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In this paper, we present a second order parameter-uniform numerical method for a singularly perturbed Volterra delay-integro-differential equation on a Bakhvalov-type mesh. The equation is discretized by using the variable two-step backward differentiation formula of the first derivative term and the trapezoidal formula of the integral term. The stability and convergence of the numerical method in the discrete maximum norm are proved. Finally, the theoretical results are verified by some numerical experiments. [ABSTRACT FROM AUTHOR]

Copyright of Rare Metals is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the Cuckoo Search Algorithm (CSA) and the Quantum-Behavior Particle Swarm Optimization (QPSO), this paper propose a hybrid cuckoo quantum-behavior particle swarm optimization (C-QPSO). At first, the QPSO algorithm is modified by the weighted mean best position and the rapid decreasing contraction-expansion coefficient. After that, elite cooperative mechanism, selection mechanism and the mechanism for preventing premature puberty are designed in C-QPSO. To test the performance of the proposed hybrid algorithm, 12 benchmark functions with different dimensions are solved. It is shown from experiments that the algorithm has strong global optimization ability. Furthermore, our presented C-QPSO algorithm is applied to estimate the parameters of a nonlinear Muskingum model. Finally, some numerical results are given to illustrate the effectiveness of C-QPSO algorithm. [ABSTRACT FROM AUTHOR]

This paper discusses the Richardson extrapolation technique of an upwind finite difference scheme on a modified Bakhvalov-type mesh (named Vulanović–Bakhvalov mesh) for a model singularly perturbed convection–diffusion problem in two dimensions. We give a rigorous convergence analysis for the Richardson extrapolation method, which is shown that the use of Richardson extrapolation technique improves the ε -uniform accuracy of the presented scheme in the discrete maximum norm from O N - 1 to O N - 2 , where N is the number of mesh-intervals. Then we also propose a new numerical method to obtain the optimization mesh parameters of the Vulanović–Bakhvalov mesh. Finally some numerical experiments are provided to validate our theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central South University is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A novel parameter-uniform finite difference scheme on a Shishkin-type mesh for a singularly perturbed Volterra integro-differential equation is studied. The problem is discretized by the variable two-step backward differentiation formula (BDF2) for the first-order derivative term and the trapezoidal formula for the integral term. The stability of the proposed numerical method is carried out. It is shown from the convergence analysis that our presented method is almost second-order uniformly convergent with respect to the perturbation parameter ε in the discrete maximum norm. Numerical results are given to support our theoretical result. [ABSTRACT FROM AUTHOR]

In this paper, we combine the ideas of multilevel augmentation methods for solving integral equations and the shifted-inverse power method to develop a new multilevel augmentation method for solving eigen-problem of compact integral operators with smooth kernels. We first solve an eigen-problem in a suitable initial coarse level and then seek a more accurate approximation from solving a linear system on a finer mesh. Moreover, we need only to deal with a small linear system corresponding to the initial coarse level when we solve the linear system on a finer mesh. The method exhibits to be convenient for implementing adaptivity, and reduces the computational cost greatly and leads to the method faster. Numerical examples are presented to illustrate the theoretical estimates for the error of these methods. [ABSTRACT FROM AUTHOR]

The main reason for the high strength in near-β titanium alloys is the ultrafine precipitation of the acicular secondary α phase in the β matrix. The purpose of this study is to use the pseudo-spinodal mechanism to obtain the ultrafine α phase for the design of a new high-strength near-β titanium alloy. Thermodynamic calculations and TC21-(TC21 + 15Mo) diffusion couple composition gradient experiments were used to demonstrate that TC21 + 3Mo alloy can undergo a pseudo-spinodal decomposition to obtain the ultrafine α phase, resulting in a high-strength alloy. By adjusting the heat treatment process to obtain a bimodal microstructure, the alloy exhibits a good balance between ultimate tensile strength (1351 MPa) and plasticity (8.5% strain). Thus, it was demonstrated that the pseudo-spinodal mechanism combined with a high-throughput diffusion couple technique is an effective method for designing high-strength titanium alloys. Pseudo-spinodal mechanism combined with high-throughput diffusion couple technique is an effective method for designing high-strength titanium alloys. TC21 + 3Mo alloy can undergo a pseudo-spinodal decomposition to obtain the ultrafine α phase, resulting in a high-strength alloy. Compared with other alloys, there is considerable potential for application of TC21 + 3Mo alloy. [ABSTRACT FROM AUTHOR]

Pituitary adenylate cyclase activating polypeptide (PACAP) is a neuropeptide that has been found to reduce liver inflammation and protect liver from steatosis. We aimed to measure the level of plasma PACAP in patients with liver cirrhosis and to correlate its level with disease severity and laboratory parameters. 113 patients with clinically diagnosed liver cirrhosis and 110 healthy individuals were selected. Child–Pugh score was performed to evaluate disease severity. Liver biopsy was performed using the Knodell modified histology activity index (KmHAI). The L3 skeletal muscle index (L3SMI) was calculated to evaluate the nutrition status. Plasma PACAP concentrations were detected using ELISA. Receiver operating characteristic (ROC) curve analysis was performed to evaluate the sensitivity and specificity of PACAP for detecting the severity of liver cirrhosis. Plasma PACAP levels were found to be significantly downregulated in patients with liver cirrhosis compared with healthy controls. The case group included 38 Child–Pugh A patients, 39 Child–Pugh B patients, and 36 Child–Pugh C patients. Cirrhosis patients with Child–Pugh C had significantly lower plasma PACAP levels compared with those with Child–Pugh B and A. Cirrhosis patients with Child–Pugh B demonstrated markedly decreased plasma PACAP concentrations compared with those with Child–Pugh A. ROC curve analysis indicated that low level of plasma PACAP may act as a potential indicator for disease progression of liver cirrhosis determined by Child–Pugh classification at both compensation stage (Child–Pugh A developed to Child–Pugh B) and decompensation stage (Child–Pugh B developed to Child–Pugh C).In addition, plasma PACAP levels were inversely associated with KmHAI and ALT as well as AST levels. In both male and female patients, plasma PACAP levels were positively related to L3SMI score. Decreased plasma PACAP levels are linked with disease severity in patients with liver cirrhosis. Reduced plasma PACAP may serve as a biomarker for detection and assessment of the severity of liver cirrhosis. [ABSTRACT FROM AUTHOR]

A system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method. [ABSTRACT FROM AUTHOR]

The design and fabrication of conductive hydrogels with high stretchability, compressibility, self-healing properties and good adhesion remains a significant challenge. We have fabricated composite hydrogels by random polymerization of acrylic acid (AA) and dopamine (DA) in the presence of multi-walled carbon nanotubes (MWCNTs). The π-π interaction between DA and MWCNTs makes MWCNTs stably and homogenously dispersed in water. The fabricated PAA-PDA/CNT composite hydrogels possess relatively high mechanical strength (maximum Young's modulus: 800 kPa) and can be stretched to 1280% strain and compressed to 80% strain. The multiple hydrogen bonding formed between functional groups of PAA-PDA and MWCNTs can effectively dissipate energy and quickly achieve self-healing. The composite hydrogels also show good adhesion and can easily adhere to various inorganic or organic surfaces. In addition, the hydrogel reveals stable strain sensitivity and can be used as skin sensors. [ABSTRACT FROM AUTHOR]

Isothermal sections of the Fe-Cr-Si ternary system at 1000 and 1100 °C were studied using x-ray diffraction, scanning electron microscopy and electron probe micro-analysis. Isothermal sections were identified with seven and six three-phase regions at 1000 and 1100 °C, respectively. The σ phase contains 6.2-20.2 at.% Si at 1000 °C and 8.3-21.2 at.% Si at 1100 °C. Fe and Cr can be entirely substituted by each other to form the continuous solid-solution ε or CrSi phases. The η phase is stable at 1100 °C because of the dissolution of Cr. Additionally, large solubility was detected in some binary compounds, e.g., up to 26.6 and 19.6 at.% Fe in αCr5Si3 and Cr3Si at 1000 °C, respectively. [ABSTRACT FROM AUTHOR]

The traditional compressed sensing method for improving resolution is realized in the frequency domain. This method is affected by noise, which limits the signal-to-noise ratio and resolution, resulting in poor inversion. To solve this problem, we improved the objective function that extends the frequency domain to the Gaussian frequency domain having denoising and smoothing characteristics. Moreover, the reconstruction of the sparse reflection coefficient is implemented by the mixed L1_L2 norm algorithm, which converts the L0 norm problem into an L1 norm problem. Additionally, a fast threshold iterative algorithm is introduced to speed up convergence and the conjugate gradient algorithm is used to achieve debiasing for eliminating the threshold constraint and amplitude error. The model test indicates that the proposed method is superior to the conventional OMP and BPDN methods. It not only has better denoising and smoothing effects but also improves the recognition accuracy of thin interbeds. The actual data application also shows that the new method can effectively expand the seismic frequency band and improve seismic data resolution, so the method is conducive to the identification of thin interbeds for beach-bar sand reservoirs. [ABSTRACT FROM AUTHOR]

In this paper, the numerical solution of a nonlinear first-order singularly perturbed differential equation with integral boundary condition is considered. The discrete method is generated by a backward Euler formula and the grid is obtained by equidistributing a monitor function based on arc-length. We first give a rigorous error analysis for the numerical method of this problem on a grid that is constructed adaptively from a knowledge of the exact solution. A first-order rate of convergence, independent of the perturbation parameter, is established. Then, an a posteriori error bound and the corresponding convergence result are derived for the presented numerical scheme on an adaptive grid, which is constructed adaptively from a discrete approximation of the exact solution. At last, numerical experiments are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

A singularly perturbed Volterra integro-differential equation with an integrable singularity in the integral term is considered. The upwind difference method is used to discretize the singularly perturbed Volterra integro-differential equation. The stability properties and a posteriori error analysis for the discrete scheme are given. Since a priori information of the exact solution may be difficult to obtain, a posteriori adaptive algorithm based on a posteriori error analysis is established by equidistributing arc-length monitor function which attempts to automatically detect the singular behavior of the solution. Numerical experiments support this theoretical result. [ABSTRACT FROM AUTHOR]

The high-throughput diffusion-multiple technique and thermodynamics databases were used to design new high-strength Ti alloys. The composition–microstructure–property relationships of the Ti64–xMo alloys were obtained. The phase fraction and composition of the α and β phases of the Ti64–xMo alloys were calculated using the Thermo-Calc software. After aging at 600°C, the Ti64–6Mo alloy precipitated ultrafine α phases. This phenomenon was explained on the basis of the pseudo-spinodal mechanism by calculating the Gibbs energy curves of the α and β phases of the Ti64–xMo alloys at 600°C. Bulk forged Ti64–6Mo alloy exhibited high strength and moderate plasticity after α/β-phase-field solution treatment plus aging. The tensile properties of the alloy were determined by the size and morphology of the primary and secondary α phases and by the β grain size. [ABSTRACT FROM AUTHOR]

Biomass in karst terrain has rarely been measured because the steep mountainous limestone terrain has limited the ability to sample woody plants. Satellite observation, especially at high spatial resolution, is an important surrogate for the quantification of the biomass of karst forests and shrublands. In this study, an artificial neural network (ANN) model was built using Pléiades satellite imagery and field biomass measurements to estimate the aboveground biomass (AGB) in the Houzhai River Watershed, which is a typical plateau karst basin in Central Guizhou Province, Southwestern China. A back-propagation ANN model was also developed. Seven vegetation indices, two spectral bands of Pléiades imagery, one geomorphological parameter, and land use/land cover were selected as model inputs. AGB was chosen as an output. The AGB estimated by the allometric functions in 78 quadrats was utilized as training data (54 quadrats, 70%), validation data (12 quadrats, 15%), and testing data (12 quadrats, 15%). Data-model comparison showed that the ANN model performed well with an absolute root mean square error of 11.85 t/ha, which was 9.88% of the average AGB. Based on the newly developed ANN model, an AGB map of the Houzhai River Watershed was produced. The average predicted AGB of the secondary evergreen and deciduous broadleaved mixed forest, which is the dominant forest type in the watershed, was 120.57 t/ha. The average AGBs of the large distributed shrubland, tussock, and farmland were 38.27, 9.76, and 11.69 t/ha, respectively. The spatial distribution pattern of the AGB estimated by the new ANN model in the karst basin was consistent with that of the field investigation. The model can be used to estimate the regional AGB of karst landscapes that are distributed widely over the Yun-Gui Plateau. [ABSTRACT FROM AUTHOR]

Many numerical methods applied on a Shishkin mesh are very popular in solving the singularly perturbed problems. However, few approaches are used to obtain the Shishkin mesh transition parameter. Thus, in this paper, we first use the cubic B-spline collocation method on a Shishkin mesh to solve the singularly perturbed convection-diffusion problem with two small parameters. Then, we transform the Shishkin mesh transition parameter selection problem into a nonlinear unconstrained optimization problem which is solved by using the self-adapting differential evolution (jDE) algorithm. To verify the performance of our presented method, a numerical example is employed. It is shown from the experiment results that our approach is efficient. Compared with other evolutionary algorithms, the jDE algorithm performs better and with more stability. [ABSTRACT FROM AUTHOR]

On the basis of considering the heterogeneity and using the finite element numerical simulation, this thesis investigates the damage of the roof and coal as well as the failure of evolutionary process during the re-exploitation of the residual coal. According to the analysis of the damage field, stress field and the failure process, it explores the damage evolution, stress distribution laws and the damage models. Besides, this thesis puts forward the idea of penetrating and establishing drilling steels aimed at solving the problem of wall carving and roof fall, meanwhile this suggestion accomplishes the successful application effect in the testing ground. This thesis demonstrates that the re-exploitation of the residual coal can be carried out and the safe production can be ensured by adopting some measures. What’s more, the research result provides the theoretical and practical experience for the re-exploitation of the residual coal in the similar conditions. [ABSTRACT FROM AUTHOR]

In this paper, a system of singularly perturbed Volterra integro-differential equations is considered. The backward Euler formula is used to discretize the differential part and the right-hand rectangle rule is applied to approximate the integral term. The stabilities of the continuous and discrete solutions are carried out using the Grönwall's inequality, respectively. The a posterior error bounds are given to design an adaptive grid generation algorithm. Numerical results complement the theoretical results. [ABSTRACT FROM AUTHOR]

The isothermal section of Ag-Ti-Zr ternary system at 1023 K was determined by diffusion triple and electron probe microanalysis. The results indicate that four binary intermetallic phases of AgTi, AgTi2, AgZr and AgZr2 are found in Ag-Ti-Zr ternary system at 1 023 K. AgZr2 and AgTi2 form a continuous solid solution, namely Ag(Ti,Zr)2. Four three-phase regions: AgTi + AgZr + Ag, AgTi + AgZr + Ag (Ti, Zr)2, α-Zr+β(Ti, Zr) + Ag (Ti, Zr)2 and α-Ti + β(Ti, Zr) + Ag (Ti, Zr)2 exist in the isothermal section. No ternary compound is observed. [ABSTRACT FROM AUTHOR]

The original version of this article unfortunately contained a mistake. [ABSTRACT FROM AUTHOR]

In this paper, we propose a numerical scheme for a system of two linear singularly perturbed parabolic convection-diffusion equations. The presented numerical scheme consists of a classical backward-Euler scheme on a uniform mesh for the time discretization and an upwind finite difference scheme on an arbitrary nonuniform mesh for the spatial discretization. Then, for the time semidiscretization scheme, an a priori and an a posteriori error estimations in the maximum norm are obtained. It should be pointed out that the a posteriori error bound is suitable to design an adaptive algorithm, which is used to generate an adaptive spatial grid. It is proved that the method converges uniformly in the discrete maximum norm with first-order time and spatial accuracy, respectively, for the fully discrete scheme. At last, some numerical results are given to validate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the stability and accuracy of a streamline diffusion finite element method (SDFEM) for the singularly perturbed differential-difference equation of convection term with a small shift is considered. With a special choice of the stabilization quadratic bubble function and by using the discrete Green’s function, the new method is shown to have an optimal second order in the sense that ‖u-uh‖∞≤Cinfvh∈Vh‖u-vh‖∞, where uh is the SDFEM approximation of the exact solution u in linear finite element space Vh. At last, a second order uniform convergence result for the SDFEM is obtained. Numerical results are given to confirm the ε-uniform convergence rate of the nodal errors. [ABSTRACT FROM AUTHOR]