Oscillation properties of nonlinear impulsive delay differential equations and applications to population models

AbstractComparison theorem and explicit sufficient conditions are obtained for oscillation and nonoscillation of solutions of nonlinear impulsive delay differential equations which can be utilized to population dynamic models. Our results in this paper generalize and improve several known results

Oscillation criteria for third-order neutral differential equations with continuously distributed delay

AbstractThe purpose of this paper is to study the oscillation of a certain class of third-order neutral differential equations with continuously distributed delay. By using a generalized Riccati transformation and integral averaging technique, we establish some new sufficient conditions which ensure that every solution of this equation oscillates or converges to zero

Oscillation Theorems for Second-Order Half-Linear Neutral Delay Dynamic Equations with Damping on Time Scales

We establish the oscillation criteria of Philos type for second-order half-linear neutral delay dynamic equations with damping on time scales by the generalized Riccati transformation and inequality technique. Our results are new even in the continuous and the discrete cases

New Oscillatory Behavior of Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

We establish four new oscillation criteria of Grace-type for the second-order nonlinear dynamic equations with damping. These criteria extend known criteria for corresponding dynamic equations. Our results are new even in the continuous and the discrete cases

On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of =ℝ and =ℤ

On the Oscillation for Second-Order Half-Linear Neutral Delay Dynamic Equations on Time Scales

We discuss oscillation criteria for second-order half-linear neutral delay dynamic equations on time scales by using the generalized Riccati transformation and the inequality technique. Under certain conditions, we establish four new oscillation criteria. Our results in this paper are new even for the cases of T = R and T = Z

New Oscillatory Behavior of Third-Order Nonlinear Delay Dynamic Equations on Time Scales

A class of third-order nonlinear delay dynamic equations on time scales is studied. By using the generalized Riccati transformation and the inequality technique, four new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially improve earlier ones. Some examples are considered to illustrate the main results

Observation of the 5p Rydberg states of sulfur difluoride radical by resonance-enhanced multiphoton ionization spectroscopy

Sulfur difluoride radicals in their ground state have been produced by a "laser-free" pulsed dc discharge of the SF$_{6}$/Ar gas mixtures in a supersonic molecular beam and detected by mass-selective resonance-enhanced multilphoton ionization (REMPI) spectroscopy in the wavelength range of 408 - 420 nm. Analyses of the (3 + 1) REMPI excitation spectrum have enabled identification of three hitherto unknown Rydberg states of this radical. Following the Rydberg state labeling in our previous work [see J. Phys. Chem. A 102, 7233 (1998)], these we label the K(5p$_{1}$) [$nu_{0-0}$ = 71 837 cm$^{-1}$, $omega_{1}^{'}$(a$_{1}$ sym str) = 915 cm$^{-1}$], L(5p$_{2}$) [$nu_{0-0}$ = 72 134 cm$^{-1}$, $omega_{1}^{'}$(a$_{1}$ sym str) = 912 cm$^{-1}$], and M(5p$_{3}$) [$nu_{0-0}$ = 72 336 cm$^{-1}$, $omega_{1}^{'}$(a$_{1}$ sym str) = 926 cm$^{-1}$] Rydberg states, respectively. [Origins, relative to the lowest vibrational level of the X$^{1}$A$_{1}$ ground state, and vibrational frequencies of the symmetric S-F stretching mode are suggested by the numbers in brackets.] Photofragmentation process of SF$_{2}$$^{+}$--SF$^{+}$ + F that relates to the REMPI spectrum was discussed.Comment: 17 pages, 1 table, 2 figure

Performance of several simple, noninvasive models for assessing significant liver fibrosis in patients with chronic hepatitis B

Aim To compare the performance of several simple, noninvasive models comprising various serum markers in diagnosing significant liver fibrosis in the same sample of patients with chronic hepatitis B (CHB) with the same judgment standard. Methods A total of 308 patients with CHB who had undergone liver biopsy, laboratory tests, and liver stiffness measurement (LSM) at the Southwest Hospital, Chongqing, China between March 2010 and April 2014 were retrospectively studied. Receiver operating characteristic (ROC) curves and area under ROC curves (AUROCs) were used to analyze the results of the models, which incorporated ageplatelet (PLT) index (API model), aspartate transaminase (AST) to alanine aminotransferase (ALT) ratio (AAR model), AST to PLT ratio index (APRI model), γ-glutamyl transpeptidase (GGT) to PLT ratio index (GPRI model), GGT-PLT-albumin index (S index model), age-AST-PLT-ALT index (FIB-4 model), and age-AST-PLT-ALT-international normalized ratio index (Fibro-Q model). Results The AUROCs of the S index, GPRI, FIB-4, APRI, API, Fibro-Q, AAR, and LSM for predicting significant liver fibrosis were 0.726 (P < 0.001), 0.726 (P < 0.001), 0.621 (P = 0.001), 0.619 (P = 0.001), 0.580 (P = 0.033), 0.569 (P = 0.066), 0.495 (P = 0.886), and 0.757 (P < 0.001), respectively. The S index and GPRI had the highest correlation with histopathological scores (r = 0.373, P < 0.001; r = 0.372, P < 0.001, respectively) and LSM values (r = 0.516, P < 0.001; r = 0.513, P < 0.001, respectively). When LSM was combined with S index and GPRI, the AUROCs were 0.753 (P < 0.001) and 0.746 (P < 0.001), respectively. Conclusion S index and GPRI had the best diagnostic performance for significant liver fibrosis and were robust predictors of significant liver fibrosis in patients with CHB for whom transient elastography was unavailable