Flow pattern analysis of linear gradient flow distribution

This paper uses the Oseen transformation to solve the differential equations governing motion of the vertical linear gradient flow distribution close to a wall surface. The Navier-Stokes equations are used to consider the inertia term along the flow direction. A novel contour integral method is used to solve the complex Airy function. The boundary conditions of linear gradient flow distribution for finite problems are determined. The vorticity function, the pressure function, and the turbulent velocity profiles are provided, and the stability of particle trajectories is studied. An Lx-function form of the third derivative circulation is used to to simplify the solution. Theoretical results are compared with the experimental measurements with satisfactory agreement.

Accurate assessment of antibiotic susceptibility and screening resistant strains of a bacterial population by linear gradient plate

The dynamics of a bacterial population exposed to the minimum inhibitory concentration （MIC） of an antibiotic is an important issue in pharmacological research. Therefore, a novel antibiotic susceptibility test is urgently needed that can both precisely determine the MIC and accurately select antibiotic-resistant strains from clinical bacterial populations. For this purpose, we developed a method based on Fick＇s laws of diffusion using agar plates containing a linear gradient of antibiotic. The gradient plate contained two layers. The bottom layer consisted of 15 mL agar containing the appropriate concentration of enrofloxacin and allowed to harden in the form of a wedge with the plate slanted such that the entire bottom was just covered. The upper layer consisted of 15 mL plain nutrient agar added with the plate held in the horizontal position. After allowing vertical diffusion of the drug from the bottom agar layer for 12 h, the enrofloxacin concentration was diluted in proportion to the ratio of the agar layer thicknesses. The uniform linear concentration gradient was verified by measuring the enrofloxacin concentration on the agar surface. When heavy bacterial suspensions were spread on the agar surface and incubated for more than 12 h, only resistant cells were able to form colonies beyond the boundary of confluent growth of susceptible cells. In this way, the true MIC of enrofloxacin was determined. The MICs obtained using this linear gradient plate were consistent with those obtained using conventional antibiotic susceptibility tests. Discrete colonies were then spread onto a gradient plate with higher antibiotic concentrations; the boundary line increased significantly, and gene mutations conferring resistance were identified. This new method enables the rapid identification of resistant strains in the bacterial population. Use of the linear gradient plate can easily identify the precise MIC and reveal the dynamic differentiation of bacteria near the MIC. This method allows the study of genetic and physiological characteristics of individual strains, and may be useful for early warning of antibiotic resistance that may occur after use of certain antirnicrobial agents, and guide clinical treatment.

A Node-Based Smoothed Finite Element Method with Linear Gradient Fields for Elastic Obstacle Scattering Problems

In this paper,a node-based smoothed finite element method(NS-FEM)with linear gradient fields(NS-FEM-L)is presented to solve elastic wave scattering by a rigid obstacle.By using Helmholtz decomposition,the problem is transformed into a boundary value problem with coupled boundary conditions.In numerical analysis,the perfectly matched layer(PML)and transparent boundary condition(TBC)are introduced to truncate the unbounded domain.Then,a linear gradient is constructed in a node-based smoothing domain(N-SD)by using a complete order of polynomial.The unknown coefficients of the smoothed linear gradient function can be solved by three linearly independent weight functions.Further,based on the weakened weak formulation,a system of linear equation with the smoothed gradient is established for NS-FEM-L with PML or TBC.Some numerical examples also demonstrate that the presented method possesses more stability and high accuracy.It turns out that the modified gradient makes the NS-FEM-L-PML and NS-FEM-L-TBC possess an ideal stiffness matrix,which effectively overcomes the instability of original NS-FEM.Moreover,the convergence rates of L 2 and H1 semi-norm errors for the two NS-FEM-L models are also higher.

The principle of optimization of binary mobile phase composition of multi-step linear gradient elution

The basic principle of optimal method called “moving overlapping resolution mapping Method” to select the optimal binary mobile phase composition of multi-step linear gradient liquid chromatography is discussed with simultaneously considering effects of position of solute inside the column and mobile phase composition on peak resolution and retention value, then a BASIC program based on this principle is developed in IBM-PC computer. The validities of both principle of optimization and BASIC program are confirmed by separation of samples Containing bile acids and PAHs in RP-HPLC.

C^1 natural element method for strain gradient linear elasticity and its application to microstructures

C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.

GRADIENT ESTIMATES AND LIOUVILLE THEOREMS FOR LINEAR AND NONLINEAR PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

In this article, we will derive local elliptic type gradient estimates for positive solutions of linear parabolic equations （△-e/et）u（x,t）＋q（x,t）u^p（x,t）=0 and nonlinear parabolic equations （△-e/et）u（x,t）＋h（x,t）u^p（x,t）=0（p 〉 1） on Riemannian manifolds.As applications, we obtain some theorems of Liouville type for positive ancient solutions of such equations. Our results generalize that of Souplet-Zhang （[1], Bull. London Math. Soc. 38（2006）, 1045-1053） and the author （[2], Nonlinear Anal. 74 （2011）, 5141-5146）.

Multi-segment linear gradient optimization strategy based on resolution map in HPLC

Based on the mechanism of chromatographic retention (the relationship between the retention of solute and the mobile phase conditions) and method of resolution map, several methods of optimizing multi-segment linear gradient elution conditions were proposed according to the different separation requirements of various samples. These methods were verified using literature data. Moreover, the advantages and disadvantages of these methods were compared. It was proved that the third method is a fast optimization method which is capable of separating all the components with relatively high resolution.

Linear Regression and Gradient Descent Method for Electricity Output Power Prediction

Regulating the power output for a power plant as demand for electricity fluctuates throughout the day is important for both economic purpose and the safety of the generator. In this work, gradient descent method together with regularization is investigated to study the electricity output related to vacuum level and temperature in the turbine. Ninety percent of the data was used to train the regression parameters while the remaining ten percent was used for validation. Final results showed that 99% accuracy could be obtained with this method. This opens a new window for electricity output prediction for power plants.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

A New Conjugate Gradient Projection Method for Solving Stochastic Generalized Linear Complementarity Problems

In this paper, a class of the stochastic generalized linear complementarity problems with finitely many elements is proposed for the first time. Based on the Fischer-Burmeister function, a new conjugate gradient projection method is given for solving the stochastic generalized linear complementarity problems. The global convergence of the conjugate gradient projection method is proved and the related numerical results are also reported.

GLOBAL CONVERGENCE RESULTS OF A THREE TERM MEMORY GRADIENT METHOD WITH A NON-MONOTONE LINE SEARCH TECHNIQUE

In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.

Robust Lane Detection in Shadows and Low Illumination Conditions using Local Gradient Features

This paper presents a method for lane boundaries detection which is not affected by the shadows, illumination and un-even road conditions. This method is based upon processing grayscale images using local gradient features, characteris-tic spectrum of lanes, and linear prediction. Firstly, points on the adjacent right and left lane are recognized using the local gradient descriptors. A simple linear prediction model is deployed to predict the direction of lane markers. The contribution of this paper is the use of vertical gradient image without converting into binary image(using suitable thre-shold), and introduction of characteristic lane gradient spectrum within the local window to locate the preciselane marking points along the horizontal scan line over the image. Experimental results show that this method has greater tolerance to shadows and low illumination conditions. A comparison is drawn between this method and recent methods reported in the literature.

Fully Nonlinear Boussinesq-Type Equations with Optimized Parameters for Water Wave Propagation

For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with pad6 approximation.

A NEW GRADIENT PROJECTION METHOD AND ITS CONVERGENCE

In this paper, by using a new projection, we construct a variant of Zhang’s algorithm and prove its convergence. Specially, the variant of Zhang’s algorithm has quadratic termination and superlinear convergence rale under certain conditions. Zhang’s algorithm hasn’t these properties.

PROPERTIES AND ALGORITHM ON PRECONDITIONED CONJUGATE GRADIENT METHOD

Some properties of the preconditioned gradient conjugate method are given.It may happen that loss of significant digits, when the norm of residual is very small. To avoid this, a variant algorithm which does not use the residual is put forward.

Global Convergence of a Hybrid Conjugate Gradient Method

Conjugate gradient method is one of successful methods for solving the unconstrained optimization problems. In this paper, absorbing the advantages of FR and CD methods, a hybrid conjugate gradient method is proposed. Under the general Wolfe linear searches, the proposed method can generate the sufficient descent direction at each iterate,and its global convergence property also can be established. Some preliminary numerical results show that the proposed method is effective and stable for the given test problems.

Spectral Gradient Algorithm Based on the Generalized Fiser-Burmeister Function for Sparse Solutions of LCPS

This paper considers the computation of sparse solutions of the linear complementarity problems LCP(q, M). Mathematically, the underlying model is NP-hard in general. Thus an lp(0 p < 1) regularized minimization model is proposed for relaxation. We establish the equivalent unconstrained minimization reformation of the NCP-function. Based on the generalized Fiser-Burmeister function, a sequential smoothing spectral gradient method is proposed to solve the equivalent problem. Numerical results are given to show the efficiency of the proposed method.

一种基于线性零磁场的动脉血管扫描成像方法仿真

基于磁电耦合效应的血流检测及血管成像是实现心血管疾病早期诊疗的有效方法之一。该文基于磁场与血流耦合电效应,设计一种用于动脉血管扫描成像的组合线圈结构,产生带有零磁场线(FFL)区域的线性梯度磁场;在此结构的基础上,通过控制激励电流驱动FFL实现成像区域双向扫描;结合卷积神经网络(CNN)实现磁电耦合信号与血管信息的非线性映射,进而提出一种基于线性零磁场的动脉血管扫描成像新方法。采用多物理场仿真软件COMSOL对基于线性零磁场的血管扫描成像方法进行建模,求解磁电耦合信号,验证了所提出方法的合理性和有效性。结果表明,线性梯度磁场模式下的磁电耦合信号含有血管位置、半径等信息;CNN重建血管位置误差平均值为1.5694 mm,重建血管半径的方均误差(MSE)和相关系数(CC)平均值分别为0.0548和0.9870。研究结果可用于血管成像装置设计及后续相关临床应用提供研究支撑。

考虑用户负荷率因素的电力市场偏差电量定价方法

针对偏差电量定价中尚未考虑用户的负荷率变化,导致电力交易各方的经济利益不均衡问题,提出考虑用户负荷率因素的电力市场偏差电量定价方法。以售电量时间序列为基准,完成基于多元线性回归的电力市场售电量预测。在此基础上,建立基于月用电量偏差率的惩罚机制,考虑负荷率和偏差率的变化确定对应偏差电量的电价。通过某区域电力市场交易数据试验,负荷率的波动直接影响购电公司收益,提出的偏差电量定价方法能够降低偏差考核电费对整体收益的影响,规范电量市场交易行为,在一定程度上均衡用户和售电企业各方的利益。

超高效液相色谱在洗洁精表面活性剂检测中的应用

为了能够更加精准地检测洗洁精表面活性剂含量,提出超高效液相色谱在洗洁精表面活性剂检测中的应用研究。考虑到大部分洗洁精应用的表面活性物质均为甜菜碱或氧化胺类物质,设置了以甜菜碱和氧化胺类物质为核心的超高效液相色谱试剂,选择U3000高效液相色谱仪,日本新宇宙XP-302M电雾式检测器以及Acclaim Surfactant Plus分析柱作为具体的测试装置,对测试环境温度和U3000高效液相色谱仪的流速进行定值设置后,按照乙腈洗脱执行梯度对色谱柱进行处理后,将满足线性范畴的数据作为计算洗洁精表面活性剂含量的基础参数,带入到回归方程中,确定各表面活性剂含量,对应的检测结果误差稳定在0.015%以内,单一类别洗洁精表面活性剂含量检测结果误差稳定在0.003%以内。