An integrated multipath liquid chromatography–mass spectrometry system for the simultaneous preparation,separation, and detection of proteins and small molecules

A multipath liquid chromatography with mass spectrometry instrument was constructed with the help of restricted access media to online segregate small and large molecules. This liquid chromatography system was custom built with five pumps and three two‐position six‐port valves to control the flow in a multipath system for the simultaneous analysis of small molecules and proteins. On separate chromatographic channels, small molecules trapped and proteins excluded from the online restricted access media were analyzed downstream using high‐efficiency columns and a triple quadrupole mass spectrometer. A model sample, which included five proteins and 22 small molecules with different physicochemical properties, was used to evaluate the system. Following injection, the complete multipath separation and detection was performed in 22 min. Protein exclusion by the restricted access media was not quantitative. Four commercial trap columns were evaluated for their exclusion efficiency toward the proteins. Exclusion efficiency varied from <50% to only a maximum of 75% exclusion across the trap columns tested. An attempt was made to optimize the exclusion efficiency using different flow rates, flow rate gradients, and different additives both in the sample and the mobile phases. Protein exclusion was still erratic and generally nonquantitative.     

Embedding theorem ofZ-graded Lie superalgebras

The embedding theorem ofZ-graded Lie superalgebras is given and proved. As a subsidiary result it is proved that a transitiveZ-graded restricted lie superalgebm must be isomorphic toW(m,n, 1) if the dimension ofG _i satisfies a certain condition. Project supported by the National Natural Science Foundation of China and the Science of the University Doctoral Program of CNEC.     

Enumeration of maximal subalgebras in free restricted lie algebras

Given a finitely generated restricted Lie algebra L over the finite field \(\mathbb{F}_q \), and n ≥ 0, denote by a _n (L) the number of restricted subalgebras H ? L with \(\dim _{\mathbb{F} _q} \) L/H = n. Denote by ã _n (L) the number of the subalgebras satisfying the maximality condition as well. Considering the free restricted Lie algebra L = F _d of rank d ≥ 2, we find the asymptotics of ã _n (F _d ) and show that it coincides with the asymptotics of a _n (F _d ) which was found previously by the first author. Our approach is based on studying the actions of restricted algebras by derivations on the truncated polynomial rings. We establish that the maximal subalgebras correspond to the so-called primitive actions. This means that “almost all” restricted subalgebras H ? F _d of finite codimension are maximal, which is analogous to the corresponding results for free groups and free associative algebras.     

On list‐coloring outerplanar graphs

We prove that a 2‐connected, outerplanar bipartite graph (respectively, outerplanar near‐triangulation) with a list of colors L (v ) for each vertex v such that (resp., ) can be L‐list‐colored (except when the graph is K₃ with identical 2‐lists). These results are best possible for each condition in the hypotheses and bounds. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 59–74, 2008     

List colorings with measurable sets

The measurable list chromatic number of a graph G is the smallest number ξ such that if each vertex v of G is assigned a set L(v) of measure ξ in a fixed atomless measure space, then there exist sets such that each c(v) has measure one and for every pair of adjacent vertices v and v'. We provide a simpler proof of a measurable generalization of Hall's theorem due to Hilton and Johnson [J Graph Theory 54 (2007), 179–193] and show that the measurable list chromatic number of a finite graph G is equal to its fractional chromatic number. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 229–238, 2008     

Simplified Box Orbitals (SBO) for H To Ar atoms: Exact expressions,SBO‐3G approximations,and relations with the ZDO approximation

Simplified Box Orbitals (SBO) are a kind of spatially restricted basis functions. SBOs have a similar use and value to Slater functions but, because they fulfill a version of the zero‐differential overlap approximation, they allow for a drastic reduction in the number of two‐electron integrals to be calculated when dealing with huge systems, and they seem to be specially adapted to study confined systems such as molecules in solution. In a previous study, the mathematical shape of SBOs was discussed and the necessary parameters were obtained by means of the variational method. In the present study, the parameters of each SBO were obtained by applying the condition that it is as similar as possible to the STO that would be used in a basis set without spatial restrictions. We have developed a method to achieve this likeness and deduced simple formulas to describe all the SBOs of any atom. We also present the SBO‐3G expansions of the SBOs obtained, making it possible to use these SBOs with standard quantum chemistry calculation software. Simple formulas were also deduced to directly write the SBOs and SBO‐3G corresponding to the atoms with a Z value of between 1 and 18. Finally, as a first example of the usefulness of this kind of functions, an optimized SBO‐3G basis set is proposed for atoms from H to Cl in molecules. © 2016 Wiley Periodicals, Inc.     

基于几何差异的目标识别算法

为降低目标识别算法复杂性且提高其抗噪能力,提出一种基于几何特征差异的目标识别算法。将获取到的目标图片经图像处理后提取轮廓,并以最小周长多边形算法构造目标轮廓的近似多边形;然后根据模板库标准目标做放大或缩小处理后使其面积与模板面积相等;再使用摆放算法使其与模板库图形部分重合;并提出一种改进型双向链表算法求多边形相交部分,通过计算相交部分面积大小达到识别图像的目的。经过仿真实验验证了此方法简单易行,能够快速识别目标。     

A simple algorithm to accelerate the computation of non-bonded interactions in cell-based molecular dynamics simulations

Cell lists are ubiquitous in molecular dynamics simulations--be it for the direct computation of short-range inter-atomic potentials, the short-range direct part of a long-range interaction or for the periodic construction of Verlet lists. The conventional approach to computing pairwise interactions using cell lists leads to a large number of unnecessary interparticle distance calculations. In this paper, an algorithm is presented which reduces the number of spurious distance calculations by first sorting the particles along the cell pair axis and then only interacting two particles if their distance along the axis is smaller than the cutoff distance of the interaction. This approach is shown to be more efficient than the conventional approach and similar approaches using smaller cells.     

Complexity issues on bounded restrictive H-coloring

We consider a bounded version of the restrictive and the restrictive list H-coloring problem in which the number of pre-images of certain vertices of H is taken as parameter. We consider the decision and the counting versions, as well as, further variations of those problems. We provide complexity results identifying the cases when the problems are NP-complete or #P-complete or polynomial time solvable. We conclude stating some open problems.     

Chains in Critical Fluids and Nanopores

Summary: The conformational behavior of a polymer in a critical binary solvent confined in a porous medium is studied. The size of the polymer in bulk, which is mainly governed by the correlation length of the solvent density fluctuations, depends on the proximity to the critical point of the binary mixture. We find that in contrast to the bulk behavior, the conformational properties of the polymer in a porous medium depends strongly on the pore size. The latter controls the correlation length of the solvent density fluctuations and thus determines the polymer size.