p y Δ n (t) = λ f (t, y(σ n−1 (t)), y Δ (σ n−2 (t)),..., y Δ p−1 (σ n−p (t))), t ∈ [0,1] ∩ T, y Δ i (0) = 0, 0 ≤ i ≤ p − 1, y Δ i (σ(1)) = 0, p ≤ i ≤ n − 1, where λ > 0, n ≥ 2,1 ≤ p ≤ n − 1 are fixed and T is a time scale.

We present new oscillation criteria for the second order nonlinear neutral delay differential equation ( a (t) (y (t)+ p (t) y (t − τ))′)′ + q (t) |y (σ (t))|α−1 y (σ (t)) = 0, where t ≥ t0, τ, and α are positive constants and the functions p, q, a, σ ∈ C ([t0,∞) ,R) . Our results generalize and improve some known results for oscillation of second order neutral delay differential equations. Our...