Identities of symmetry for higher-order Euler polynomials in three variables (II)

We derive twenty five basic identities of symmetry in three variables related to higher-order Euler polynomials and alternating power sums. This demonstrates that there are abundant identities of symmetry in three-variable case, in contrast to two-variable case, where there are only a few. These are all new, since there have been results only about identities of symmetry in two variables. The derivations of identities are based on the p-adic integral expression of the generating function for the higher-order Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the alternating power sums.     

Cyclic sum of certain parametrized multiple series

In the present paper, we prove the cyclic sum formulas for certain parametrized multiple series.     

Minimum sum set coloring of trees and line graphs of trees

In this paper, we study the minimum sum set coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersection of sets assigned to adjacent vertices is empty and the sum of the assigned set of numbers to each vertex of the graph is minimum. The MSSC problem occurs in two versions: non-preemptive and preemptive. We show that the MSSC problem is strongly NP-hard both in the preemptive case on trees and in the non-preemptive case in line graphs of trees. Finally, we give exact parameterized algorithms for these two versions on trees and line graphs of trees.     

一类非平稳高斯序列超过数点过程与和的渐近性

设{X_i}_(i=1)~∞是标准化非平稳高斯序列,N_n为X_1,X_2,…,X_n依次对水平μ_(n1),μ_(n2),…,μ_(nn)的超过数形成的点过程.记Υ_(ij)=X_iX_j,S_n=■X_i.当Υ_(ij)满足一定条件时,证明了N_n依分布收敛到Poisson过程,且N_n与S_n渐近独立.     

广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)

利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式.     

特征和序列C(A,i)的性质

首次引入前缀码的特征和序列的概念,讨论了它的一些性质,并给出了极大前缀码的一些性质.     

在容量较小的污染环境中二维捕食系统的持续生存与绝灭

利用极限理论及积分均值法研究了在容量较小的污染环境中毒素对二维Lotka-Volterra捕食被捕食系统持续生存与绝灭的影响,给出了捕食种群与食饵种群弱平均持续生存和绝灭的充分条件.     

二次李三系的分解定理

有限维李三系称为二次的,如果它容许一个非退化的不变对称双线性型.无论是李三系分解为不可分解理想的直和,还是二次李三系分解为不可分解非退化理想的正交直和,证明了这两类分解在同构意义下都是唯一的.     

Effects of first dimension eluent composition in two-dimensional liquid chromatography

Comprehensive two-dimensional liquid chromatography (LC×LC) has received a great deal of attention during the past few years because of its extraordinary resolving power. The biggest advantage of this technique is that very high peak capacities can be generated in a relatively short time. Numerous approaches to maximize the peak capacity in LC×LC have been employed. In this work we investigate the impact of the first dimension mobile phase on selectivity. LC×LC has several potential advantages over one-dimensional LC (1DLC) in that unconventional solvents, at least in reversed-phase LC, can be used. For example, solvents which strongly adsorb in the UV in the first dimension are not problematic in LC×LC. This so because the UV detector is placed after the second dimensional column, as pulses of the first dimension eluent arrive at the second dimensional column, they elute well before the solutes of interest and therefore do not interfere at all with detection of solute peaks. So far, the most widely used solvents in reversed-phase 1DLC are methanol and acetonitrile. However, the "UV advantage" of 2DLC allows us to employ UV active solvents, such as acetone. We compare their differential selectivities to that of acetonitrile for the separation of 23 indole acetic acids of interest in plant biology. We also apply them to the separation of a maize seed extract, a very complex sample. In both sample sets, mobile phase composition can be an important parameter to increase the orthogonality of the two dimensions and thus, to increase the effective peak capacity of LC×LC.     

Ultra-high capacity liquid chromatography chip/quadrupole time-of-flight mass spectrometry for pharmaceutical analysis

Nanoflow liquid chromatography/mass spectrometry (nano-LC/MS) has attracted increasing interest in virtue of high sensitivity, low sample consumption, and minimal matrix effect. In this work a HPLC-Chip/quadrupole time-of-flight (Q-TOF) MS device with a new ultra-high capacity small molecule chip (UHC-Chip) which features a 500 nL enrichment column and a 150 mm × 75 μm analytical column, was evaluated with a drug mixture covering a wide range of polarities. Excellent chromatographic precision with 0.1-0.5% RSD for retention time and 1.7-9.0% RSD for peak area, low limit of detection, good chip-to-chip reproducibility and linearity were obtained by using this UHC-Chip. Compared with the standard HPLC-Chip with 40 nL trapping column, the UHC-Chip showed higher enrichment capability and hence gave a higher response in signal detection. Additionally, 4-30 times increase in sensitivity was obtained compared with conventional LC/MS, which indicated that UHC-Chip/MS was a valuable tool for the quantitative analysis of low level impurities and degradation products in pharmaceuticals. Moreover, satisfactory results obtained from trace drug analysis of serum samples further proved its practicality and potential for use in drug testing and development.