Infinite-dimensional 4-manifold of finite cohomological dimension under the continuum hypothesis

Under the assumption of the continuum hypothesis, a differentiable 4-manifoldM of dimension dimM=∞ and cohomological dimension cA—dimM=4 is constructed. The spaceM is perfectly normal and hereditarily separable. Translated fromMatematicheskie Zametki, Vol. 66, No. 5, pp. 664–670, November, 1999.     

密度泛函理论研究Gd（H2O）n^3＋（n=8，9）化合物的结构及相对稳定性

用密度泛函理论方法研究了气相和水溶液中Gd（H2O）n^3＋（n=8，9）化合物的结构和相对稳定性，其中水溶剂效应利用极化连续介质方法结合多种溶质空腔模型进行模拟．气相计算得到的化合物结构与实验观察结果一致．计算结果表明，在气相中9配位Gd（H2O）9^3＋比8配位Gd（H2O）8^3＋稳定，而在水溶液中稳定顺序刚好相反，这一结果不依赖于计算中采用的空腔模型种类，而且也与实验结果吻合．最后，通过采用各种空腔模型计算Gd^3＋的水合自由能，并与实验值比较，发现当化合物只包含第一层配位水分子时，UA0、UAHF及UAKS空腔模型最适合研究Gd^3＋在水溶液中的性质．     

On small homotopies of loops

Two natural questions are answered in the negative:

• “If a space has the property that small nulhomotopic loops bound small nulhomotopies, then are loops which are limits of nulhomotopic loops themselves nulhomotopic?”

• “Can adding arcs to a space cause an essential curve to become nulhomotopic?”

The answer to the first question clarifies the relationship between the notions of a space being homotopically Hausdorff and π₁-shape injective.

假设检验中p值的灵活运用

给出假设检验中p值的定义以及双边检验p值与单边检验p值的关系,介绍了利用p值将三种检验同时进行的方法及意义,最后给出应用实例.     

Substituent and solvent effects on the structural bioactivity and anticancer characteristic of catechin as a bioactive constituent of green tea

In this study, quantum chemical calculations using density functional theory and 6‐311G (d) basis set have been applied to analyze the substituent effect on the electronic structural properties including thermochemical parameters as well as anticancer characteristics of catechin as a bioactive constituent of green tea. It has been found out that different substituents with two kinds of electron donating and electron withdrawing groups including ? NO₂, ? NH₂, ? Cl, ? OCH₃, and ? CH₃ leaded to different structural stabilities. The catechin with chloro substituents has been referred to the most stable catechin derivatives based on the minimum energy of investigated compounds. In this study, the calculated values have been compared in gas phase and different solvent media with a wide range of solvent dielectrics using the self‐consistent reaction field method with polarizable continuum model. Relative interaction energies between solute and solvent as well as dipole moment values have been analyzed. The results of solvent effect study revealed that the formation of hydrogen bonds accounts for the stabilization of catechin. These calculated data were found to be a logical way in predicting the relative stability of catechin derivatives and can be useful for drug design of anticancer drugs and would open a new door for the researchers who are interested in natural products. The results presented in this article will be helpful to improve existing model and will open up a whole new arena of study to understand the anticancer characteristic of these antioxidant drugs derived from natural products against the photosensitizing DNA damage induce by catechin extracts and enable a much clearer understanding of how anticancer drugs mediate their effects on the specific spot. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Determination of Lead in Human Hair by High Resolution Continuum Source Graphite Furnace Atomic Absorption Spectrometry with Microwave Digestion and Solid Sampling

The content of lead in human hair was measured by high resolution continuum source graphite furnace atomic absorption spectrometry (HR-CS GFAAS) combined with microwave-assisted digestion (MAD) and direct solid sampling (DSS). Hair strands were washed, dried, and then cut into three parts (root, middle portion, and tip). For MAD-GFAAS assays, approximately 0.25 g of hair was completely digested using a mixture of concentrated nitric acid and hydrogen peroxide in a closed system. In the DSS-GFAAS assays, 0.1–0.2 mg of dried hair was directly introduced into a graphite furnace using a solid autosampler. The temperature programs were optimized and the effects of various added modifiers were compared. The results indicated that NH₄H₂PO₄ was the optimal modifier for analysis of Pb using GFAAS. Use of the optimal modifier and temperature program gave similar limits of detection for MAD-GFAAS and DSS-GFAAS of 1.16 ng/g and 0.82 ng/g, respectively. Both methods also produced satisfactory recoveries ranging from 98.69% to 103.14%. There was no significant difference observed between the Pb contents of hair strands determined by the MAD-GFAAS and DSS-GFAAS assays, which both indicated that the Pb levels increased along the hair strands. Comparison of the two methods revealed that DSS-GFAAS had several advantageous characteristics over MAD-GFAAS, including the need for much less sample material and having a less time-consuming procedure, lower sample blank absorbance, lower memory effect, and no risk of environmental pollution by digesting chemicals. The direct solid sampling technique can be employed as a good alternative to conventional wet digestion in AAS assays.     

A hybrid DSMC/Navier–Stokes frame to solve mixed rarefied/nonrarefied hypersonic flows over nano‐plate and micro‐cylinder

We extend a hybrid DSMC/Navier–Stokes (NS) approach to unify the DSMC and the NS simulators in one framework capable of solving the mixed non‐equilibrium and near‐equilibrium flow regions efficiently. Furthermore, we use a one‐way state‐based coupling (Dirichlet–Dirichlet boundary‐condition coupling) to transfer the required information from the continuum region to the rarefied one. The current hybrid DSMC–NS frame is applied to the hypersonic flows over nanoflat plate and microcylinder cases. The achieved solutions are compared with the pure DSMC and NS solutions. The results show that the current hybrid approach predicts the surface heat transfer rate and shear stress magnitudes very accurately. Some important conclusions can be drawn from this study. For example, although the shock wave region would be a non‐equilibrium region, it is not necessary to use a pure DSMC simulator to solve it entirely. This is important when the researchers wish to predict the surface properties such as velocity slip, temperature jump, wall heat flux rate, and friction drag magnitudes accurately. Our investigation showed that our hybrid solution time would be at least 40% (for the flat plate) and 35% (for the cylinder) of the time that must be spent by a pure DSMC solver to attain the same accuracy.Copyright © 2013 John Wiley & Sons, Ltd.     

The nonexistence of sensitive commutative group actions on dendrites

In this paper, using the integral method observed by Mai Jiehua recently, we show that no dendrite admits a sensitive commutative group action.     

Study on the behavior of oscillating solitons using the (2+1)-dimensional nonlinear system

By means of an extended homogeneous balance method and a variable separation hypothesis, a broad general variable separation solution with three specific arbitrary functions of the nonlinear (2+1)-dimensional Broer-Kaup (BK) equations was derived. Based on the derived solution, a number of abundant oscillating solitons, such as dromion, multi-dromion, solitoff, ring, multi-lump and so on, have been revealed in this study by selecting appropriate functions of the general variable separation solution.     

Super-Instantons, Perfect Actions, Finite-Size Scaling, and the Continuum Limit

We discuss some aspects of the continuum limit of some lattice models, in particular the 2DO(N) models. The continuum limit is taken either in an infinitevolume or in a box whose size is a fixed fraction of the infinite-volume correlation length. We point out that in this limit the fluctuations of the lattice variables must be O(1) and thus restore the symmetry which may have been broken by the boundary conditions (b.c.). This is true in particular for the socalled super-instanton b.c. introduced earlier by us. This observation leads to a criterion to assess how close a certain lattice simulation is to the continuum limit and can be applied to uncover the true lattice artefacts, present even in the so-called “perfect actions”. It also shows that David’s recent claim that superinstanton b.c. require a different renormalization must either be incorrect or an artefact of perturbation theory.