O6-Alkylguanine DNA Alkyltransferase Mediated Disassembly of a DNA Tetrahedron

Tetrahedron DNA structures were formed by the assembly of three-way junction ( TWJ ) oligonucleotides containing O⁶-2′-deoxyguanosine-alkylene-O⁶-2′-deoxyguanosine (butylene and heptylene linked) intrastrand cross-links (IaCLs) lacking a phosphodiester group between the 2′-deoxyribose residues. The DNA tetrahedra containing TWJs were shown to undergo an unhooking reaction by the human DNA repair protein O⁶-alkylguanine DNA alkyltransferase (hAGT) resulting in structure disassembly. The unhooking reaction of hAGT towards the DNA tetrahedra was observed to be moderate to virtually complete depending on the protein equivalents. DNA tetrahedron structures have been explored as drug delivery platforms that release their payload in response to triggers, such as light, chemical agents or hybridization of release strands. The dismantling of DNA tetrahedron structures by a DNA repair protein contributes to the armamentarium of approaches for drug release employing DNA nanostructures.     

Seed‐Mediated Synthesis of Gold Tetrahedra in High Purity and with Tunable,Well‐Controlled Sizes

We report a facile synthesis of Au tetrahedra in high purity and with tunable, well‐controlled sizes via seed‐mediated growth. The success of this synthesis relies on the use of single‐crystal, spherical Au nanocrystals as the seeds and manipulation of the reaction kinetics to induce an unsymmetrical growth pattern for the seeds. In particular, the dropwise addition of a precursor solution with a syringe pump, assisted by cetyltrimethylammonium chloride and bromide at appropriate concentrations, was found to be critical to the formation of Au tetrahedra in high purity. Their sizes could be readily tuned in the range of 30–60 nm by simply varying the amount of precursor added to the reaction solution. The current strategy not only enables the synthesis of Au tetrahedra with tunable and controlled sizes but also provides a facile and versatile approach to reducing the symmetry of nanocrystals made of a face‐centered cubic lattice.     

Some useful integer arrays for the teaching of generalization skills

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example presented, the subjects in question are absolute values, graphs and solutions of equations, and domains of definition. These are unified by the problem of finding an analytic expression for a square and triangle and their interiors. In the course of the development, basic notions such as the additive property of areas and convexity are introduced. The approach presented in the article was tried with secondary school teachers participating in professional development workshops and with students at a technical college; the teachers and students responded enthusiastically to the material.     

基于错误矩阵方程的解决城市交通拥堵决策研究

针对解决城市交通拥堵决策问题,首先给出了错误优化矩阵的概念,在此基础上引出错误矩阵方程的概念,利用消错理论中的错误优化矩阵方程,从错误优化的角度来研究并解决城市交通拥堵的决策方法.相应结合实际状况给出当前状态矩阵,从而进行下一步的求解,步步推理获得了决策人满意的方案集,为决策者提供最优建议.     

温度对CaO-MgO-Al_2O_3-SiO_2系纳米晶玻璃陶瓷结构影响的拉曼光谱研究

采用熔融法制备了CaO-MgO-Al2O3-SiO2系纳米晶玻璃陶瓷材料。在-190~310℃温度范围,利用显微共聚焦拉曼光谱测量分析了该体系纳米晶玻璃陶瓷硅氧四面体结构的变化规律。结果表明,随着温度的降低具有不同非桥氧键的硅氧四面体结构单元变化并不一致,位于三维硅氧四面体结构边缘的具有二个非桥氧键的硅氧四面体(Q2)和具有三个非桥氧键的硅氧四面体(Q1),以及完全独立于三维硅氧网络结构外的具有四个非桥氧键的硅氧四面体(Q0)受温度影响明显,其拉曼光谱均向高波数移动,键的力常数变强,硅氧键长变短。为丰富外环境对纳米晶玻璃陶瓷材料结构与性能影响的研究提供了实验依据,也为控制该体系纳米晶玻璃陶瓷材料的膨胀系数提供了一定的实验依据。     

Elementary formulas for a hyperbolic tetrahedron

We derive some elementary formulas expressing the relation between the dihedral angles and edge lengths of a tetrahedron in hyperbolic space.     

Nonobtuse Tetrahedral Partitions that Refine Locally Towards Fichera-Like Corners

Linear tetrahedral finite elements whose dihedral angles are all nonobtuse guarantee the validity of the discrete maximum principle for a wide class of second order elliptic and parabolic problems. In this paper we present an algorithm which generates nonobtuse face-to-face tetrahedral partitions that refine locally towards a given Fichera-like corner of a particular polyhedral domain. The first author was supported by the Swedish Foundation for Strategic Research, the second author was supported by Grant No. 49051 of the Academy of Finland, the third author was supported by Grant No. A 1019201 of the Academy of Sciences of the Czech Republic and by Institutional Research Plan AV0Z 10190503.     

Bodies of constant width in arbitrary dimension

We give a number of characterizations of bodies of constant width in arbitrary dimension. As an application, we describe a way to construct a body of constant width in dimension n, one of its (n – 1)‐dimensional projection being given. We give a number of examples, like a four‐dimensional body of constant width whose 3D‐projection is the classical Meissner's body. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Three-dimensional integrable models and associated tangle invariants

In this paper we show that the Boltzmann weights of the three-dimensional Baxter-Bazhanov model give representations of the braid group if some suitable spectral limits are taken. In the trigonometric case we classify all possible spectral limits which produce braid group representations. Furthermore, we prove that for some of them we get cyclotomic invariants of links and for others we obtain tangle invariants generalizing the cyclotomic ones.