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Discusses the 2‐D minimum free energy (MFE) parameter and spectral estimation method and presents an algorithm for its implementation. Notes a profound lack of results in the literature on 2‐D spectral estimation methods and on their comparison. To address this issue and to impart an overall impression of the performance of 2‐D MFE, compares results from the Levinson method, a maximum entropy method (MEM), and a hybrid method with 2‐D MFE. Points out that 2‐D MFE can provide superior spectral estimates to that produced with MEM and that, in general, MFE requires a larger area of correlation support than the hybrid method. Also notes that 2‐D MFE can provide superior spectral estimation over the 2‐D Levinson algorithm.

The low Mach number approximation of the Navier—Stokes equations is of similar nature to the equations for incompressible flow. A major difference, however, is the appearance of a space‐ and time‐varying density that introduces a supplementary non‐linearity. In order to solve these equations with spectral space discretization, an iterative solution method has been constructed and successfully applied in former work to two‐dimensional natural convection and isobaric combustion with one direction of periodicity. For the extension to other geometries efficiency is an important point, and it is therefore desirable to devise a direct method which would have, in the best case, the same stability properties as the iterative method. The present paper discusses in a systematic way different approaches to this aim. It turns out that direct methods avoiding the diffusive time step limit are possible, indeed. Although we focus for discussion and numerical investigation on natural convection flows, the results carry over for other problems such as variable viscosity flows, isobaric combustion, or non‐homogeneous flows.

In order to overcome the uncertainty and improve the accuracy of spectral estimation, this paper aims to establish a grey fuzzy prediction model of soil organic matter content by using grey theory and fuzzy theory.

Based on the data of 121 soil samples from Zhangqiu district and Jiyang district of Jinan City, Shandong Province, firstly, the soil spectral data are transformed by spectral transformation methods, and the spectral estimation factors are selected according to the principle of maximum correlation. Then, the generalized greyness of interval grey number is used to modify the estimation factors of modeling samples and test samples to improve the correlation. Finally, the hyper-spectral prediction model of soil organic matter is established by using the fuzzy recognition theory, and the model is optimized by adjusting the fuzzy classification number, and the estimation accuracy of the model is evaluated using the mean relative error and the determination coefficient.

The results show that the generalized greyness of interval grey number can effectively improve the correlation between soil organic matter content and estimation factors, and the accuracy of the proposed model and test samples are significantly improved, where the determination coefficient R² = 0.9213 and the mean relative error (MRE) = 6.3630% of 20 test samples. The research shows that the grey fuzzy prediction model proposed in this paper is feasible and effective, and provides a new way for hyper-spectral estimation of soil organic matter content.

The research shows that the grey fuzzy prediction model proposed in this paper can not only effectively deal with the three types of uncertainties in spectral estimation, but also realize the correction of estimation factors, which is helpful to improve the accuracy of modeling estimation. The research result enriches the theory and method of soil spectral estimation, and it also provides a new idea to deal with the three kinds of uncertainty in the prediction problem by using the three kinds of uncertainty theory.

The paper succeeds in realizing both the grey fuzzy prediction model for hyper-spectral estimating soil organic matter content and effectively dealing with the randomness, fuzziness and grey uncertainty in spectral estimation.

This paper aims to effectively achieve endmembers and relative abundances simultaneously in hyperspectral image unmixing yield. Hyperspectral unmixing, which is an important step before image classification and recognition, is a challenging issue because of the limited resolution of image sensors and the complex diversity of nature. Unmixing can be performed using different methods, such as blind source separation and semi-supervised spectral unmixing. However, these methods have disadvantages such as inaccurate results or the need for the spectral library to be known a priori.

This paper proposes a novel method for hyperspectral unmixing called fuzzy c-means unmixing, which achieves endmembers and relative abundance through repeated iteration analysis at the same time.

Experimental results demonstrate that the proposed method can effectively implement hyperspectral unmixing with high accuracy.

The proposed method present an effective framework for the challenging field of hyperspectral image unmixing.

This paper aims to provide a framework of the supervised hyperspectral classification, to study the traditional flowchart of hyperspectral image (HIS) analysis and processing. HSI technology has been proposed for many years, and the applications of this technology were promoted by technical advancements.

First, the properties and current situation of hyperspectral technology are summarized. Then, this paper introduces a series of common classification approaches. In addition, a comparison of different classification approaches on real hyperspectral data is conducted. Finally, this survey presents a discussion on the classification results and points out the classification development tendency.

The core of this survey is to review of the state of the art of the classification for hyperspectral images, to study the performance and efficiency of certain implementation measures and to point out the challenges still exist.

The study categorized the supervised classification for hyperspectral images, demonstrated the comparisons among these methods and pointed out the challenges that still exist.

Deals with the formulation and application of temporal and spatial spectral element approximations for the solution of convection‐diffusion problems. Proposes a new high‐order splitting space‐time spectral element method which exploits space‐time discontinuous Galerkin for the first hyperbolic substep and space continuous‐time discontinuous Galerkin for the second parabolic substep. Analyses this method and presents its characteristics in terms of accuracy and stability. Also investigates a subcycling technique, in which several hyperbolic substeps are taken for each parabolic substep; a technique which enables fast, cost‐effective time integration with little loss of accuracy. Demonstrates, by a numerical comparison with other coupled and splitting space‐time spectral element methods, that the proposed method exhibits significant improvements in accuracy, stability and computational efficiency, which suggests that this method is a potential alternative to existing schemes. Describes several areas for future research.

In the first part of this paper a new method of applying the Maximum Entropy Principle (MEP) is presented, which makes use of a “frequency related” entropy, and which is valid for all stationary processes. The method is believed valid only in the case of discrete spectra. In the second part of the paper, a method of estimating continuous spectra in the presence of noise is presented, which makes use of the Mutual Information Principle (MIP). Although the method proceeds smoothly in mathematical terms, there appear to be some difficulties in interpreting the physical meaning of some of the expressions. Examples in the use of both methods are presented, for the usual practical problem of estimating a power spectrum for a process whose autocorrelation function is partially known a priori.

The purpose of this paper is to focus on the application of Chebyshev spectral collocation methodology with Gauss Lobatto grid points to micropolar fluid over a stretching or shrinking surface. Radiation, thermophoresis and nanoparticle Brownian motion are considered. The results have attainable scientific and technological applications in systems involving stretchable materials.

The model equations governing the flow are transformed into non-linear ordinary differential equations which are then reworked into linear form using the Newton-based quasilinearization method (SQLM). Spectral collocation is then used to solve the resulting linearised system of equations.

The validity of the model is established using error analysis. The velocity, temperature, micro-rotation, skin friction and couple stress parameters are conferred diagrammatically and analysed in detail.

The study obtains numerical explanations for rapidly convergent solutions using the spectral quasilinearization method. Convergence of the numerical solutions was monitored using the residual error analysis. The influence of radiation, heat and mass parameters on the flow are depicted graphically and analysed. The study is an extension on the work by Zheng et al. (2012) and therefore the novelty is that the authors tend to take into account nanoparticles, Brownian motion and thermophoresis in the flow of a micropolar fluid.

The paper aims to propose an artificial neural network (ANN) in conjunction with spectral domain formulation for fast and accurate determination of the resonant frequency and quality factor of circular microstrip antenna printed on isotropic or anisotropic substrate. This neurospectral approach reduces the problem complexity.

The moment method implemented in the spectral domain provides good accuracy but its computational cost is high due to the evaluation of the slowly decaying integrals and the iterative nature of the solution process. The paper introduces the electromagnetic knowledge combined with ANN in the analysis of circular microstrip antenna on isotropic or uniaxially anisotropic substrate to reduce the complexity of the spectral approach and to minimize the CPU time necessary to obtain the numerical results.

The resonant frequency results obtained from the neural model are in very good agreement with the experimental and theoretical results available in the literature. Finally, numerical results for the substrate anisotropy effect on the resonant frequency, quality factor and radiation pattern are also presented.

The paper develops fast and accurate model based on ANN technique to calculate the resonant frequencies and quality factors of circular microstrip antennas. ANN is used to model the relationship between the parameters of the microstrip antenna and the resonant frequencies and quality factors obtained from the spectral domain approach. This relatively simple model allows designers to predict accurately the resonant frequencies and quality factors for a given design without having to develop or run the spectral method codes themselves. The main advantages of the method are: less computing time than the spectral model, results with accuracy equivalent to that of full-wave models and cost effectiveness, since the client can use a simple PC for implementation. Another advantage of the proposed ANN model is that it takes into account the uniaxial anisotropy in the substrate without increasing the network size. This is done by combining ANN with electromagnetic knowledge.

The purpose of this paper is to present some numerical methods based on different time stepping and space discretization methods for the Allen‐Cahn equation with non‐periodic boundary conditions.

In space the equation is discretized by the Chebyshev spectral method, while in time the exponential time differencing fourth‐order Runge‐Kutta (ETDRK4) and implicit‐explicit scheme are used. Also, for comparison the finite difference scheme in both space and time is used.

It is found that the use of implicit‐explicit scheme allows use of a large time‐step, since an explicit method has less order of accuracy as compared to implicit‐explicit method. In time‐stepping the proposed ETDRK4 does not behave well for this special kind of partial differential equation.

The paper presents some numerical methods based on different time stepping and space discretization methods for the Allen‐Cahn equation with non‐periodic boundary conditions.