Coloring mixed hypertrees

A mixed hypergraph is a triple (V,C,D) where V is its vertex set and C and D are families of subsets of V, called C-edges and D-edges, respectively. For a proper coloring, we require that each C-edge contains two vertices with the same color and each D-edge contains two vertices with different colors. The feasible set of a mixed hypergraph is the set of all k's for which there exists a proper coloring using exactly k colors. A hypergraph is a hypertree if there exists a tree such that the edges of the hypergraph induce connected subgraphs of the tree.We prove that feasible sets of mixed hypertrees are gap-free, i.e., intervals of integers, and we show that this is not true for precolored mixed hypertrees. The problem to decide whether a mixed hypertree can be colored by k colors is NP-complete in general; we investigate complexity of various restrictions of this problem and we characterize their complexity in most of the cases.     

具有唯一4度最大度点的图的全色数

一个图Ｇ的全色数χ_T（Ｇ）是使得Ｖ（Ｇ）∪Ｅ（Ｇ）中相邻或相关联元素均染不同颜色的最少颜色数．文中证明了，若图Ｇ只有唯一的一个４度最大度点，则χ_T（Ｇ）＝Δ（Ｇ）＋１．     

Complete assignments of 1H and 13C NMR data for 10 phenylethanoid glycosides

Ten phenylethanoid glycosides, including two new ones, isolated from the aerial parts of the mangrove plant Acanthus ilicifolius were identified. The first complete assignments of the 1H and 13C NMR chemical shifts for these glycosides were achieved by means of 2D NMR techniques, including 1H-1H COSY, TOCSY, HSQC and HMBC spectra.     

On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Two-dimensional commensurate soliton structures

A phase diagram of pinned soliton structures in two dimensions has been found for a repulsive interactionU(x) between solitons withU(x)>0. The critical fugacity of the commensurate soliton structure is shown to be proportional toU(l), wherel is the period of this structure.     

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.     

A study for quality evaluation of Taxilli Herba from different hosts based on fingerprint-activity relationship modeling and multivariate statistical analysis

In this study, a fingerprint-activity relationship modeling between chemical fingerprints and antirheumatic activity was established, and multivariate statistical analysis was used to evaluate the quality of Taxilli Herba (TH) from different hosts. Characteristic fingerprints of 20 batches of TH samples were generated by high-performance liquid chromatography coupled with triple quadrupole-time of flight tandem mass spectrometry (HPLC-Triple TOF-MS/MS), and the similarity analysis was calculated based on thirteen common characteristic peaks by hierarchical clustering analysis (HCA). Subsequently, nine efficacy markers were discovered by combining fingerprints and antirheumatic activity through grey correlation analysis (GCA) and bivariate correlation analysis (BCA). Meanwhile, the content of 5 constituents in 9 markers was determined by high-performance liquid chromatography coupled with triple quadrupole-linear ion trap tandem mass spectrometry (HPLC-QTRAP-MS/MS). The comprehensive quality of TH was assessed using multivariate statistical analysis, including principal components analysis (PCA) and technique for order preference by similarity to ideal solution (TOPSIS). The results showed that a high dose of TH extract could markedly ameliorate arthritis damage compared to other doses, with flavonoids playing an important role in the antirheumatic activity. The comprehensive quality of samples from Morus alba L. (SS) was superior to those from Liquidambar formosana Hance (FXS). The present study will demonstrate the markers associated with efficacy, and provide an applicable strategy for more comprehensive quality control and evaluation of TH.     

关于两两NQD列的若干极限性质

本文讨论了两两ＮＱＤ列的Ｍａｒｃｉｎｋｉｅｗｉｃｚ型弱大数律及Ｊａｍｉｓｏｎ型加权和的强稳定性，指出了两两ＮＱＤ列与独立列的一个本质性区别，从而提出了解决两两ＮＱＤ旬几乎处处收敛和完全收敛的一种方式。     

Heat Capacity Estimation Using a Complete Set of Homodesmotic Reactions for Organic Compounds

Reliable information about isobaric heat capacities C_P is necessary to determine the energies of organic compounds and chemical processes at an arbitrary temperature. In this work, the possibility of theoretical estimation of C_P by the homodesmotic method is analyzed. Three cases of C_P calculation applying the methodology of the complete set of homodesmotic reactions (CS HDRs) are considered: the gas- and liquid-phase C_P of organic compounds of various classes at 298 K (the mean absolute value of reaction heat capacity, MA ΔC_P = 1.44 and 2.83 J/mol·K for the gas and liquid phase, correspondingly); and the gas-phase C_P of n-alkanes C₂–C₁₀ in the temperature range of 200–1500 K with an average error in calculating the heat capacity of 0.93 J/mol·K. In the latter case, the coefficients of the Shomate equation are determined for all n-alkanes that satisfy the homodesmoticity condition. New values of gas- and liquid-phase heat capacities are obtained for 41 compounds. The CS HDRs-based approach for estimating the C_P of organic compounds is characterized by high accuracy, which is not inferior to that of the best C_P-additive schemes and allows us to analyze the reproducibility of the calculation results and eliminate unreliable reference data.     

水中硝基苯胺类化合物酶免疫化学分析技术研究

采用戊二醛法, 将4-硝基苯乙胺与牛血清蛋白(BSA)和卵清蛋白(OVA)共价偶联, 分别合成了免疫原4-硝基苯乙胺-BSA和包被原4-硝基苯乙胺-OVA, 经紫外分光光度计及飞行时间质谱扫描鉴定. 用合成的免疫抗原免疫新西兰大白兔, 并用合成的包被原进行间接竞争酶联免疫(ELISA)试验, 获得的抗血清效价达1∶32000. 方阵实验确定了包被抗原最佳浓度(0.5 mg/L)及抗血清最佳稀释度(1∶6000), 并建立了间接竞争ELISA方法. 工作曲线表明在1～1000 μg/L浓度范围内呈良好的线性关系, 该法IC₅₀值为(52.73±2.67) μg/L, 检测限为5.12 μg/L. 其它类似结构不干扰硝基苯胺的测定. 成功地建立了硝基苯胺类化合物的间接竞争酶免疫化学分析方法．