Z4-Kerdock Codes, Orthogonal Spreads, and Extremal Euclidean Line-Sets

When m is odd, spreads in an orthogonal vector space of type⁺(2m + 2,2) are related to binary Kerdock codes and extremalline-sets in 2^{m + 1} with prescribed angles. Spreads in a 2m-dimensionalbinary symplectic vector space are related to Kerdock codesover Z₄ and extremal line-sets in with prescribed angles. These connections involve binary, realand complex geometry associated with extraspecial 2-groups.A geometric map from symplectic to orthogonal spreads is shownto induce the Gray map from a corresponding Z₄-Kerdock codeto its binary image. These geometric considerations lead tothe construction, for any odd composite m, of large numbersof Z₄-Kerdock codes. They also produce new Z₄-linear Kerdockand Preparata codes. 1991 Mathematics Subject Classification:primary 94B60; secondary 51M15, 20C99.     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

A pericyclic cascade to the stereocontrolled synthesis of 9-cis-retinoids

A domino reaction that is pericyclic in nature is thought to be triggered upon treatment of alkenynol 10 with arylsulfenyl chlorides. The process comprises an ordered sequence of sigmatropic rearrangements: a reversible [2,3]-allyl sulfenate to allyl sulfoxide shift, followed by a [2,3]-propargyl sulfenate to allenyl sulfoxide rearrangement, and last a stereodifferentiating [1,5]-sigmatropic hydrogen migration leading to polyene 13. The occurrence of the C7 to C11 hydrogen migration has been demonstrated by labeling experiments. The double diastereoselection of the [1,5]-sigmatropic hydrogen shift to afford a single isomer of the final polyene 13 is thought to arise from a combination of the electronic effect of the sulfoxide at one terminus, and the steric effect imparted by the bulky trimethylcyclohexenyl substituent at the other terminus. The overall process thus constitutes a stereoselective synthesis of an E,Z,Z-triene fragment from an alkenynol and, in particular, a retinoid with the 7E,9Z,11Z,13E configuration on the conjugated polyenic side chain. Application of this method to the synthesis of retinoids, including labeled analogues, is straightforward.     

Model-theoretic aspects of the Gurarij operator system

We establish some of the basic model theoretic facts about the Gurarij operator system GS recently constructed by the second-named author. In particular, we show: (1) GS is the unique separable 1-exact existentially closed operator system; (2) GS is the unique separable nuclear model of its theory; (3) every embedding of GS into its ultrapower is elementary; (4) GS is the prime model of its theory; and (5) GS does not have quantifier-elimination, whence the theory of operator systems does not have a model companion. We also show that, for any q ∈ ?, the theories of M_q-spaces and M_q-systems do have a model companion, namely the Fra¨?ssé limit of the class of finite-dimensional M_q-spaces and M_q-systems respectively; moreover, we show that the model companion is separably categorical. We conclude the paper by showing that no C* algebra can be existentially closed as an operator system.     

Preparation and comparison of supported gold nanocatalysts on anatase, brookite, rutile, and P25 polymorphs of TiO2 for catalytic oxidation of CO

Nanosized anatase (< or = 10 nm), rutile (< or = 10 nm), and brookite (approximately 70 nm) titania particles have been successfully synthesized via sonication and hydrothermal methods. Gold was deposited with high dispersion onto the surfaces of anatase, rutile, brookite, and commercial titania (P25) supports through a deposition-precipitation (D-P) process. All catalysts were exposed to an identical sequence of treatment and measurements of catalytic CO oxidation activity. The as-synthesized catalysts have high activity with concomitant Au reduction upon exposure to the reactant stream. Mild reduction at 423 K produces comparably high activity catalysts for every support. Deactivation of the four catalysts was observed following a sequence of treatments at temperatures up to 573 K. The brookite-supported gold catalyst sustains the highest catalytic activity after all treatments. XRD and TEM results indicate that the gold particles supported on brookite are smaller than those on the other supports following the reaction and pretreatment sequences.     

Semileptonic (Λ b → Λcev) decay in a field theoretic quark model

The semileptonic decay width of heavy baryons such as (Λ _b → Λcev) has been estimated in the framework of a nonrelativistic field theoretic quark model where four component quark field operators along with a harmonic oscillator wave function are used to describe translationally invariant hadronic states. The present estimation does not make an explicit use of heavy quark symmetry and has a reasonable agreement with the experimentally measured decay width, polarisation ratio and form factors with the harmonic oscillator radii and quark momentum distribution inside the hadron as free parameters.     

The Ramsey property for Banach spaces and Choquet simplices,and applications

We show that the class of finite-dimensional Banach spaces and the class of finite-dimensional Choquet simplices have the Ramsey property. As an application, we show that the group $\mathrm{Aut}(\mathbb{G})$ of surjective linear isometries of the Gurarij space $\mathbb{G}$ is extremely amenable, and that the canonical action $\mathrm{Aut}(\mathbb{P})?\mathbb{P}$ is the universal minimal flow of the group $\mathrm{Aut}(\mathbb{P})$ of affine homeomorphisms of the Poulsen simplex $\mathbb{P}$. This answers questions of Melleray–Tsankov and Conley–Törnquist.     

High density piecewise syndeticity of sumsets

Renling Jin proved that if A and B   are two subsets of the natural numbers with positive Banach density, then A+B$A+B$ is piecewise syndetic. In this paper, we prove that, under various assumptions on positive lower or upper densities of A and B  , there is a high density set of witnesses to the piecewise syndeticity of A+B$A+B$. Most of the results are shown to hold more generally for subsets of Z^d${\mathbb{Z}}^d$. The key technical tool is a Lebesgue density theorem for measure spaces induced by cuts in the nonstandard integers.     

Detection of single atoms and buried defects in three dimensions by aberration-corrected electron microscope with 0.5-a information limit

The ability of electron microscopes to analyze all the atoms in individual nanostructures is limited by lens aberrations. However, recent advances in aberration-correcting electron optics have led to greatly enhanced instrument performance and new techniques of electron microscopy. The development of an ultrastable electron microscope with aberration-correcting optics and a monochromated high-brightness source has significantly improved instrument resolution and contrast. In the present work, we report information transfer beyond 50 pm and show images of single gold atoms with a signal-to-noise ratio as large as 10. The instrument's new capabilities were exploited to detect a buried Sigma3 {112} grain boundary and observe the dynamic arrangements of single atoms and atom pairs with sub-angstrom resolution. These results mark an important step toward meeting the challenge of determining the three-dimensional atomic-scale structure of nanomaterials.