Evaluation of near-surface soil water status through the inversion of soil–canopy radiative transfer models in the reflective optical domain

Knowledge of the spatial and temporal variability of surface soil water content (SWC) is important to understand the linkage between hydrological, ecological and geological processes in a region. Optical Earth observation (EO) data offer the possibility to retrieve surface soil water information, since an overall decrease of soil reflectance corresponds to increasing SWC. Sensitivity analysis of the combined leaf (PROSPECT) and canopy (SAILH) reflectance models (PROSAIL) to soil reflectance variations was carried out, and remote sensing and ground data from different experimental agricultural sites (ESA Spectra Barrax Campaigns (SPARC) 2004 SPARC DATA ACQUISITION REPORT, 2004, Contract no: 18307/04/NL/FF, University Valencia.  [Google Scholar], ESA Airborne SAR and Optic Campaigns (AgriSAR) 2006 and participatory multi-level EO-assisted tools for irrigation water management and agricultural decision-support (PLEIADeS) 2007) were exploited. A simple look-up table (LUT) inversion technique was implemented to estimate canopy and soil variables. High negative relationships (r?=??0.87) between the soil reflectance factor of the model and the measured SWC were found for several crop types and different locations exhibiting a low fractional vegetation cover (fCover). Even though quantification of SWC is difficult, the method could be useful to obtain relative SWC information, especially before the start and at the beginning of the growing season. Furthermore, the physically based estimation approach offers the possibility of getting information about soil and canopy characteristics concurrently from optical EO data. The methodology presented in this article may also represent a suitable complement in the retrieval of SWC from active microwave.     

A review on the describing function calculation of double-valued characteristics. The inverse problem†

A review on the method for the calculation of the describing function of double valued characteristics is presented here with extension to the inverse describing function problem. With this method the calculation of the DF of a characteristic is obtained by considering the function of the characteristic alone without the need of expanding the output waveform into Fourier series. In addition the method Leads to analytical forms from which the inverse problem, of finding special characteristics from their given describing functions, can be solved.     

Simplification of the z-transfer function via Padé approximation of the squared-magnitude function

A method based on approximating the squared-magnitude function in the bilinear-transformed domain is presented for the simplification of z-transfer functions. In order to guarantee that the initial output response of the simplified model is the same as that of the original system, the bilinear transformation is performed on the numerator and the denominator polynomials or the z-transfer function itself. The main advantage of the method is that it may give a satisfactory approximation while preserving the stability and minimum-phase characteristics.     

On the definition of ‘transfer function’†

The optimal asymptotically stabilizing control problem is formulated, and the theorem for the sufficient condition that guarantees its existence and uniqueness is stated and proved. The close relationship with Pontryagin's equations is discussed. It is shown that the control problem falls into the framework of optimal linear regulators with quadratic cost functionals. Furthermore, an alternate approach is presented that, for the problem solved, leads to the same optimal control.     

Approximation of Laplace transform of fractional derivatives via Clenshaw–Curtis integration

In this paper, we approximate the Laplace transform of fractional derivatives via Clenshaw–Curtis integration. The idea of applying Chebyshev polynomial to the numerical computation of integrals is extended to Laplace transform of fractional derivatives. The numerical stability of forward recurrence relations is considered, which depends on the asymptotic behaviour of the coefficients. Error estimation for the Laplace approximation of the fractional derivatives is also considered. Finally, from the numerical examples, the method seems to be promising for approximation of the Laplace transform of fractional derivative.     

Note on ‘ On the definition of transfer function ’

An algorithm for directly obtaining the canonical state-space model corresponding to the Cauer third form of continued fraction expansion (CFE) from a given general state-space model is presented. The algorithm can be used to determine the transfer function of linear time-invariant system from its state-space model as well as to obtain the reduced order models..Two new similarity matrices, one transforms a state-space equation from a general form to a Cauer third CFE canonical form, and the other transforms a state-space model in phase-variable form to a state-space model in a Cauer third CFE canonical form, are derived. Using these matrices an approximate relationship between the original state vector and the state-vector of reduced model obtained by the method of Cauer third CFE is established     

The solitary wave solution of coupled Klein–Gordon–Zakharov equations via two different numerical methods

In this research, we propose two different methods to solve the coupled Klein–Gordon–Zakharov (KGZ) equations: the Differential Quadrature (DQ) and Globally Radial Basis Functions (GRBFs) methods. In the DQ method, the derivative value of a function with respect to a point is directly approximated by a linear combination of all functional values in the global domain. The principal work in this method is the determination of weight coefficients. We use two ways for obtaining these coefficients: cosine expansion (CDQ) and radial basis functions (RBFs-DQ), the former is a mesh-based method and the latter categorizes in the set of meshless methods. Unlike the DQ method, the GRBF method directly substitutes the expression of the function approximation by RBFs into the partial differential equation. The main problem in the GRBFs method is ill-conditioning of the interpolation matrix. Avoiding this problem, we study the bases introduced in Pazouki and Schaback (2011) [44]. Some examples are presented to compare the accuracy and easy implementation of the proposed methods. In numerical examples, we concentrate on Inverse Multiquadric (IMQ) and second-order Thin Plate Spline (TPS) radial basis functions. The variable shape parameter (exponentially and random) strategies are applied in the IMQ function and the results are compared with the constant shape parameter.     

The gradient of a sampled function†

One of the applications of digital computers in processing sampled data is in determining the gradient of a sampled function. In this paper an algorithm is found for determining the gradient in N dimensions of an N-dimensional wave-number-limited function from its samples. The gradient is found at the sampling points. An upper bound to the truncation error is calculated. The dependence of this error on the pitch of the sampling lattice, the number of samples and the maximum exeursion is found for a cardinal reconstruction function.     

On the pole of non-square transfer function matrix Moore–Penrose pseudo-inverses

An essential step in many controller design approaches is computing the inverse of the plant. For a square plant, its inverse is stable if the plant is minimum phase (MP). Nevertheless, this conclusion does not hold for a non-square plant. In this paper, the pole feature of the Moore–Penrose pseudo-inverse of a non-square transfer function matrix is analysed. Instead of complicated advanced mathematical tools, only basic results of polynomial theory and the Binet–Cauchy theorem are used in the analysing procedure. The condition for testing the stability of the Moore–Penrose pseudo-inverse of an MP non-square transfer function matrix is given. This condition implies that the Moore–Penrose pseudo-inverse of a non-square transfer function matrix cannot be directly used as the optimal controller. Numerical examples are provided to illustrate the correctness of the condition.     

The ‘transfer of skill’ and the ‘transfer of human relations’ to machine systems

The necessity and opportunity for face-to-face contact with other colleagues is being increasingly reduced as a result of factory automation (FA) or office automation (OA). This means that human functions which are a result of human contact and relationships are substituted for by the function of machine systems. This transfer of relations from the human system to the machine system causes isolation of the individual in the process of work. This chapter considers some reasons for isolation with particular reference to the computerisation of production systems. The paper addresses the serious consequences for the environmental situation in Japan and the fabric of Japanese society.     

Existence and uniqueness of a transient state for the coupled radiative–conductive heat transfer problem

This paper deals with existence and uniqueness results for a transient nonlinear radiative–conductive system in three-dimensional case. This system describes the heat transfer for a grey, semi-transparent and non-scattering medium with general boundary conditions. We reformulate the full transient state system as a fixed-point problem. The existence and uniqueness proof is based on Banach fixed point theorem.     

The importance of numerical algorithms for solving economic optimization problems †

This paper contains a brief review of the recent literature on economic applications of optimal control theory. It is not a comprehensive review, rather it serves to illustrate the assertion made in the title. Pursuit of an analytical solution confines the economic theorist to a narrow class of problems : termed here as the ' single differential equation model world '. Empirical economists searching for linear decision rule3 are also restricting themselves to a narrow class of problems. The adoption of general numerical algorithms would liberate both groups and this may yet prove to be the major contribution of systems theory to economics.     

Methods for the transfer function design of multiple narrow-band bandpass sigma–delta modulators

This paper presents the design analysis of novel tunable narrow-band bandpass sigma–delta modulators, which can achieve concurrent multiple noise-shaping for multi-tone input signals. Four different design methodologies based on the noise transfer functions of comb filters, slink filters, multi-notch filters and fractional delay comb filters are applied for the design of these multiple-band sigma–delta modulators. The latter approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter-based sigma–delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies. The merits and drawbacks of each technique for the various sigma–delta topologies are assessed in terms of in-band signal-to-noise ratios, accuracy of tunability and coefficient complexity for ease of implementation.     

A modified transfer function obtained from the commutating contact of an N-path filter†

The realization of network transfer functions by commutating the input signal to a number of low-pass filters is well established. This paper shows that such an arrangement produces more than one transfer function, depending on the phase of the output brush with respect to the input brush. It is shown that when the output is picked up from the contact undergoing commutation the output is not only of different phase but also of different magnitude from that obtained from any of the other contacts.     

Comments on ‘New algorithm for minimal balanced realization of transfer function matrix’

Gonzalez and Munro (1990) presented a new algorithm for the minimal balanced realization of a transfer function matrix. We point out that their algorithm fails generically. We also give an alternative algorithm which is both more general and computationally efficient.     

Classification of multi‐spectral remote sensing data using a local transfer function classifier

This paper introduces a new neural network, called the local transfer function classifier (LTF‐C), for classification of multi‐spectral remote sensing data. The network structure of LTF‐C is similar to that of the radial basis function neural network (RBF), but LTF‐C utilizes an entirely different learning algorithm. In particular, the network structure of LTF‐C is not predetermined, but changes dynamically during the learning. Such a learning algorithm fits well to the classification problem, and guarantees that the size of the network is as large as is needed. The classification results show that LTF‐C evidently has a better classification accuracy than the six other classifiers in the experiment.     

The numerical simulation of periodic solutions for a predator–prey system

In this article, the existence and global stability of periodic solutions for a semi-ratio-dependent predator–prey system with Holling IV functional response and time delays are investigated. Using coincidence degree theory and Lyapunov method, sufficient conditions for the existence and global stability of periodic solutions are obtained. A numerical simulation is given to illustrate the results.     

Adaptive H-infinity control of synchronous generators with steam valve via Hamiltonian function method

Based on Hamiltonian formulation, this paper proposes a design approach to nonlinear feedback excitation control of synchronous generators with steam valve control, disturbances and unknown parameters. It is shown that the dynamics of the synchronous generators can be expressed as a dissipative Hamiltonian system, based on which an adaptive H-infinity controller is then designed for the systems by using the structure properties of dissipative Hamiltonian systems. Simulations show that the controller obtained in this paper is very effective.