Commuting Graphs of Matrix Algebras

The commuting graph of a ring R, denoted by Γ(R), is a graph whose vertices are all noncentral elements of R, and two distinct vertices x and y are adjacent if and only if xy = yx. The commuting graph of a group G, denoted by Γ(G), is similarly defined. In this article we investigate some graph-theoretic properties of Γ(M _n (F)), where F is a field and n ≥ 2. Also we study the commuting graphs of some classical groups such as GL _n (F) and SL _n (F). We show that Γ(M _n (F)) is a connected graph if and only if every field extension of F of degree n contains a proper intermediate field. We prove that apart from finitely many fields, a similar result is true for Γ(GL _n (F)) and Γ(SL _n (F)). Also we show that for two fields F and E and integers n, m ≥ 2, if Γ(M _n (F))?Γ(M _m (E)), then n = m and |F|=|E|.     

Synthesis of Azabicyclic Building Blocks for Daphniphyllum Alkaloid Intermediates Featuring N‐Trichloroacetyl Enamide 5‐endo‐trig Radical Cyclizations

A general procedure is reported for the synthesis of cis ring fused azapolycyclic compounds bearing an all‐carbon quaternary stereocenter at the ring fusion and an adequate functionalization for the assembly of new rings leading to advanced synthetic intermediates for Daphniphyllum alkaloid synthesis. The key carbon?carbon bond‐forming step in this approach is a radical cyclization of an N‐cycloalkenyl trichloroacetamide derivative involving a tetrasubstituted enamide to achieve polyfunctionalized lactams.     

摩擦磨损试验机模拟活塞环-缸套摩擦行为的功能开发

参考活塞环-缸套的实际运行条件,结合SRV-4摩擦磨损试验机自身的性能特点和工作原理,通过开发设计,增加合理的硬件及软件测试条件,实现摩擦磨损试验机模拟活塞环-缸套摩擦行为的功能.系统测试结果表明：功能开发后的摩擦磨损试验机可在较短时间内获得活塞环-缸套摩擦副性能优劣的试验数据,满足快速、直观评价活塞环-缸套的摩擦磨损性能的需要,在活塞环-缸套摩擦副研究中具有重要的应用价值.     

Designing of energetic miktoarm A2B2 star‐shaped polymer by means of click chemistry and ROP techniques

Novel A₂B₂‐type energetic miktoarm star‐shaped copolymers composed of two PGN arms and two PCL arms was synthesized by the combination of ring‐opening polymerization (ROP) and “click” chemistry. Initially, diazido end‐functionalized two‐arm PGN, (PGN)₂‐(N₃)₂, was synthesized by ROP of glycidyl nitrate monomers. Subsequently, (PGN)₂‐(PCL)₂ was obtained from the click reaction between diazido end‐functionalized (PGN)₂‐(N₃)₂ polymers and propargyl‐terminated poly(ε‐caprolactone) (PTPCL). This star copolymer solves problems of PCL (lake of energy) and PGN (low T_g). The Fourier‐transform infrared (FT‐IR), ¹H nuclear magnetic resonance (NMR), and gel permeation chromatography (GPC) studies revealed that (PGN)₂‐(PCL)₂ was successfully obtained. The thermal behavior of star polymer was investigated by thermogravimetric analysis (TGA) and derivative thermogravimetry. The results show that (PGN)₂‐(PCL)₂ decomposed at two stages. The first stage is seen at 212.6°C which related to degradation of –ONO₂ group and second stage attributed to degradation of PCL group which is seen at 346.1°C.     

Facile Access to an NHC‐Coordinated Silicon Ring Compound with a Si=N Group and a Two‐Coordinate Silicon Atom

Reaction of the bicyclo[1.1.0]tetrasilatetraamide Si₄{N(SiMe₃)Dipp}₄ 1 (Dipp=2,6‐diisopropylphenyl) with 5 equiv of the N‐heterocyclic carbene NHC^Me4 (1,3,4,5‐tetramethylimidazol‐2‐ylidene) affords a bifunctional carbene‐coordinated four‐membered‐ring compound with a Si=N group and a two‐coordinate silicon atom Si₄{N(SiMe₃)Dipp}₂(NHC^Me4)₂(NDipp) 2 . When 2 reacts with 0.25 equiv sulfur (S₈), two sulfur atoms add to the divalent silicon atom in plane and perpendicular to the plane of the Si₄ ring, which confirms the silylone character of the two‐coordinate silicon atom in 2 .     

Electron‐Deficient Triborane and Tetraborane Ring Compounds: Synthesis,Structure, and Bonding

Electron‐deficient small boron rings are unique in their formation of σ‐ and π‐delocalized electron systems as well as the avoidance of “classical” structures with two‐center‐two‐electron (2c,2e) bonds. These rings are tolerant of several skeletal electron numbers, which makes their redox chemistry highly interesting. In the past few decades, a range of stable compounds have been synthesized with various electron numbers in their B₃ and B₄ cores. The electronic structures were evaluated by quantum‐chemical calculations. On the other hand, the chemistry of these rings is still very much underdeveloped, being generally limited to the protonation and redox reactions of individual systems. The linkage of several B₃ and/or B₄ ring systems should give compounds with attractive electronic properties, thus leading the way to novel boron‐based materials. By summarizing important experimental and theoretical results, this Review intends to provide the basis for the exploration of the chemistry of these rings and, in particular, their integration into larger molecular architectures.     

A widely tunable dual-wavelength erbium-doped fiber ring laser operating in single longitudinal mode

A new mechanism to induce polarization hole burning effect in Er-doped fiber ring lasers is presented. By using this effect, incorporating with the counter-propagation of the two light beams, the inhomogeneous in the gain medium broadening was significantly increased, and thus a stable dual-frequency Er-doped fiber ring laser operating in single longitudinal mode and single-frequency was demonstrated. Frequency spacing was tunable from 0.47 GHz to THz.     

Measurements of excess loss of the crossed waveguide using optical waveguide ring resonators

Crossed waveguide is widely used in optical devices, whose excess loss has a strong impact on multi-turn optical waveguide ring resonator and resonator integrated optic gyro. The resonance curve of the ring resonator is sharply dependent on the loss within the resonator. This paper presents how to get excess loss of the crossed waveguides nondestructively through the comparison of the resonance characteristics between one-turn and multi-turn optical waveguide ring resonators.     

Binding Energy of Excitons in a Quantum Ring

The binding energy of excitons confined to a quantum ring under the influence of perpendicular homogeneous magnetic field is calculated as a function of the ring radius. Calculations are made by using the method of exact diagonalization within the effective-mass approximation. The feature of binding energy of the ground state as a function of the ring radius for several values of the magnetic field has been revealed. The interesting feature of our study is that, in a quantum ring, the geometric structure of exeitons may reveal transition.     

New chromaticity compensation approach and dynamic aperture increase in the SSRF storage ring

Strong chromatic sextupoles used to compensate natural chromaticities in the third generation light source storage ring usually reduce dynamic aperture drastically. Many optimization methods can be used to find solutions that provide large dynamic apertures. This paper discusses a new optimization approach of sextupole strengths with step-by-step procedure, which is applied in the SSRF storage ring, and a better solution is obtained. Investigating driving terms generated by the sextupoles in every step can analyze their convergences and guide the weight setting among different terms in object function of the single resonance approach based on the perturbation theory.