Global existence and nonexistence for degenerate parabolic equations with nonlinear boundary flux

In this paper, by constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions of global existence for nonnegative solutions to a degenerate parabolic system with completely coupled boundary conditions, which generalize the recent results of, for instance, Cui [Z. Cui, Critical curves of the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions, Nonlinear Anal. 68 (2008) 3201–3208], Zhou–Mu [J. Zhou, C. Mu, Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007) 1185–1197] etc.     

The global solution for a class of systems of fractional nonlinear Schrödinger equations with periodic boundary condition

In this paper, we consider a class of systems of fractional nonlinear Schrödinger equations. We prove the existence and uniqueness of the global solution to the periodic boundary value problem by using the Faedo-Galërkin method.     

State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays

This paper deals with the problem of state estimation for fuzzy cellular neural networks (FCNNs) with time delay in the leakage term, discrete and unbounded distributed delays. In this paper, leakage delay in the leakage term is used to unstable the neuron states. It is challenging to develop a delay dependent condition to estimate the unstable neuron states through available output measurements such that the error-state system is globally asymptotically stable. By constructing the Lyapunov-Krasovskii functional which contains a triple-integral term, an improved delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). However, by using the free-weighting matrices method, a simple and efficient criterion is derived in terms of LMIs for estimation. The restriction such as the time-varying delay which was required to be differentiable or even its time-derivative which was assumed to be smaller than one, are removed. Instead, the time-varying delay is only assumed to be bounded. Finally, numerical examples and its simulations are given to demonstrate the effectiveness of the derived results.     

The convergence analysis and specification of the Population-Based Incremental Learning algorithm

In this paper, we investigate the global convergence properties in probability of the Population-Based Incremental Learning (PBIL) algorithm when the initial configuration p⁽⁰⁾ is fixed and the learning rate α is close to zero. The convergence in probability of PBIL is confirmed by the experimental results. This paper presents a meaningful discussion on how to establish a unified convergence theory of PBIL that is not affected by the population and the selected individuals.     

Global exponential stability in Lagrange sense for neutral type recurrent neural networks

In this paper, the global exponential stability in Lagrange sense for continuous neutral type recurrent neural networks (NRNNs) with multiple time delays is studied. Three different types of activation functions are considered, including general bounded and two types of sigmoid activation functions. By constructing appropriate Lyapunov functions, some easily verifiable criteria for the ultimate boundedness and global exponential attractivity of NRNNs are obtained. These results can be applied to monostable and multistable neural networks as well as chaos control and chaos synchronization.     

Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales

By employing time scale calculus theory, free weighting matrix method and linear matrix inequality (LMI) approach, several delay-dependent sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the neural networks with both infinite distributed delays and general activation functions on time scales. Both continuous-time and discrete-time neural networks are described under the same framework by the reported method. Illustrated numerical examples are given to show the effectiveness of the theoretical analysis. It is noteworthy that the activation functions are assumed to be neither bounded nor monotone.     

Global data computation in chordal rings

Existing Global Data Computation (GDC) protocols for asynchronous systems are round-based algorithms designed for fully connected networks. In this paper, we discuss GDC in asynchronous chordal rings, a non-fully connected network. The virtual links approach to solve the consensus problem may be applied to GDC for non-fully connected networks, but it incurs high message overhead. To reduce the overhead, we propose a new non-round-based GDC protocol for asynchronous chordal rings with perfect failure detectors. The main advantage of the protocol is that there is no notion of rounds. Every process creates two messages initially, with one message traversing in a clockwise direction and visiting each and every process in the chordal ring. The second message traverses in a counterclockwise direction. When there is direct connection between two processes, a message is sent directly. Otherwise, the message is sent via virtual links. When the two messages return, the process decides according to the information maintained by the two messages. The perfect failure detector of a process need only detect the crash of neighboring processes, and the crash information is disseminated to all other processes. Analysis and comparison with two virtual links approaches show that our protocol reduces message complexity significantly.     

Global stability analysis scheme for a class of nonlinear time delay systems

We consider a class of nonlinear time delay systems created by generalizing the model for FAST TCP, an Internet congestion control algorithm. We achieve a time delay independent sufficient condition for the global asymptotic stability of the class of systems. The sufficient condition is verified by constructing two sequences that represent the lower and upper bound variations of the system trajectory in time, and showing that the two sequences converge to the equilibrium point of the system. The simulation results exemplify that the sufficient condition is valid for global asymptotic stability, and that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for global asymptotic stability.     

An assessment of photosynthetic light use efficiency from space: Modeling the atmospheric and directional impacts on PRI reflectance

Estimation of photosynthetic light use efficiency (ε) from satellite observations is an important component of climate change research. The photochemical reflectance index, a narrow waveband index based on the reflectance at 531 and 570 nm, allows sampling of the photosynthetic activity of leaves; upscaling of these measurements to landscape and global scales, however, remains challenging. Only a few studies have used spaceborne observations of PRI so far, and research has largely focused on the MODIS sensor. Its daily global coverage and the capacity to detect a narrow reflectance band at 531 nm make it the best available choice for sensing ε from space. Previous results however, have identified a number of key issues with MODIS-based observations of PRI. First, the differences between the footprint of eddy covariance (EC) measurements and the MODIS footprint, which is determined by the sensor's observation geometry make a direct comparison between both data sources challenging and second, the PRI reflectance bands are affected by atmospheric scattering effects confounding the existing physiological signal. In this study we introduce a new approach for upscaling EC based ε measurements to MODIS. First, EC-measured ε values were “translated” into a tower-level optical PRI signal using AMSPEC, an automated multi-angular, tower-based spectroradiometer instrument. AMSPEC enabled us to adjust tower-measured PRI values to the individual viewing geometry of each MODIS overpass. Second, MODIS data were atmospherically corrected using a Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm, which uses a time series approach and an image-based rather than pixel-based processing for simultaneous retrievals of atmospheric aerosol and surface bidirectional reflectance (BRDF). Using this approach, we found a strong relationship between tower-based and spaceborne reflectance measurements (r² = 0.74, p < 0.01) throughout the vegetation period of 2006. Swath (non-gridded) observations yielded stronger correlations than gridded data (r² = 0.58, p < 0.01) both of which included forward and backscatter observations. Spaceborne PRI values were strongly related to canopy shadow fractions and varied with different levels of ε. We conclude that MAIAC-corrected MODIS observations were able to track the site-level physiological changes from space throughout the observation period.     

Effects of spectral response function on surface reflectance and NDVI measured with moderate resolution satellite sensors: Extension to AVHRR NOAA-17, 18 and METOP-A

This work extends the previous study of Trishchenko et al. [Trishchenko, A. P., Cihlar, J., & Li, Z. (2002). Effects of spectral response function on surface reflectance and NDVI measured with moderate resolution satellite sensors. Remote Sensing of Environment 81 (1), 1-18] that analyzed the spectral response function (SRF) effect for the Advanced Very High Resolution Radiometer (AVHRR) onboard the NOAA satellites NOAA-6 to NOAA-16 as well as the Moderate Resolution Imaging Spectroradiometer (MODIS), the VEGETATION sensor (VGT) and the Global Imager (GLI). The developed approach is now applied to cover three new AVHRR sensors launched in recent years on NOAA-17, 18, and METOP-A platforms. As in the previous study, the results are provided relative to the reference sensor AVHRR NOAA-9. The differences in reflectance among these three radiometers relative to the AVHRR NOAA-9 are similar to each other and range from − 0.015 to 0.015 (− 20% to + 2% relative) for visible (red) channel, and from − 0.03 to 0.02 (− 5% to 5%) for the near infrared (NIR) channel. The absolute change in the Normalized Difference Vegetation Index (NDVI) ranged from − 0.03 to + 0.06. Due to systematic biases of the visible channels toward smaller values and the NIR channels toward slightly larger values, the overall systematic biases for NDVI are positive. The polynomial approximations are provided for the bulk spectral correction with respect to the AVHRR NOAA-9 for consistency with previous study. Analysis was also conducted for the SRF effect only among the AVHRR-3 type of radiometer on NOAA-15, 16, 17, 18 and METOP-A using AVHRR NOAA-18 as a reference. The results show more consistency between sensors with typical correction being under 5% (or 0.01 in absolute values). The AVHRR METOP-A reveals the most different behavior among the AVHRR-3 group with generally positive bias for visible channel (up to + 5%, relative), slightly negative bias for the NIR channel (1%-2% relative), and negative NDVI bias (− 0.02 to + 0.005). Polynomial corrections are also suggested for normalization of AVHRR on NOAA-15, 16, 17 and METOP-A to AVHRR NOAA-18.