Calderón problem for connections

In this paper, we consider the problem of identifying a connection ? on a vector bundle up to gauge equivalence from the Dirichlet-to-Neumann map of the connection Laplacian ?*? over conformally transversally anisotropic (CTA) manifolds. This was proved in [9 Dos Santos Ferreira, D., Kenig, C., Salo, M., Uhlmann, G. (2009). Limiting Carleman weights and anisotropic inverse problems. Invent. Math. 178:119–171.[Crossref], [Web of Science ®] , [Google Scholar]] for line bundles in the case of the transversal manifold being simple—we generalize this result to the case where the transversal manifold only has an injective ray transform. Moreover, the construction of suitable Gaussian beam solutions on vector bundles is given for the case of the connection Laplacian and a potential, following the works of [11 Dos Santos Ferreira, D., Kurylev, Y., Lassas, M., Salo, M. (2016). The Calderón problem in transversally anisotropic geometries. J. Eur. Math. Soc., 18:2579–2626.[Crossref], [Web of Science ®] , [Google Scholar]]. This in turn enables us to construct the Complex Geometrical Optics (CGO) solutions and prove our main uniqueness result. We also reduce the problem to a new non-abelian X-ray transform for the case of simple transversal manifolds and higher rank vector bundles. Finally, we prove the recovery of a flat connection in general from the DN map, up to gauge equivalence, using an argument relating the Cauchy data of the connection Laplacian and the holonomy.     

隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.     

The catalytic performance study of polymerized ionic liquid synthesized in different conditions on alkylation of o‐Xylene with styrene

In this work, a series of novel acidic polymerized ionic liquids were used as heterogeneous catalyst for alkylation of o‐Xylene with styrene. And the effect of the amount of initiator and the type of acid used for ion exchange on catalyst structure and the catalytic performance of catalysts for alkylation were studied thoroughly. The experiment results show: when the percentage of the amount of initiator in the total material is 3%, the polymerized ionic liquid catalyst MPM‐SO₃H‐[C₃V][SO₃CF₃] has the most uniform with a specific surface area of 97.30 m²/g and a pore volume of 0.35 cm³/g. Benefiting from the unique structure features, MPM‐SO₃H‐[C₃V][SO₃CF₃] manifested an excellent catalytic performance for alkylation of o‐Xylene with styrene, along with the conversion of styrene was 96.8% and the yield of 1‐Phenyl‐1‐ortho‐xylene ethane was 94.7%. Therefore, this work provides a novel reference to the synthesis of polymerized ionic liquids and clearly explains the advantage of novel acidic polymerized ionic liquids on alkylation.     

Structure and Properties of Electrochemically Synthesized Silver Nanoparticles in Aqueous Solution by High-Resolution Techniques

The aim of this work was to deeply investigate the structure and properties of electrochemically synthesized silver nanoparticles (AgNPs) through high-resolution techniques such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), Zeta Potential measurements, and matrix-assisted laser desorption/ionization time of flight mass spectrometry (MALDI-TOF-MS). Strong brightness, tendency to generate nanoclusters containing an odd number of atoms, and absence of the free silver ions in solution were observed. The research also highlighted that the chemical and physical properties of the AgNPs seemed to be related to their peculiar oxidative state as suggested by X-ray photoelectron spectroscopy (XPS) and X-ray powder diffraction (XRPD) analyses. Finally, the MTT assay tested the low cytotoxicity of the investigated AgNPs.     

CuCl2/NaY体系表面分散态研究

铜负载分子筛作为催化剂或吸附剂，在石油化工、环境保护等方面有许多用途[1，2]．已有研究发现，铜交换的Y型分子筛对NO分解等反应具有较高活性及稳定性［3-5］．因此研究铜负载Y型分子筛对有关吸附剂和催化剂的制备有重要意义．我们实验室在研究活性组分在载体表面分散现象时     

Crystal growth,spectral characterization and structural studies of a luminescent coordination polymer of calcium(II) complex of benzilic acid

Single crystals of a new calcium(II) complex of benzilic acid, [Ca(C₁₄H₁₁O₃)₂(C₁₄H₁₂O₃)₂] have been successfully grown by gel diffusion technique at room temperature. Single crystal X-ray diffraction study reveals that the compound belongs to orthorhombic system with space group Fddd. The adjacent CaO₈ units are linked via O–H–O interaction to form one dimensional polymeric chains. The extensive hydrogen bonding interactions lead to a supramolecular structure. The grown crystals were further characterized by elemental analysis, FT-IR, UV–Visible, thermogravimetric, powder X-ray diffraction and solid state photoluminescence studies.     

Calcium-based coordination polymers from a solvothermal synthesis of HKUST-1 in 3D printed autoclaves

A mixed-metal 1D coordination polymer [CaCu(HBTC)₂(H2O)₈]_n (where H₃BTC – benzene-1,3,5-tric arboxylic acid) was obtained in a solvothermal synthesis of a well-known copper-containing metal–organic framework [Cu₃(BTC)₂(H₂O)₃]_n (HKUST-1) in autoclaves 3D-printed from commercial polypropylene. This material was a source of calcium ions, apparently, leaking from a colorant (calcium carbonate) promoted by glacial acetic acid as a modulator used to produce large single crystals of HKUST-1. This finding was confirmed by elemental analysis and a model experiment that resulted in a new calcium-based 1D coordination polymer [Ca(H₂BTC)₂(H₂O)₅]_n under the same solvothermal conditions with no copper or calcium salts put into a 3D-printed autoclave.     

New crystal structures of β-[Ni(NCS)2(4-methylpyridine)4] clathrates with furan,tetrahydrofuran, methylene chloride,benzene + ethanol and methylcellosolve as guest molecules

Single crystal X-ray structures of clathrates of -[Ni(NCS)₂(4-methylpyridine)₄] with furan, tetrahydrofuran, benzene + ethanol, methylene chloride, and methylcellosolve as guests molecules are reported. The location of the guest molecule in the partially decomposed clathrate with methylene chloride was defined by X-ray diffraction and compared with the fully occupied one. The host lattices of all clathrates studied are tetragonal (I4₁/a) and do not differ significantly from typical -phase clathrates of [M(NCS)₂(4-methylpyridine)₄] (M = divalent metal cation). Arrangements of guest molecules represent different types of packing: one type of guest molecule occupies both possible types of positions, two different guest molecules occupy different positions, with only one type of positions occupied by one type of guest molecule. Possible stoichiometries of clathrates with -type lattices are discussed.Presented at the Sixth International Seminar on Inclusion Compounds, Istanbul, Turkey, 27–31 August 1995.     

Synthesis and structure of 6-chloro-2,3-trimethylene-4-phenylquinoline

An X-ray structural investigation of 6-chloro- 2,3-trimethylene-4- phe nylquinoli ne obtained by the reaction of 2-amino-5-chlorobenzophenone with cyclopentanone was carried out. At 20 °C, a = 23.750,b = 9,242, c = 14.018 A, = 112,68° space group (21c,Z = 8, 2647 reflections,R = 0.047 He five-membered ring has an envelope conformation Conjugation between the quinohne fragment and the phenyl substituent is significantly distorted dm to the rotation of the latter by -62.9°Translated fromIzvestiya Akademii Nauk. Seriva Khimicheskaya, No. 7, pp. 1800–1802, July, 1996.