Note on a conjecture of toft

A conjecture of Toft [17] asserts that any 4-critical graph (or equivalently, every 4-chromatic graph) contains a fully odd subdivision ofK ₄. We show that if a graphG has a degree three nodev such thatG-v is 3-colourable, then eitherG is 3-colourable or it contains a fully oddK ₄. This resolves Toft's conjecture in the special case where a 4-critical graph has a degree three node, which is in turn used to prove the conjecture for line-graphs. The proof is constructive and yields a polynomial algorithm which given a 3-degenerate graph either finds a 3-colouring or exhibits a subgraph that is a fully odd subdivision ofK ₄. (A graph is 3-degenerate if every subgraph has some node of degree at most three.)     

Slutsky定理在样本分位数的极限分布证明上的应用

为了更好地理解和应用样本分位数的极限分布,利用Slutsky定理,推导了样本分位数的极限分布.     

Molecular dynamics simulation of P-V-T relationship of ZnO with rock-salt structure using pair-wise interactions

Molecular dynamics (MD) method is used to investigate the behavior of the pressure-volume-temperature (P-V-T) relationship, lattice constant and thermal expansivity for ZnO with rock-salt structure at high pressures and temperatures. The interionic potential is taken to be the sum of pair-wise additive Coulomb, van der Waals attraction, and repulsive interactions. The isothermal and isobaric properties are discussed from the corresponding P-V-T relationship, and it is shown that the MD simulation is successful in reproducing the measured volumes of ZnO over a wide range of temperature and pressure. Meanwhile, the equations of state parameters including lattice constant, linear thermal expansion coefficient, and isothermal bulk modulus are calculated and compared with the available experimental data and the latest theoretical results. At an extended pressure and temperature range, P-V-T relationship, lattice constant, and linear thermal expansion coefficient have been predicted. The structural and thermodynamic properties of ZnO with rock-salt structure are summarized in the pressure 0-100 GPa ranges and the temperature up to 3100 K.     

关于非光滑不变凸多目标规划的Wolfe型对偶

本文讨论定义在Banach空间上的,既具有等式约束又具有不等式约束的,非光滑(F,P)不变凸多目标规划的Wolfe对偶性,Mond-Weir型对偶性可类似讨论之。     

A Local Analysis of Congruences in the (p, p) Case: Part I

Given an irreducible, modular, mod p representation p, we analyse the local components at p of newforms f which give rise to it.     

关于CVD 矩阵的n- 宽度

本文证明了d_2k =δ_2k =d^2k ≥b_2k，其中d_2k ,δ_2k , b_2k分别表示Ａ（Ｂｌ^M_p）在ｌ^N_q下的Ｋｏｌｍｏｇｏｒｏｖ，线性，Ｂｅｒｎｓｔｅｉｎ ２ｋ－宽度，ｄ^2k 表示Ａ^Ｔ（Ｂｌ^N相似文献   

Raman spectroscopy study of REH3 under pressure

The Raman spectroscopic studies of two rare earth trihydrides: Y H₃, HoH₃, have been performed in the pressure range from ambient up to 16 GPa and 25 GPa respectively. For the first time samples of REH₃ in the form of powder have been studied by Raman spectroscopy using the Diamond Anvil Cell (DAC) technique. A rapid decrease of Raman activity has been observed for the hydrides under pressure values in the vicinity of structural phase transition. Metallization as a possible reason for the observed dramatic change of the REH₃ Raman activity has been discussed.     

复制缺陷型人泡沫病毒载体辅助质粒pΔGP的构建及转染小肠癌细胞的研究

在人泡沫病毒原病毒全长克隆pHRSV13的基础上,缺失突变gag和pol基因,并且用SV40polyA加尾信号替代人泡沫病毒的3′LTR,构建辅助质粒pΔGP.将复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP和辅助质粒pΔGP分别转染和共转染小肠癌HIC细胞系,荧光显微镜检测发现共转染pGPSNI EGFP和pΔGP的HIC细胞能够强烈表达绿色荧光蛋白,转染有复制缺陷型人泡沫病毒载体质粒pGPSNI EGFP的HIC细胞能够表达少量的绿色荧光蛋白,而转染有辅助载体pΔGP的HIC细胞不表达绿色荧光.结果证明复制缺陷型人泡沫病毒载体的构建成功,表明人泡沫病毒env基因3′端的内部启动子IP具有弱启动子的活性,并且bel基因产生的调控蛋白能够反式激活人泡沫病毒内部启动子IP和5′LTR的启动子.     

Effective-field theory and the nuclear many-body problem

We review many-body calculations of the equation of state of dilute neutron matter in the context of effective-field theories of the nucleon-nucleon interaction.