Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus

We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we investigate how this estimation can be sharpened under the assumption that the abelian surface does not contain low genus curves. This approach naturally leads us to consider Weil restrictions of elliptic curves and abelian surfaces which do not admit a principal polarization.     

Phase transitions in graphs on orientable surfaces

Let be the orientable surface of genus and denote by the class of all graphs on vertex set with edges embeddable on . We prove that the component structure of a graph chosen uniformly at random from features two phase transitions. The first phase transition mirrors the classical phase transition in the Erd?s‐Rényi random graph chosen uniformly at random from all graphs with vertex set and edges. It takes place at , when the giant component emerges. The second phase transition occurs at , when the giant component covers almost all vertices of the graph. This kind of phenomenon is strikingly different from and has only been observed for graphs on surfaces.     

基于自由曲面反射镜的低投射比超短焦投影物镜的光学设计

为了设计低投射比的超短焦投影物镜,本文采用自由曲面和折反式的光路结构设计了一种具有低投射比的超短焦投影物镜系统。该物镜由一个旋转对称的折射透镜组和一个自由曲面反射镜组成。采用11.938 mm的数字微镜器件(DMD)作为空间光调制器产生图像源。采用法线加权迭代优化的方法计算自由曲面。最后,分析了系统的性能。仿真结果表明:超短焦投影物镜可在580 mm的投影距离处实现3048 mm尺寸的大屏幕投影,系统的投射比低至0.19,系统的最大畸变小于0.72%。能够满足低投射比超短焦投影物镜的设计要求。该投影系统具有低投射比、低畸变、投影效果好等优点,可为超短焦投影系统的进一步发展提供有益参考。     

Comparison of monomethoxy‐, dimethoxy‐, and trimethoxysilane anchor groups for surface‐initiated RAFT polymerization from silica surfaces

The immobilization of reversible addition–fragmentation chain transfer (RAFT) agents on silica for surface‐initiated RAFT polymerizations (SI‐RAFT) via the Z‐group approach was studied systematically in dependence of the functionality of the RAFT‐agent anchor group. Monoalkoxy‐, dialkoxy‐, and trialkoxy silyl ether groups were incorporated into trithiocarbonate‐type RAFT agents and bound to planar silica surfaces as well as to silica nanoparticles. The immobilization efficiency and the structure of the bound RAFT‐agent film varied strongly in dependence of the used solvent (toluene vs. 1,2‐dimethoxyethane) and the anchor group functionality, as evidenced by atomic force microscopy, transmission electron microscopy, dynamic light scattering, and UV/Vis spectroscopy. Surface‐initiated RAFT polymerizations using functionalized silica nanoparticles revealed that grafted oligomers, which often occur in SI‐RAFT, are not formed within the crosslinked structures that originate from the immobilization, and that RAFT‐agent films that show less aggregation during the immobilization are more efficient during SI‐RAFT in terms of polymer grafting density. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 103–113     

Chemorheology investigation of a glassy epoxy thermoset on tensile plastic flow and fracture morphology

Reproducible and uncharacteristic tensile stress–strain behavior of cured glassy epoxy‐amine networks produces distinctive fracture surfaces. Test specimens exhibiting plastic flow result in mirror‐like fracture surfaces, whereas samples that fail during yield or strain softening regions possess nominal mirror‐mist‐hackle topography. Atomic force microscopy and scanning electron microscopy reveal branched nodule morphologies in the 50‐nm size scale that may be responsible for the unusual tensile properties. Current hypothesis is that plastic flow of the glassy thermoset occurs through the existence and deformation of these nodular nanostructures. The thermal cure profile of the epoxy‐amine thermoset affects the size and formation of the nodular nanostructure. Eliminating vitrification during thermoset polymerization forms a more continuous phase, reduction in size of the nodules, and eliminates the capacity of the material to yield in plastic flow. This maximizes nanostructure connectivity of the glassy epoxy‐amine thermoset and reduces strain to failure significantly. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1333–1344.     

Synthesis,Hirshfeld surface analysis,luminescence and thermal properties of three first-row transition metal complexes containing 4′-hydroxy-2,2′:6′,2″-terpyridine: Application for preparation of nano metal oxides

A series of new mono- and bis-terpyridine complexes [Mn(tpyOH)Cl₂] ( 1 ), [Ni(tpyOH)₂](PF₆)₂ ( 2 ) and [Zn(tpyO)(η¹-OCOCH₃)(H₂O)]⋅3H₂O ( 4 ) containing 4′-hydroxy-2,2′:6′,2″-terpyridine (tpyOH) were synthesized and structurally characterized using elemental analysis, infrared spectroscopy and single-crystal X-ray diffraction. The reaction of MnCl₂ with tpyOH in a mixture of methanol and CH₂Cl₂ resulted in the formation of 1 . The X-ray crystal structure of 1 reveals that Mn(II) is penta-coordinated by three nitrogen atoms from tpyOH and two Cl⁻ in a slightly distorted trigonal bipyramidal geometry. Complex 2 was also prepared by the reaction of nickel(II) chloride with tpyOH in a methanolic medium in the presence of NH₄PF₆. Notably, the complex [Ni(tpyOH)(tpyO)]PF₆ ( 3 ), obtained during the crystallization of 2 from dichloromethane, was characterized using X-ray crystallography which shows that six nitrogen atoms from terpyridine ligands occupy the coordination sites around the Ni(II) centre in a distorted octahedral geometry with four longer bonds and two shorter Ni N bonds. The reaction of zinc(II) acetate with tpyOH in a mixture of methanol and CH₂Cl₂ led to the formation of 4 . The crystal structure of 4 reveals the formation of penta-coordinated Zn(II) complex containing three nitrogen atoms from tpyO, a monodentate acetate ligand and one coordinated water molecule. Hirshfeld surface analyses and two-dimensional fingerprint plots show that the main interactions are O…H/H…O contacts in 1 , 3 and 4 . The thermal decomposition reactions of 1 , 2 and 4 were studied using thermogravimetric analysis in detail due to their different structures. The solution luminescence features of 1 , 2 and 4 include high-energy intense π → π* intraligand and low-energy metal-to-ligand charge transfer transitions at room temperature. The calcination of the coordination complexes led to the formation of corresponding nano metal oxides. The products were structurally characterized using infrared spectroscopy, scanning electron microscopy and energy-dispersive X-ray spectroscopy. The average particle size using Scherrer's equation was calculated to be below 50 nm.     

Exploring Potential Energy Surfaces for Aggregation‐Induced Emission—From Solution to Crystal

Aggregation‐induced emission (AIE) is a phenomenon where non‐luminescent compounds in solution become strongly luminescent in aggregate and solid phase. It provides a fertile ground for luminescent applications that has rapidly developed in the last 15 years. In this review, we focus on the contributions of theory and computations to understanding the molecular mechanism behind it. Starting from initial models, such as restriction of intramolecular rotations (RIR), and the calculation of non‐radiative rates with Fermi's golden rule (FGR), we center on studies of the global excited‐state potential energy surfaces that have provided the basis for the restricted access to a conical intersection (RACI) model. In this model, which has been shown to apply for a diverse group of AIEgens, the lack of fluorescence in solution comes from radiationless decay at a CI in solution that is hindered in the aggregate state. We also highlight how intermolecular interactions modulate the photophysics in the aggregate phase, in terms of fluorescence quantum yield and emission color.     

Generalization of the Kelvin equation for arbitrarily curved surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equation's applicability for arbitrarily curved surface has been long debated and is severe problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to the vapor/fluid interfaces in chemical equilibrium conditions nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.