High accuracy non-equidistant method for singular perturbation reaction-diffusion problem

Singular perturbation reaction-diffusion problem with Dirichlet boundary condition is considered. It is a multi-scale problem. Presence of small parameter leads to boundary layer phenomena in both sides of the region. A non-equidistant finite difference method is presented according to the property of boundary layer. The region is divided into an inner boundary layer region and an outer boundary layer region according to transition point of Shishkin. The steps sizes are equidistant in the outer boundary layer region. The step sizes are gradually increased in the inner boundary layer region such that half of the step sizes are different from each other. Truncation error is estimated. The proposed method is stable and uniformly convergent with the order higher than 2. Numerical results are given, which are in agreement with the theoretical result.

A Novel Non-Equidistant Grey GRM(1,1) Model Based on Reciprocal Accumulated Generating

Applying the reciprocal accumulated generating and the reconstruction method of GRM(1,1) model’s background value of non-equidistant sequence based on the exponential trait of grey model and the definition of integral for the problem of lower precision as well as lower adaptability in non-equidistant GM(1,1) model, the calculation formulas were deduced and a novel non-equidistant GRM(1,1) model generated by reciprocal accumulated generating was put forward. The grey GRM(1,1) model can be used in non-equidistant interval & equidistant interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.

Mitigating end effects of EMD using non-equidistance grey model

Aiming at mitigating end effects of empirical mode decomposition （EMD）, a new approach motivated by the non- equidistance grey model （NGM） termed as NGM（1,1） is proposed. Other than trapezoid formulas, the cubic Hermite spline is put forward to improve the accuracy of derivative to the accumulated generating operation （AGO） series. Hopefully, it is worth stressing that the proposed NGM（1,1） model is particularly useful for predicting uncertainty data. Qualitative and quantitative comparisons between the proposed approach and other well-known algorithms are carried out through computer simulations on synthetic as well as natural signals. Simulation results demonstrate the proposed method can reduce end effects and improve the decomposition results of EMD.

A UNIFORM NUMERICAL METHOD FOR QUASILINEAR SINGULAR PERTURBATION PROBLEM WITH A TURNING POINT

A nonlinear difference scheme is given for solving a quasilinear singularly perturbed two-point boundary value problem with a turning point. The method uses non-equidistant discretization meshes. The solution of the scheme is shown to be first order accurate in the discrete L￣∞ norm, uniformly in the perturbation parameter.

Nonequidistant two-dimensional antenna arrays based on Latin squares

Non-equidistant sparse antenna arrays constructed on the basis of Latin squares are considered. A method for their construction and a synthesis algorithm are proposed,and the properties of two-dimensional antennas based on them,which ensure,at a high degree of rarefaction,a sufficiently small lateral radiation are studied. The features and main characteristics of such antennas are studied.

Modeling mechanism of a novel fractional grey mode based on matrix analysis

To fully display the modeling mechanism of the novelfractional order grey model （FGM （q,1））, this paper decomposesthe data matrix of the model into the mean generation matrix, theaccumulative generation matrix and the raw data matrix, whichare consistent with the fractional order accumulative grey model（FAGM （1,1））. Following this, this paper decomposes the accumulativedata difference matrix into the accumulative generationmatrix, the q-order reductive accumulative matrix and the rawdata matrix, and then combines the least square method, findingthat the differential order affects the model parameters only byaffecting the formation of differential sequences. This paper thensummarizes matrix decomposition of some special sequences,such as the sequence generated by the strengthening and weakeningoperators, the jumping sequence, and the non-equidistancesequence. Finally, this paper expresses the influences of the rawdata transformation, the accumulation sequence transformation,and the differential matrix transformation on the model parametersas matrices, and takes the non-equidistance sequence as an exampleto show the modeling mechanism.

Analysis and Forecast of China’s Grain Supply and Demand Quality Grade Structural Balance

Based on the analysis of China’s grain production and demand quality grade, this paper uses the non-equidistance GM (1,1) model and the inference algorithm to predict the structural balance of the supply and demand grades of China’s four major grain crops. The results show that the supply and demand for wheat, corn and rice can maintain a quantitative balance. While, it’s difficult to achieve a quality grade balance in wheat and rice and keep a supply and demand balance in terms of quantity and quality of soybean. Simultaneously, the supply of premium grade corn is greater than the demand. The analysis and prediction results can reflect the existing structural balance matter of grain supply and demand at different quality grades in China, and provide theoretical basis for governments to formulate relevant policies.

Non-equidistance DGM(1,1) Model Based on the Concave Sequence and Its Application to Predict the China’s Per Capita Natural Gas Consumption

Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved, such as for the DGM(1,1) model, based on a concave sequence, the modeling error will be larger. In this paper,firstly the definition of sequence convexity is given out, and it is proved that the output sequence of DGM(1,1) model is a convex sequence. Next, the residual change law of DGM(1,1) model based on the concave sequence is discussed, and the non-equidistance DGM(1,1) model is proposed. Finally, by introducing the symmetry transformation, a concave sequence is transformed into a convex sequence, called the symmetric sequence of the concave sequence, and then construct the non-equidistance DGM(1,1)model based on the convex sequence. The example results show that the novel method is more accurate than the direct modeling for a concave sequence.

Primate phylogeny:molecular evidence for a pongid clade excluding humans and a prosimian clade containing tarsiers

Unbiased readings of fossils are well known to contradict some of the popular molecular groupings among primates,particularly with regard to great apes and tarsiers.The molecular methodologies today are however flawed as they are based on a mistaken theoretical interpretation of the genetic equidistance phenomenon that originally started the field.An improved molecular method the 'slow clock' was here developed based on the Maximum Genetic Diversity hypothesis,a more complete account of the unified changes in genotypes and phenotypes.The method makes use of only slow evolving sequences and requires no uncertain assumptions or mathematical corrections and hence is able to give definitive results.The findings indicate that humans are genetically more distant to orangutans than African apes are and separated from the pongid clade ～17.6 million years ago.Also,tarsiers are genetically closer to lorises than simian primates are.Finally,the fossil times for the radiation of mammals at the K/T boundary and for the Eutheria-Metatheria split in the Early Cretaceous were independently confirmed from molecular dating calibrated using the fossil split times of gorilla-orangutan,mouse-rat,and opossum-kangaroo.Therefore,the re-established primate phylogeny indicates a remarkable unity between molecules and fossils.