Synthesis and Crystal Structure of a New 2D Honeycomb—like Cadmium （Ⅱ） Complex with Tripodal Ligand

A new cadmium (II) coordination polymer, [Cd(TTTMB)₂]‐(SO₄) · 21H₂O, where TTTMB =1,3, 5‐tris (imidazol‐1‐yl‐methyl)‐2,4,6‐trimethylbenzene, was obtained by self‐assembly of tripodal ligand TTTMB with CdSO₄·2.7H₂O in acetonitrile, and characterized by X‐ray crystallography. The crystal data belongs to monoclinic space group C_c with cell parameters a = 1.16891(4) nm, b=2.06671(6) nm, c = 2.48185(7) nm, β = 97.8560(10)°, R = 0.0487, wR = 0.1211. The results of structure analysis indicate that each TTTMB ligand coordinates three metal atoms and in turn each Cd(II) atom with octahedral coordination geometry connects six nitrogen atoms of imidazole group from six different TTTMB ligands to produce a 2D honeycomb network structure. There are a lot of water molecules linked by hydrogen bonds and occupied the channels formed intra‐ and inter‐sheets.     

On the structure of positive solutions of a class of fourth order nonlinear differential equations

A detailed analysis is made of the structure of positive solutions of fourth-order differential equations of the form

Transfer impedance and effectiveness of SMA receptacle for wideband measurement of discharge current due to human ESD

In order to investigate the effectiveness of an SMA receptacle as wideband measurement electrode for human ESD, we derived the transfer impedance of a 50-Ω SMA receptacle, and measured its frequency characteristics from 300 kHz to 20 GHz. With a 12-GHz digital oscilloscope, measurement of discharge currents through a hand-held metal bar from a charged human was made, and thereby the injected currents on the SMA receptacle were reconstructed from the measured transfer impedance. The results show that at a charge voltage of 1500 V the reconstructed current waveform agrees well with the observed voltage waveform divided by 50 Ω.     

The Distribution of the Sojourn Time for the Brownian Excursion

The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula.     

Synthesis,Crystal Structure and Photoluminescence Property of Zinc(II), Cadmium(II), and Lead(II) Complexes with Bidentate Ligand: 1‐(1‐Imidazolyl)‐4‐(imidazol‐1‐ylmethyl)benzene (IIMB)

Assembly of bidentate ligand 1‐(1‐imidazolyl)‐4‐(imidazol‐1‐ylmethyl)benzene (IIMB) with varied metal salts of Zn^II, Cd^II and Pb^II provide three new complexes, [Zn(IIMB)₂](ClO₄)₂·2H₂O ( 1 ), [Cd(IIMB)₂(SCN)₂] ( 2 ) and [Pb(IIMB)₂(SCN)](SCN) ( 3 ). Single crystal X‐ray diffraction studies revealed that complexes 1 and 2 display a similar one‐dimensional double stranded chain structure, while complex 3 is a slight distorted rhombohedral grid network with (4,4) topology. The results indicate that the coordination geometry of the metal ion and the counter anion have great impact on the structure of the complexes. In addition, the photoluminescence properties of ligand IIMB and complexes 1 – 3 were studied in the solid state at room temperature.