The Lattice of Completions of an Ordered Set

For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind–MacNeille completion P. The lattice K(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closure operators on any complete lattice. In particular, if K(P) is finite, then it is an upper semimodular lattice and an upper bounded homomorphic image of a free lattice, and hence meet semidistributive.     

Substitution effects in the 15N NMR chemical shifts of heterocyclic azines evaluated at the GIAO‐DFT level

A systematic study of the accuracy factors for the computation of ¹⁵N NMR chemical shifts in comparison with available experiment in the series of 72 diverse heterocyclic azines substituted with a classical series of substituents (CH₃, F, Cl, Br, NH₂, OCH₃, SCH₃, COCH₃, CONH₂, COOH, and CN) providing marked electronic σ‐ and π‐electronic effects and strongly affecting ¹⁵N NMR chemical shifts is performed. The best computational scheme for heterocyclic azines at the DFT level was found to be KT3/pcS‐3//pc‐2 (IEF‐PCM). A vast amount of unknown ¹⁵N NMR chemical shifts was predicted using the best computational protocol for substituted heterocyclic azines, especially for trizine, tetrazine, and pentazine where experimental ¹⁵N NMR chemical shifts are almost totally unknown throughout the series. It was found that substitution effects in the classical series of substituents providing typical σ‐ and π‐electronic effects followed the expected trends, as derived from the correlations of experimental and calculated ¹⁵N NMR chemical shifts with Swain–Lupton's F and R constants.     

GO-spaces with -closed discrete dense subsets

In this paper we study the question ``When does a perfect generalized ordered space have a -closed-discrete dense subset?' and we characterize such spaces in terms of their subspace structure, -mappings to metric spaces, and special open covers. We also give a metrization theorem for generalized ordered spaces that have a -closed-discrete dense set and a weak monotone ortho-base. That metrization theorem cannot be proved in ZFC for perfect GO-spaces because if there is a Souslin line, then there is a non-metrizable, perfect, linearly ordered topological space that has a weak monotone ortho-base.

     

Investigation of Hybrid Optical Amplifiers for Dense Wavelength Division Multiplexed System with Reduced Spacings at Higher Bit Rates

Abstract

This article proposes various combinations of optical amplifiers for a dense wavelength division multiplexed system and investigates the impact of reduced channel spacing at high bit rates in terms of quality factor, bit error rate, eye closure, and output power. It is reported that the hybrid optical amplifier (Raman–erbium-doped fiber amplifier [EDFA]) provides better results with a maximum covered single span distance (220 km) at channel spacing of 6.25 GHz. The maximum acceptable bit rate for the 12.5-GHz channel spacing dense wavelength division multiplexed system is also investigated, and the recommendation is provided that for the Raman–EDFA, Raman–EDFA–Raman, EDFA–Raman–EDFA, and EDFA–semiconductor optical amplifier–EDFA, the operating bit rate should not be greater than 20, 16, 19, and 20 Gbps, respectively.     

Dense coding scheme using superpositions of Bell-states and its NMR implementation

Dense coding using superpositions of Bell-states is proposed. The generalized Grover's algorithm is used to prepare the initial entangled states, and the reverse process of the quantum algorithm is used to determine the entangled state in the decoding measurement. Compared with the previous schemes, the superpositions of two Bell-states are exploited. Our scheme is demonstrated using a nuclear magnetic resonance (NMR) quantum computer. The corresponding manipulations are obtained. Experimental results show a good agreement between theory and experiment. We also generalize the scheme to transmit eight messages by introducing an additional two-state system.     

Implementation of a multiple round quantum dense coding using nuclear magnetic resonance

~~Implementation of a multiple round quantum dense coding using nuclear magnetic resonance1. Bennett, C. H., Wiesner, S. J., Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 1992, 69(20): 2881-2884. 2. Mattle, K., Weinfurter, H., Kwiat, P. G. et al., Dense coding in experimental quantum communication, Phys. Rev. Lett., 1996, 76(25): 4656-4659. 3. Fang, X. M., Zhu, X. W., Feng, M. et al., Experimental implementation of dens…     

Finding the Maximal Eigenpair for a Large,Dense,Symmetric Matrix based on Mufa Chen's Algorithm

A hybrid method is presented for determining maximal eigenvalue and its eigenvector(called eigenpair)of a large,dense,symmetric matrix.Many problems require finding only a small part of the eigenpairs,and some require only the maximal one.In a series of papers,efficient algorithms have been developed by Mufa Chen for computing the maximal eigenpairs of tridiagonal matrices with positive off-diagonal elements.The key idea is to explicitly construet effective initial guess of the maximal eigenpair and then to employ a self-closed iterative algorithm.In this paper we will extend Mufa Chen's algorithm to find maximal eigenpair for a large scale,dense,symmetric matrix.Our strategy is to first convert the underlying matrix into the tridiagonal form by using similarity transformations.We then handle the cases that prevent us from applying Chen's algorithm directly,e.g.,the cases with zero or negative super-or sub-diagonal elements.Serval numerical experiments are carried out to demonstrate the efficiency of the proposed hybrid method.     

Non-traceability of large connected claw-free graphs

Let G be a connected claw-free graph on n vertices. Let ς₃(G) be the minimum degree sum among triples of independent vertices in G. It is proved that if ς₃(G) ≥ n − 3 then G is traceable or else G is one of graphs G_n each of which comprises three disjoint nontrivial complete graphs joined together by three additional edges which induce a triangle K₃. Moreover, it is shown that for any integer k ≥ 4 there exists a positive integer ν(k) such that if ς₃(G) ≥ n − k, n > ν(k) and G is non-traceable, then G is a factor of a graph G_n. Consequently, the problem HAMILTONIAN PATH restricted to claw-free graphs G = (V, E) (which is known to be NP-complete) has linear time complexity O(|E|) provided that ς₃(G) ≥ . This contrasts sharply with known results on NP-completeness among dense graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 75–86, 1998     

Total Vertex Irregularity Strength of Dense Graphs

Consider a graph of minimum degree δ and order n. Its total vertex irregularity strength is the smallest integer k for which one can find a weighting such that for every pair of vertices of G. We prove that the total vertex irregularity strength of graphs with is bounded from above by . One of the cornerstones of the proof is a random ordering of the vertices generated by order statistics.     

纳米粒子稳定乳液及其在纳米结构合成中的应用*

本文在介绍常规乳状液、微乳液和固体稳定乳液的基础上,着重综述了纳米粒子稳定乳液的特点及其在纳米结构合成中的应用进展,并对目前该研究领域亟待解决的问题进行了分析。纳米粒子稳定乳液具有独特的油、水、固三相环境和水油、水固、油固三个相界面,分散相液滴尺寸可以在微米、亚微米乃至纳米尺度调节,因而可以作为合成组成、结构和性能极为丰富多样的纳米结构的介质。纳米粒子对乳液稳定作用的机理,以及纳米粒子稳定乳液中化学反应的特殊规律还有待深入研究。本文在介绍固体稳定乳液的基础上,着重综述了纳米粒子稳定乳液的特点及其在纳米结构合成中的应用进展,并对目前该研究领域亟待解决的问题进行了分析。纳米粒子稳定乳液具有独特的油、水、固三相环境和水油、水固、油固三个相界面,分散相液滴尺寸可以在微米、亚微米乃至纳米尺度调节,因而可以作为合成组成、结构和性能极为丰富多样的纳米结构的介质。纳米粒子对乳液稳定作用的机理,以及纳米粒子稳定乳液中化学反应的特殊规律还有待深入研究。