The preview control of a class of linear systems and its application in the fault-tolerant control theory

In the fault-tolerant control theory based on model following control, the desired signal of the control system is the output of a reference system. This paper is concerned with the design of the preview controller for a class of fault system

Scattering of the three-dimensional cubic nonlinear Schrödinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schrödinger equation (NLS) with partial harmonic potential \begin{equation} \left\{\begin{array}{l} i\partial_tu + \left(\Delta_{\mathbb{R}^3}-x^2\right)u = |u|^2u, \\ u|_{t=0} = u_0 \\ \end{array}\right. \tag{NLS} \end{equation} Out main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approxmate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson [29, 31, 32] in his study of scattering for the mass-critical nonlinear Schrödinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle [61,62] applies

Scattering of the three-dimensional cubic nonlinear Schr\"odinger equation with partial harmonic potentials

In this paper, we consider the following three dimensional defocusing cubic nonlinear Schr\"odinger equation (NLS) with partial harmonic potential \begin{equation*}\tag{NLS} i\partial_t u + \left(\Delta_{\mathbb{R}^3 }-x^2 \right) u = |u|^2 u, \quad u|_{t=0} = u_0. \end{equation*} Our main result shows that the solution $u$ scatters for any given initial data $u_0$ with finite mass and energy. The main new ingredient in our approach is to approximate (NLS) in the large-scale case by a relevant dispersive continuous resonant (DCR) system. The proof of global well-posedness and scattering of the new (DCR) system is greatly inspired by the fundamental works of Dodson \cite{D3,D1,D2} in his study of scattering for the mass-critical nonlinear Schr\"odinger equation. The analysis of (DCR) system allows us to utilize the additional regularity of the smooth nonlinear profile so that the celebrated concentration-compactness/rigidity argument of Kenig and Merle applies.Comment: 71 page

Procedural modeling of water caustics and foamy water for cartoon animation

We propose a method for procedural modeling and animation of cartoon water effects such as water caustics and foamy water. In our method we emulate the visual abstraction of these cartoon effects by the use of Voronoi diagrams and the motion abstraction by designing relevant controlling mechanisms corresponding to each effect. Our system enables the creation of cartoon effects with minimal intervention from the animator. Through high-level initial specification, the effects are animated procedurally in the style of hand-drawn cartoons. © 2010 IEEE

Effect of Tumor Necrosis Factor-α on Neutralization of Ventricular Fibrillation in Rats with Acute Myocardial Infarction

The purpose of this study was to explore the effects of tumor necrosis factor-α (TNF-α) on ventricular fibrillation (VF) in rats with acute myocardial infarction (AMI). Rats were randomly classified into AMI group, sham operation group and recombinant human tumor necrosis factor receptor:Fc fusion protein (rhTNFR:Fc) group. Spontaneous and induced VFs were recorded. Monophasic action potentials (MAPs) among different zones of myocardium were recorded at eight time points before and after ligation and MAP duration dispersions (MAPDds) were calculated. Then expression of TNF-α among different myocardial zones was detected. After ligation of the left anterior descending coronary artery, total TNF-α expression in AMI group began to markedly increase at 10 min, reached a climax at 20–30min, and then gradually decreased. The time-windows of VFs and MAPDds in the border zone performed in a similar way. At the same time-point, the expression of TNF-α in the ischemia zone was greater than that in the border zone, and little in the non-ischemia zone. Although the time windows of TNF-α expression, the MAPDds in the border zone and the occurrence of VFs in the rhTNFR:Fc group were similar to those in the AMI group, they all decreased in the rhTNFR:Fc group. Our findings demonstrate that TNF-α could enlarge the MAPDds in the border zone, and promote the onset of VFs

New multiple positive solutions for elliptic equations with singularity and critical growth

In this note, the existence of multiple positive solutions is established for a semilinear elliptic equation −∆u = λ u γ + u 2 ∗−1 , x ∈ Ω, u = 0, x ∈ ∂Ω, where Ω is a smooth bounded domain in RN (N ≥ 3), 2∗ = 2N N−2 , γ ∈ (0, 1) and λ > 0 is a real parameter. We show by the variational methods and perturbation functional that the problem has at least two positive solutions w0(x) and w1(x) with w0(x) < w1(x) in Ω

More examples of breakdown the 1:1 partner specificity between figs and fig wasps

Background The obligate mutualism between fig trees (Ficus, Moraceae) and pollinating fig wasps (Agaonidae) is a model system for studying co-evolution due to its perceived extreme specificity, but recent studies have reported a number of examples of trees pollinated by more than one fig wasp or sharing pollinators with other trees. This will make the potential of pollen flow between species and hybridization more likely though only few fig hybrids in nature have been found. We reared pollinator fig wasps from figs of 13 Chinese fig tree species and established their identity using genetic methods in order to investigate the extent to which they were supporting more than one species of pollinator (co-pollinator). Results Our results showed (1) pollinator sharing was frequent among closely-related dioecious species (where pollinator offspring and seeds develop on different trees); (2) that where two pollinator species were developing in figs of one host species there was usually one fig wasp with prominent rate than the other. An exception was F. triloba, where its two pollinators were equally abundant; (3) the extent of co-pollinator within one fig species is related to the dispersal ability of them which is stronger in dioecious figs, especially in small species. Conclusions Our results gave more examples to the breakdown of extreme specificity, which suggest that host expansion events where pollinators reproduce in figs other than those of their usual hosts are not uncommon among fig wasps associated with dioecious hosts. Because closely related trees typically have closely related pollinators that have a very similar appearance, the extent of pollinator-sharing has probably been underestimated. Any pollinators that enter female figs carrying heterospecific pollen could potentially generate hybrid seed, and the extent of hybridization and its significance may also have been underestimated

The effect credit term structure of monetary policy on firms' "short-term debt for long-term investment" behavior: empirical evidence from China

This paper examines the effects and mechanism paths of monetary policy on firms' "short-term debt for long-term investment (SDFLI)" behavior using panel data of Chinese A-share listed firms from 2007-2019. The findings indicate that loose monetary policy suppresses corporate SDFLI behavior by lengthening corporate credit maturity structure through the credit maturity structure channel. In addition, heterogeneity analysis shows that loose monetary policy significantly inhibits the SDFLI behavior of state-owned enterprises(SOEs), non-high-tech firms, and firms in regions with high bank competition levels through the credit term structure channel, and the monetary policy credit term structure channel fails for non-state-owned enterprises(non-SOEs), high-tech firms, and firms in regions with low bank competition levels. The results of the heterogeneity analysis validate the plausibility that monetary policy affects firms' SDFLI behavior through the credit term structure channel

Association between cognitive impairment and risk of atrial fibrillation: The Atherosclerosis Risk in Communities study

Background: Atrial fibrillation (AF) is reportedly a risk factor for cognitive impairment. Interestingly, recent studies have emphasized that impaired cognition is probably an initiating factor of cardiovascular disease. Thus, we aimed to explore the association between impaired cognition and the risk of AF, and clarify the potential mechanisms. Methods: Participants of visit 2 (1991–1993) in the Atherosclerosis Risk in Communities study were included. Global cognition z-scores and factor scores were calculated using the word fluency, delayed word recall, and digit symbol substitution tests. AF incidents were diagnosed by electrocardiography and inpatient records. The association of cognitive decline with AF risk and left atrial volume index (LAVI) was explored using Cox proportional hazards and linear regression models, respectively. Results: During the median follow-up of 18.2 ± 6.2 years, 2056/11,675 (17.6%) participants developed AF. Participants in the lowest quartile of global cognition z- and factor scores had a higher risk of AF (hazard ratio [HR]: 1.271, 95% confidence interval [CI]: 1.094–1.477, p = 0.002; HR: 1.305, 95% CI: 1.110–1.535, p = 0.001, respectively) than those in the highest quartile. Global cognition z- and factor scores were negatively correlated with the LAVI (B: –0.411, 95% CI: –0.749 to –0.074, p = 0.017; B: –0.425, 95% CI: –0.833 to –0.017, p = 0.041, respectively). Conclusions: Cognitive decline is significantly associated with a higher risk of AF, with atrial remodeling being a potential mechanism. Our results extend previous findings of the brain-heart axis and indicate the effects of cognitive injury on cardiac function and structure. Registration: URL: https://www.clinicaltrials.gov; unique identifier: NCT0000513