81 research outputs found

    The Minimal Total Irregularity of Graphs

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    In \cite{2012a}, Abdo and Dimitov defined the total irregularity of a graph G=(V,E)G=(V,E) as \hskip3.3cm irrt\rm irr_{t}(G)=12u,vVdG(u)dG(v),(G) = \frac{1}{2}\sum_{u,v\in V}|d_{G}(u)-d_{G}(v)|, \noindent where dG(u)d_{G}(u) denotes the vertex degree of a vertex uVu\in V. In this paper, we investigate the minimal total irregularity of the connected graphs, determine the minimal, the second minimal, the third minimal total irregularity of trees, unicyclic graphs, bicyclic graphs on nn vertices, and propose an open problem for further research.Comment: 13 pages, 4 figure

    The Maximal Total Irregularity of Bicyclic Graphs

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    In 2012, Abdo and Dimitrov defined the total irregularity of a graph G=(V,E) as irrtG=1/2∑u,v∈VdGu-dGv, where dGu denotes the vertex degree of a vertex u∈V. In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs on n vertices

    Plasma-Assisted Chemical Vapor Deposition of Titanium Oxide Films by Dielectric Barrier Discharge in TiCl4/O-2/N-2 Gas Mixtures

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    National Natural Science Foundation of China [10875025, 20803007]; Fundamental Research Funds for Central Universities of China [DC12010116, DC13010106]; Program for Liaoning Excellent Talents in University [LJQ20l3128]Low-pressure dielectric barrier discharge (DBD) TiCl4/O-2 and N-2 plasmas have been used to deposit titanium oxide films at different power supply driving frequencies. A home-made large area low pressure DBD reactor was applied, characterized by the simplicity of the experimental set-up and a low consumption of feed gas and electric power, as well as being easy to operate. Atomic force microscopy, scanning electron microscopy, energy dispersive spectroscopy, and contact angle measurements have been used to characterize the deposited films. Experimental results show all deposited films are uniform and hydrophilic with a contact angle of about 15 degrees. Compared to titanium oxide films deposited in TiCl4/O-2 gas mixtures, those in TiCl4/O-2/N-2 gas mixtures are much more stable. The contact angle of titanium oxide films in TiCl4/O-2/N-2 gas mixtures with the addition of 50% N-2 and 20% TiCl4 is still smaller than 20 degrees, while that of undoped titanium oxide films is larger than 640 when they are measured after one week. The low-pressure TiCl4/O-2 plasmas consist of pulsed glow-like discharges with peak widths of several microseconds, which leads to the uniform deposition of titanium oxide films. Increasing a film thickness over several hundreds of nm leads to the film's fragmentation due to the over-high film stress. Optical emission spectra (OES) of TiCl4/O-2 DBD plasmas at various power supply driving frequencies are presented

    Plasma-assisted chemical vapor deposition of titanium oxide films by dielectric barrier discharge in TiCl4/O2/N2 gas mixtures

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    Low-pressure dielectric barrier discharge (DBD) TiCl4/O2 and N2 plasmas have been used to deposit titanium oxide films at different power supply driving frequencies. A homemade large area low pressure DBD reactor was applied, characterized by the simplicity of the experimental set-up and a low consumption of feed gas and electric power, as well as being easy to operate. Atomic force microscopy, scanning electron microscopy, energy dispersive spectroscopy, and contact angle measurements have been used to characterize the deposited films. Experimental results show all deposited films are uniform and hydrophilic with a contact angle of about 15°. Compared to titanium oxide films deposited in TiCl4/O2 gas mixtures, those in TiCl4/O2/N2 gas mixtures are much more stable. The contact angle of titanium oxide films in TiCl4/O2/N2 gas mixtures with the addition of 50% N2 and 20% TiCl4 is still smaller than 20°, while that of undoped titanium oxide films is larger than 64° when they are measured after one week. The low-pressure TiCl4/O2 plasmas consist of pulsed glow-like discharges with peak widths of several microseconds, which leads to the uniform deposition of titanium oxide films. Increasing a film thickness over several hundreds of nm leads to the film's fragmentation due to the over-high film stress. Optical emission spectra (OES) of TiCl4/O2 DBD plasmas at various power supply driving frequencies are presented

    Nonlinear Flutter Analysis for a Long-Span Suspension Bridge

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    The wind-induced flutter of the long-span suspension bridge structure is extremely harmful to the bridge. Therefore, it is necessary to study the nonlinear problem of wind-induced flutter. Here, the nonlinear flutter problem of a long-span suspension bridge with cubic torsional stiffness is analyzed by the equivalent linearization method. The system has Hopf bifurcation and limit cycle oscillations (LCOs) under critical wind speed. Replacing the nonlinear stiffness term of the original nonlinear equation with the equivalent linear stiffness, we can obtain the equivalent linearized equation of the nonlinear flutter system and the solution, critical wind speed, and flutter frequency of the suspension bridge flutter system. At the same time, the system has a limit cycle vibration, and the Hopf bifurcation point is obtained. Compared with the numerical method, the calculation results are consistent. The influence of the damping ratio on the flutter system is analyzed. Increasing the system damping ratio can increase the flutter critical wind speed and reduce the amplitude of LCOs. The influence of cubic torsional stiffness on the flutter system is analyzed. The increase of the cubic stiffness coefficient does not change the critical state of flutter, but reduces the amplitude of LCOs
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