Values Of First-order Derivatives Research Articles

New finite difference unequal-sized Hermite WENO scheme for Navier-Stokes equations

In this paper, a new finite difference unequal-sized Hermite weighted essentially non-oscillatory (US-HWENO) scheme is proposed for solving multi-dimensional Navier-Stokes equations on structured meshes, which could achieve sixth-order accuracy in one dimension and fifth-order accuracy in two and three dimensions, respectively. The high-order spatial reconstruction procedure uses a convex combination of one quintic polynomial and two linear polynomials defined on three unequal-sized central or biased spatial stencils. Compared with the classical finite difference, finite volume, or mixed finite difference and finite volume HWENO schemes [32] , [33] , the new scheme uses same largest stencil and only three stencils in spatial reconstruction procedures, and the first-order derivative values in auxiliary equations can be obtained directly rather than using complex HWENO-type reconstruction methodologies [32] , [33] . Moreover, the associated viscosity terms could be directly computed from the function values and first-order derivative values by using the characteristic of the WENO-type spatial reconstructions. Meanwhile, the linear weights can be any positive numbers on condition that their summation equals one, which avoids the problem of negative linear weights in classical HWENO schemes [24] , [25] . So the new finite difference US-HWENO scheme is more suitable for solving Navier-Stokes equations, and can be easily implemented to multi-dimensions on structured meshes. Some benchmark viscous examples are illustrated to verify the good performance of this new finite difference US-HWENO scheme.

Pattern Generation and Design of Floral Patterns Based on Newton’s Iterative Algorithm

Fashionable FMCG clothing brands have emerged in large numbers, and fast fashionable and personalized clothing is increasingly favored by young people. In this era of rapid renewal, clothing has obviously become a fast moving consumer good. China’s textile industry continues to develop, and the speed of development accelerates, coupled with the introduction and promotion of the use of Western textile technology, making the pattern design of Chinese textiles develop more quickly. The long-term disconnection between product pattern design and product production has led to the fact that the research on product pattern has been only on the plane, so there is an urgent need to improve the design level of product pattern and the market competitiveness of products through systematic research on product pattern. Newton’s iteration is an important research content of nonlinear theory, which is a hot spot in the field of scientific research at present. Newton’s iteration is a common method for finding the roots of nonlinear equations, which has at least second-order convergence speed, but requires the calculation of first-order derivative values. In this paper, a preliminary discussion on the design method of pattern design based on Newton’s iterative algorithm is conducted to explore a new way of personalized pattern design while using nonlinear graphs as pattern design materials. The experimental results show that the average value of EME of Newton’s iteration algorithm is 3.479 and 2.072 higher than that of AVG Filter and CB Filter, respectively, and the difference of pattern generation accuracy between CB Filter and AVG Filter is not much, so the accuracy of Newton’s iteration algorithm for pattern generation is better than that of CB Filter and AVG Filter. Therefore, it is proved that it is feasible to transform the special texture effect based on Newton’s iteration algorithm into fabric.

Multi-resolution HWENO schemes for hyperbolic conservation laws

In this paper, a new type of high-order finite volume and finite difference multi-resolution Hermite weighted essentially non-oscillatory (HWENO) schemes are designed for solving hyperbolic conservation laws on structured meshes. Here we only use the information defined on a hierarchy of nested central spatial stencils but do not introduce any equivalent multi-resolution representation, the terminology of multi-resolution HWENO follows that of the multi-resolution WENO schemes (Zhu and Shu, 2018) [29]. The main idea of our spatial reconstruction is derived from the original HWENO schemes (Qiu and Shu, 2004) [19], in which both the function and its first-order derivative values are evolved in time and used in the reconstruction. Our HWENO schemes use the same large stencils as the classical HWENO schemes which are narrower than the stencils of the classical WENO schemes for the same order of accuracy. Only the function values need to be reconstructed by our HWENO schemes, the first-order derivative values are obtained from the high-order linear polynomials directly. Furthermore, the linear weights of such HWENO schemes can be any positive numbers as long as their sum equals one, and there is no need to do any modification or positivity-preserving flux limiting in our numerical experiments. Extensive benchmark examples are performed to illustrate the robustness and good performance of such finite volume and finite difference HWENO schemes.

Identification of the Best Hyperspectral Indices in Estimating Plant Species Richness in Sandy Grasslands

Numerous spectral indices have been developed to assess plant diversity. However, since they are developed in different areas and vegetation type, it is difficult to make a comprehensive comparison among these indices. The primary objective of this study was to explore the optimum spectral indices that can predict plant species richness across different communities in sandy grassland. We use 7339 spectral indices (7217 we developed and 122 that were extracted from literature) to predict plant richness using a two-year dataset of plant species and spectra information at 270 plots. For this analysis, we employed cluster analysis, correlation analysis, and stepwise linear regression. The spectral variability within the 420–480 nm and 760–900 nm ranges, the first derivative value at the sensitive bands, and the normalized difference at narrow spectral ranges correlated well with plant species richness. Within the 7339 indices that were investigated, the first-order derivative values at 606 and 583 nm, the reflectance combinations on red bands: (R802 − R465)/(R802 + R681) and (R750 − R550)/(R750 + R550) showed a stable performance in both the independent calibration and validation datasets (R2 > 0.27, p < 0.001, RMSE < 1.7). They can be regarded as the best spectral indices to estimate plant species richness in sandy grasslands. In addition to these spectral variation indices, the first derivative values or the normalized difference of the sensitive bands also reflect plant diversity. These results can help to improve the estimation of plant diversity using satellite-based airborne and hand-held hyperspectral sensors.

Gauss-Lobatto-Legendre-Birkhoff pseudospectral scheme for the time fractional reaction–diffusion equation with Neumann boundary conditions

ABSTRACTIn this paper, an efficient numerical scheme for the time fractional reaction–diffusion equation with Neumann boundary conditions is proposed combining finite-difference method in time and Gauss-Lobatto-Legendre-Birkhoff (GLLB) pseudospectral method in space. GLLB quadrature formula involves first-order derivative values at endpoints, which allows a natural and exact imposition of Neumann boundary conditions. It is proved that the scheme is unconditionally stable and convergent with order , where τ, N and m stand for the time step, polynomial degree and spatial regularity of the exact solution. Numerical experiment is carried out to support theoretical analysis.

Fluorometric titration approach for calibration of quantity of binding site of purified monoclonal antibody recognizing epitope/hapten nonfluorescent at 340 nm.

A fluorometric titration approach was proposed for the calibration of the quantity of monoclonal antibody (mcAb) via the quench of fluorescence of tryptophan residues. It applied to purified mcAbs recognizing tryptophan-deficient epitopes, haptens nonfluorescent at 340 nm under the excitation at 280 nm, or fluorescent haptens bearing excitation valleys nearby 280 nm and excitation peaks nearby 340 nm to serve as Förster-resonance-energy-transfer (FRET) acceptors of tryptophan. Titration probes were epitopes/haptens themselves or conjugates of nonfluorescent haptens or tryptophan-deficient epitopes with FRET acceptors of tryptophan. Under the excitation at 280 nm, titration curves were recorded as fluorescence specific for the FRET acceptors or for mcAbs at 340 nm. To quantify the binding site of a mcAb, a universal model considering both static and dynamic quench by either type of probes was proposed for fitting to the titration curve. This was easy for fitting to fluorescence specific for the FRET acceptors but encountered nonconvergence for fitting to fluorescence of mcAbs at 340 nm. As a solution, (a) the maximum of the absolute values of first-order derivatives of a titration curve as fluorescence at 340 nm was estimated from the best-fit model for a probe level of zero, and (b) molar quantity of the binding site of the mcAb was estimated via consecutive fitting to the same titration curve by utilizing such a maximum as an approximate of the slope for linear response of fluorescence at 340 nm to quantities of the mcAb. This fluorometric titration approach was proved effective with one mcAb for six-histidine and another for penicillin G.

A Nonparametric Derivative-Based Method for R Wave Detection in ECG

QRS detection is very important in cardiovascular disease diagnosis and ECG (electrocardiogram) monitor, because it is the precondition of the calculation of correlative parameters and diagnosis. This paper presents a non-parametric derivative-based method for R wave detection in ECG signal. This method firstly uses a digital filter to cut out noises from ECG signals, utilizes local polynomial fitting that is a non-parametric derivative-based method to estimate the derivative values, and then selects appropriate thresholds by the difference, and the algorithm adaptively adjusts the size of thresholds periodically according to the different needs. Afterwards, the position of R wave is detected by the estimation of the first-order derivative values with nonparametric local polynomial statistical model. In addition, in order to improve the accuracy of detection, the method of redundant detection and missing detection are applied in this paper. The clinical experimental data are used to evaluate the effectiveness of the algorithm. Experimental results show that the method in the process of the detection of R wave is much smoother, compared with differential threshold algorithm and it can detect the R wave in the ECG signals accurately.

An accurate multimoment constrained finite volume transport model on Yin-Yang grids

A global transport model is proposed in which a multimoment constrained finite volume (MCV) scheme is applied to a Yin-Yang overset grid. The MCV scheme defines 16 degrees of freedom (DOFs) within each element to build a 2D cubic reconstruction polynomial. The time evolution equations for DOFs are derived from constraint conditions on moments of line-integrated averages (LIA), point values (PV), and values of first-order derivatives (DV). The Yin-Yang grid eliminates polar singularities and results in a quasi-uniform mesh. A limiting projection is designed to remove nonphysical oscillations around discontinuities. Our model was tested against widely used benchmarks; the competitive results reveal that the model is accurate and promising for developing general circulation models.

A high-order compact local integrated-RBF scheme for steady-state incompressible viscous flows in the primitive variables

This study is concerned with the development of integrated radialbasis- function (IRBF) method for the simulation of two-dimensional steady-state incompressible viscous flows governed by the pressure-velocity formulation on Cartesian grids. Instead of using low-order polynomial interpolants, a high-order compact local IRBF scheme is employed to represent the convection and diffusion terms. Furthermore, an effective boundary treatment for the pressure variable, where Neumann boundary conditions are transformed into Dirichlet ones, is proposed. This transformation is based on global 1D-IRBF approximators using values of the pressure at interior nodes along a grid line and first-order derivative values of the pressure at the two extreme nodes of that grid line. The performance of the proposed scheme is investigated numerically through the solution of several linear (analytic tests including Stokes flows) and non-linear (recirculating cavity flow driven by combined shear & body forces and lid-driven cavity flow) problems. Unlike the global 1D-IRBF scheme, the proposed method leads to a sparse system matrix. Numerical results indicate that (i) the present solutions are more accurate and converge faster with grid refinement in comparison with standard finite-difference results; and (ii) the proposed boundary treatment for the pressure is more effective than conventional direct application of the Neumann boundary condition.

Research on effectiveness of hyperspectral data on identifying rice of different genotypes

The objective of this study is to validate the effectiveness of hyperspectral data and select hyperspectral variables to indicate differences between the non-transgenic parent and the progenies of transgenic rice regardless of gene expression. Statistically significant differences were observed in the range 510–735 nm. More differences could be observed from first-order derivative than from the original reflectance spectra. Spectral position- and index-based variables were calculated to find out the potential indicators. Both the maximum value of first-order derivative and the sum of first-order derivative in the ranges 490–530 and 560–650 nm, photochemical reflectance index (PRI) and modified chlorophyll absorption ratio index (MCARI) were different between parent group and progeny groups of transgenic rice.

Vapour generation Fourier transform infrared spectrometry. A new analytical technique

A new technique has been developed for the direct introduction of samples in Fourier transform infrared (FT-IR) spectrometric analysis. The technique is based on the injection of discrete sample volumes into an electrically heated Pyrex glass reactor in which the compounds to be determined are volatilized. The vapour phases generated are transported by means a carrier gas inside an IR gas cell and the corresponding flow injection recording registered as a function of time. In the present study the effect of the main experimental variables on both the sensitivity and the precision of the analytical measurements have been evaluated, and the method has been applied to the determination of ethanol in chloroform. For this test system vapour generation FT-IR spectrometry provides a 3σ limit of detection of 0.02% (v/v) using peak height absorbance ratios between the bands of ethanol at 1066 cm −1 and chloroform at 931 cm −1 or alternatively between the first-order derivative values corresponding to these. Results obtained in the analysis of commercial samples of CHC1 3, stabilized with ethanol, were comparable with those found by a reference procedure based on flow injection-near infrared analysis.

Rate of change (modulation) of serum growth hormone concentrations is a more important factor in determining growth rate than duration of exposure.

To determine whether duration of exposure to GH and/or rate of change of serum GH concentration are important factors in determining the growth rate of short children. An analysis of parameters of occupancy percentage and rate of change of serum GH concentration was performed as part of a prospective study investigating the relationship between growth and GH in childhood. Sixty-four short prepubertal children (48 male, 16 female) aged between 4.7 and 11.9 years were studied. Thirty-one children were growing with a height velocity standard deviation score between 0 and -0.8 and were defined as short normal. Thirty-three children were growing with a height velocity standard deviation score less than -0.8 and were defined as short slowly growing. Twenty-four hour serum GH concentration profiles were constructed by withdrawing samples at 20-minute intervals. Analysis of occupancy percentage was performed on each data array by determining cumulative distributions and plotting these as linear probits against log serum GH concentration. Estimates of peak (OC95), intermediate (OC50) and trough (OC5) occupancies were calculated. A first-order derivative of the concentration-time data array was determined for each profile as a measure of rate changes. First-order derivative values were significantly greater in the short normal group than in the short slowly growing children (short normal median 1.41 mU/l/min; short slowly growing median 0.72 mU/l/min; P less than 0.001). OC95 values were significantly higher in the short normal group (median 19.31 mU/l) than the short slowly growing group (median 7.69 mU/l) (P less than 0.001). There was no difference in OC50 values. OC5 values were lower in short normal children (median 0.20 mU/l) than in the short slowly growing children (0.55 mU/l) (P less than 0.003). The most important factor in determining growth rate was the rate of change in serum GH concentration (FOD). Occupancy percentage played no part in the relationship. The regression equation was Height velocity SDS = 1.16 (In FOD) - 1.03; r = 0.75; P less than 0.001 These data suggest that the pattern of presentation of GH in the circulation is an important factor in determining target organ response. Although occupancy percentages at differing serum GH concentrations differ between short slowly growing and short normal children, it is the rate of change of the hormone in the circulation which appears to be the more important 'signal' in terms of modulating growth.