The Gleason theorem for the field of rational numbers and residue fields

Charges taking values in a fieldF and defined on orthomodular partially ordered sets (logics) of all projectors in some finite-dimensional linear space overF are considered. In the cases whereF is the field of rational numbers or a residue field, the Gleason representation , where is a linear operator, is proved.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 584–591, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 96-01-01265.     

Some nearly Boolean orthomodular posets

Let be an orthomodular partially ordered set (``a quantum logic"). Let us say that is nearly Boolean if is set-representable and if every state on is subadditive. We first discuss conditions under which a nearly Boolean OMP must be Boolean. Then we show that in general a nearly Boolean OMP does not have to be Boolean. Moreover, we prove that an arbitrary Boolean algebra may serve as the centre of a (non-Boolean) nearly Boolean OMP.

     

Benzannulation of 5-methyl-7-phenyl-4,7-dihydrotetrazolo[1,5-a]pyrimidine with chalcones and their synthetic equivalents as a method for the synthesis of tetrazolo[5,1-b]quinazolines

Derivatives of tetrahydrotetrazolo[5,1-b]quinazolines were synthesized by the reactions of 5-methyl-7-phenyl-4,7-dihydrotetrazolo[1,5-a]pyrimidine with α,β-unsaturated carbonyl compounds and their synthetic equivalents in methanol in the presence of sodium methoxide. The spontaneous or specifically target oxidation of these derivatives gives rise to aromatic tetrazoloquinazolines. The reaction pathways and mechanisms were discussed. The structures of the resulting compounds were confirmed by IR and ¹H NMR spectroscopy, mass spectrometry, and elemental analysis. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1971–1976, September, 2008.     

How often are two permutations comparable?

Two permutations of are comparable in the Bruhat order if one is closer, in a natural way, to the identity permutation, , than the other. We show that the number of comparable pairs is of order at most, and at least. For the related weak order, the corresponding bounds are and , where . In light of numerical experiments, we conjecture that for each order the upper bound is qualitatively close to the actual number of comparable pairs.

     

Electro-optic properties of nematic and ferroelectric liquid crystalline nanocolloids doped with partially reduced graphene oxide

Flakes of partially reduced graphene oxide (PRGO) were doped in nematic liquid crystals (NLCs) and ferroelectric liquid crystals (FLCs), respectively. The dielectric and electro-optical properties of NLCs doped with those flakes have been investigated. Threshold voltage and switching times are reduced by 30%–50%. This is primarily due to the decrease of the elastic properties of the nanocolloids compared to the non-doped nematics. The influence of the PRGO flakes on the spontaneous polarization, tilt angle and switching time of FLCs was investigated too. Such flakes reduce the response time by 40%–60%, increases spontaneous polarization by 20%–25% and increase the tilt angle by 15%–20%.     

Robust guaranteed cost control for discrete‐time systems via partially delay‐dependent controller with linear fractional uncertainties

In this article, a partially delay‐dependent controller is designed to analyze the guaranteed performance analysis of a class of uncertain discrete‐time systems with time‐varying delays. By constructing suitable Lyapunov–Krasovskii Functional (LKF), sufficient conditions are derived to ensure the system to be robustly stochastically stable in mean square sense by using Wirtinger‐based inequality and convex reciprocal lemma. The proper cost function is chosen to guarantee an adequate level of performance. The derived conditions are expressed in terms of linear matrix inequalities (LMIs) which can be easily solved by LMI Toolbox in MATLAB. Further, the advantage of employing the obtained results is illustrated via numerical examples. © 2016 Wiley Periodicals, Inc. Complexity 21: 113–122, 2016     

半序度量空间中公共二元随机重合点定理及其应用

在完备可分的半序度量空间中,引入了随机映射对(F,G)关于g随机半序弱增以及(F,G)随机半序弱增的定义,研究了在满足一定非线性压缩条件下的随机映射列F_k:Ω×X×X→X,k=1,2…,g:Ω×X→X和h:Ω×X→X的公共二元随机重合点与公共二元随机不动点问题,所得结果推广了已有文献中的一些不动点定理.     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

Efficiently navigating a random Delaunay triangulation

Planar graph navigation is an important problem with significant implications to both point location in geometric data structures and routing in networks. However, whilst a number of algorithms and existence proofs have been proposed, very little analysis is available for the properties of the paths generated and the computational resources required to generate them under a random distribution hypothesis for the input. In this paper we analyse a new deterministic planar navigation algorithm with constant spanning ratio (w.r.t the Euclidean distance) which follows vertex adjacencies in the Delaunay triangulation. We call this strategy cone walk. We prove that given n uniform points in a smooth convex domain of unit area, and for any start point z and query point q; cone walk applied to z and q will access at most sites with complexity with probability tending to 1 as n goes to infinity. We additionally show that in this model, cone walk is ‐memoryless with high probability for any pair of start and query point in the domain, for any positive ξ. We take special care throughout to ensure our bounds are valid even when the query points are arbitrarily close to the border. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 95–136, 2016     

空间编码与灰度投影相结合实现高效3-D形貌测量的研究

介绍了一种结合空间编码与灰度投影来实现高效三维形貌测量的方法。用空间编码完成对被测空间的粗略编码,用灰度投影完成精确编码,将它们结合起来得到被测物体表面丰富的编码信息,作为一种基于三角法的三维形貌测量方法,能够在物体表面非常不连续和外部光照造成的背景光强分布不确定的情况下工作良好。同时,与传统的空间编码方法相比,它大大提高了空间编码的效率。实验表明,该方法用５ 幅图像取得了与灰度码１０幅图像相当的测量结果。