The discrete dynamics of nonlinear infinite-delay-differential equations

AbstractThis paper deals with numerical stability of nonlinear infinite-delay systems of the form y′(t) = ƒ(t,y(t),y(pt)) (p ∈ (0, 1), t > 0). Recently, linear stability properties of some numerical methods for infinite delay systems have been studied by several authors (cf. [1–9]). However, few results have been devoted to the nonlinear case. This paper considers global and asymptotic stability of one-leg θ-methods for the above nonlinear systems. Some stability criteria are obtained

Effect of Earth-Moon's gravity on TianQin's range acceleration noise. II. Impact of orbit selection

The paper is a sequel to our previous work (Zhang et al. Phys. Rev. D 103, 062001 (2021)). For proposed geocentric space-based gravitational wave detectors such as TianQin, gLISA, and GADFLI, the gravity-field disturbances, i.e., the so called ``orbital noise'', from the Earth-Moon system on the sensitive intersatellite laser interferometric measurements should be carefully evaluated and taken into account in the concept studies. Based on TianQin, we investigate how the effect, in terms of frequency spectra, varies with different choices of orbital orientations and radii through single-variable studies, and present the corresponding roll-off frequencies that may set the lower bounds of the targeted detection bands. The results, including the special cases of geostationary orbits (gLISA/GADFLI) and repeat orbits, can provide a useful input to orbit and constellation design for future geocentric missions.Comment: 8 pages, 9 figure

Metformin exerts renoprotective effect by reducing proteinuria in spontaneously-hypertensive rats

Purpose: To study the mechanism involved in metformin (DMBG)-induced reduction of albuminuria in spontaneously-hypertensive rats (SHRs). Methods: The SHRs were divided into DMBG SHR group (n = 30) given DMBG (300 mg/kg) and NC SHR group (n = 10) given distilled water (2 ml/day), while Wistar-Kyoto rats (WKY) rats were divided into DMBG WKY group (n = 30) given DMBG (300 mg/kg ) and NC WKY group (n = 10) administered distilled water (2 ml/day). Urinary protein levels were measured and compared. Inflammatory infiltration in renal tissue, and expression of vascular endothelial growth factor (VEGF) were assessed. Abdominal aortic blood was used to measure serum levels of creatinine and blood urea nitrogen (BUN). Results: Urinary protein was markedly elevated in SHRs, while BUN in SHRs was lowered, relative to WKY rats (p < 0.05). Moreover, inflammatory cell population was lower in DMBG SHRs group than in WKY rats (p < 0.05). Kidney expressions of VEGF in SHR and WKY rats treated with metformin  were significantly reduced, relative to those in untreated rats, but VEGF-A in DMBG SHR rats was markedly elevated, relative to NC SHR group, and was also raised in DMBG WKY, when compared with NC WKY rats (p < 0.05). Conclusion: Metformin reduces albuminemia in spontaneously hypertensive rats by up-regulating VEGF expression, thereby exerting renoprotective effect. This finding provides ideas for research and development of other therapeutic approaches. Keywords: Metformin, Spontaneous hypertension, Renoprotective, Albuminuria, Kidney, Vascular endothelial growth factor (VEGF

Effect of solar free oscillations on TianQin's range acceleration noise

TianQin is a proposed space-based gravitational-wave detector mission to be deployed and operated in high Earth orbits. As a sequel to [Zhang et al. Phys. Rev. D 103, 062001 (2021)], we investigate a type of ``orbital noise'' in TianQin's range acceleration that is caused by gravitational perturbation associated with solar free oscillations. Frequencies of such oscillations are typically within TianQin's measurement band of 0.1 mHz--1 Hz, and the disturbance level needs careful assessment. By using high-precision orbit propagation and adding the Sun's time-variable oblateness $J_2$ to detailed gravity-field models, we examine the effect in the frequency domain and show that the solar free oscillation noise is expected to be two orders of magnitude lower than the noise requirement on single links and hence has little impact on the mission.Comment: 10 pages, 5 figure