π1-classification of real arrangements with up to eight lines

One of the open questions in the geometry of line arrangements is to what extent does the incidence lattice of an arrangement determine its fundamental group. Line arrangements of up to 6 lines were recently classified by K.M. Fan (Michigan Math. J. 44(2) (1997) 283), and it turns out that the incidence lattice of such arrangements determines the projective fundamental group. We use actions on the set of wiring diagrams, introduced in (Garber et al. (J. Knot Theory Ramf.), to classify real arrangements of up to 8 lines. In particular, we show that the incidence lattice of such arrangements determines both the affine and the projective fundamental groups.     

Identifying several biased coins encountered by a hidden random walk

Suppose that attached to each site z ∈ ? is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}_z∈?, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of ?. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

SDR走向军用领域

JTRS正致力于将可互换SDR(软件无线电)带入军用领域。但SDR对商业应用是否也是足够好的选择呢?SDR(软件无线电)并不是一种新技术。过去业界就已经尝试实现SDR,但都没有达到目标。最近激发起对SDR兴趣的是创新性软硬件技术的出现,这些技术能够以市场可承受的价格提供足够的灵活性、性能和功率效率。例如,宽带变换器现在可以工作在宽频率范围内,根据一种特定的位分辨率处理接收到的波形,而高频处理器可以直接与信号工作,从而省掉IF(中频)级,并降低成本。     

catena‐Poly[tetra­kis(3‐phenyl­propyl­ammonium) [iodo­plumbate(II)‐tri‐μ‐iodo‐plumbate(II)‐tri‐μ‐iodo‐iodo­plumbate(II)‐di‐μ‐iodo]]

The title compound, {(C₉H₁₄N)₄[Pb₃I₁₀]}_n, crystallizes as an organic–inorganic hybrid. As such, the structure consists of a two‐dimensional inorganic layer of [Pb₃I₁₀]_n⁴ⁿ⁻ ions extending along [100]. The asymmetric unit contains two independent Pb atoms, viz. one in a general position and the other on an inversion centre. Each Pb atom is octa­hedrally coordinated by six iodide ions and exhibits both face‐ and corner‐sharing with adjacent atoms in the inorganic layer. These anionic layers alternate with 3‐phenyl­propyl­ammonium cations, which hydrogen bond to the iodides. Simple face‐to‐edge σ–π stacking inter­actions are observed between the aromatic rings that stabilize the overall three‐dimensional structure. This net structure has only been observed five times previously.     

机柜也需要细心呵护!

作为一家专业机柜生产厂商,所生产的产品主要在恶劣的环境中为电气和电子部件提供保护,有时客户会要求厂商现场协助解决一些设计和使用中碰到的问题。进行现场评估时,会经常发现基本的机柜设计并没有问题,导致问题的是一些其它因素。有时是安装不正确。例如,安装不正确的液体密封导管配件或电缆衬垫会导致灰尘或水进入机柜,幸运的是,此类问题通常在安装后不久就可发现并可快速解决。然而,对于那些需要数月或数年时间才会逐渐显现的问题怎么办?暖气炉在每个取暖季节前都会进行清洁,每3000英里汽车机油也需要更换,我们自己更是(或应该)进行例…     

Romanovski polynomials in selected physics problems

We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties. We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula.     

Identification,synthesis and conformational study of a CN(R,S) synthon by-product: (5R, 10R)-5,10-diphenyl-1,6-diaza-3,8-dioxabicyclo[4.4.1]undecane

The title compound, containing a new heterocyclic skeleton, was identified by X-ray crystallography as the product of condensation of (R)-phenylglycinol with an excess of formaldehyde. The molecule adopts a rigid double twist-chair conformation in both solid and solution states.