Improvement of proteome coverage using hydrophobic monolithic columns in shotgun proteome analysis

Monolithic columns are widely used in shotgun proteome analysis. However, it is difficult to increase the separation capability and proteome coverage by using conventionally organic polymer-based monolithic column due to the difficulty of controlling homogeneity of the overall pore structure (both pores and microglobules), which leads to relatively low column efficiency. Therefore, we studied the effect of constitute and percentage of porogenic solvent, functional monomer, column length, and separation gradient on the peak capacity and proteome coverage by methacrylate-based reversed phase monolithic columns. It was demonstrated that the porous property of the hydrophobic monolith, which was mainly determined by the porogenic solvent, was crucial to the proteome coverage when similar methacrylate monomer was utilized and a ternary porogenic solvent was adopted to prepare C12 monolithic column with relatively homogeneous overall pore structure. It was also shown that high proteome coverage could be reliably obtained with online multidimensional separation using totally monolithic columns system with the length of analytical column at 85 cm and reversed phase separation gradient at 210 min.     

一类Gauss-Jacobi数值求积公式的极限性质

讨论了形如∫aa+h(x-a)βf(x)dx的Gauss-Jacobi求积公式,当积分区间长度趋向于零时,确定了求积公式的余项中介点η的渐近性,并给出了校正公式,比原公式提高了两次代数精度.此外,本文的结论包含了文[3]的结果.     

AN EFFICIENT ADER DISCONTINUOUS GALERKIN SCHEME FOR DIRECTLY SOLVING HAMILTON-JACOBI EQUATION

This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.     

A HIGH-ORDER ACCURACY METHOD FOR SOLVING THE FRACTIONAL DIFFUSION EQUATIONS

In this paper, an efficient numerical method for solving the general fractional diffusion equations with Riesz fractional derivative is proposed by combining the fractional compact difference operator and the boundary value methods. In order to efficiently solve the generated linear large-scale system, the generalized minimal residual (GMRES) algorithm is applied. For accelerating the convergence rate of the iterative, the Strang-type, Chan-type and P-type preconditioners are introduced. The suggested method can reach higher order accuracy both in space and in time than the existing methods. When the used boundary value method is $A_{k1,k2}$-stable, it is proven that Strang-type preconditioner is invertible and the spectra of preconditioned matrix is clustered around 1. It implies that the iterative solution is convergent rapidly. Numerical experiments with the absorbing boundary condition and the generalized Dirichlet type further verify the efficiency.     

A new approach of a limiting process for multi-dimensional flows

An enhanced Multi-dimensional Limiting Process (e-MLP) is developed for the accurate and efficient computation of multi-dimensional flows based on the Multi-dimensional Limiting Process (MLP). The new limiting process includes a distinguishing step and an enhanced multi-dimensional limiting process. First, the distinguishing step, which is independent of high order interpolation and flux evaluation, is newly introduced. It performs a multi-dimensional search of a discontinuity. The entire computational domain is then divided into continuous, linear discontinuous and nonlinear discontinuous regions. Second, limiting functions are appropriately switched according to the type of each region; in a continuous region, there are no limiting processes and only higher order accurate interpolation is performed. In linear discontinuous and nonlinear discontinuous regions, TVD criterion and MLP limiter are respectively used to remove oscillation. Hence, e-MLP has a number of advantages, as it incorporates useful features of MLP limiter such as multi-dimensional monotonicity and straightforward extensionality to higher order interpolation. It is applicable to local extrema and prevents excessive damping in a linear discontinuous region through application of appropriate limiting criteria. It is efficient because a limiting function is applied only to a discontinuous region. In addition, it is robust against shock instability due to the strict distinction of the computational domain and the use of regional information in a flux scheme as well as a high order interpolation scheme. This new limiting process was applied to numerous test cases including one-dimensional shock/sine wave interaction problem, oblique stationary contact discontinuity, isentropic vortex flow, high speed flow in a blunt body, planar shock/density bubble interaction, shock wave/vortex interaction and, particularly, magnetohydrodynamic (MHD) cloud-shock interaction problems. Through these tests, it was verified that e-MLP substantially enhances the accuracy and efficiency with both continuous and discontinuous multi-dimensional flows.     

A stable and high-order accurate conjugate heat transfer problem

This paper analyzes well-posedness and stability of a conjugate heat transfer problem in one space dimension. We study a model problem for heat transfer between a fluid and a solid. The energy method is used to derive boundary and interface conditions that make the continuous problem well-posed and the semi-discrete problem stable. The numerical scheme is implemented using 2nd-, 3rd- and 4th-order finite difference operators on Summation-By-Parts (SBP) form. The boundary and interface conditions are implemented weakly. We investigate the spectrum of the spatial discretization to determine which type of coupling that gives attractive convergence properties. The rate of convergence is verified using the method of manufactured solutions.     

海表白冠覆盖率的散射计资料反演研究

针对波浪破碎海况,采用考虑波浪破碎的KHCC03散射模式和散射计卫星遥感资料,对白冠覆盖率进行了反演研究,并得到了白冠覆盖率的反演公式.经检验,在10 m高度处风速取值为7 m/s—16 m/s时,利用文中给出的公式得到的白冠覆盖率反演结果与实测数据相比,优于以往其他计算公式的对应结果.这表明,利用散射计资料和波浪破碎的散射模式,可以反演白冠覆盖率.而且,这种方法不同于人们通常采用的被动遥感方法. 关键词： 白冠覆盖率 KHCC03散射模式 波浪破碎     

Effect of media-induced modification of travel rates on disease transmission in a multiple patch setting

A general SIS epidemic model is formulated that incorporates media-induced modification of travel rates. Basic local properties of solutions to the model are established. In particular, it is shown that the basic reproduction number does not involve parameters related to the effect of media on travel. The general model is subsequently specialised to two-patch models, with two different scenarios regarding patch population size. Qualitative analyses show that the basic reproduction number acts as a sharp threshold between disease persistence and extinction. The concept of uniform weak persistence is used to prove the existence of an endemic equilibrium and disease uniform strong persistence under a certain condition. Numerical investigations are carried out to gain insight into the analytically tractable and intractable cases, highlighting the importance of considering not only the basic reproduction number but also other measures of disease severity.     

High-order compact solution of the one-dimensional heat and advection–diffusion equations

In this work, we propose a high-order accurate method for solving the one-dimensional heat and advection–diffusion equations. We apply a compact finite difference approximation of fourth-order for discretizing spatial derivatives of these equations and the cubic C¹$C^1$-spline collocation method for the resulting linear system of ordinary differential equations. The cubic C¹$C^1$-spline collocation method is an A-stable method for time integration of parabolic equations. The proposed method has fourth-order accuracy in both space and time variables, i.e. this method is of order O(h⁴,k⁴)$O(h^4\text{,}{k}^4)$. Additional to high-order of accuracy, the proposed method is unconditionally stable which will be proved in this paper. Numerical results show that the compact finite difference approximation of fourth-order and the cubic C¹$C^1$-spline collocation method give an efficient method for solving the one-dimensional heat and advection–diffusion equations.