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91.
A connected graph G can be disconnected or reduced to a single vertex by removing an appropriate subset of the vertex set V(G), and can be disconnected by removing a suitable subset of the edge set E(G). Attention has usually been centered on separating sets having minimum cardinality, and parameters called the vertex connectivity and the edge connectivity defined. These classical concepts are generalized by using separating sets which are minimal. By considering the maximum as well as the minimum cardinality of such sets, one defines vertex and edge connectivity parameters. Sharp upper bounds are established for these numbers and their values computed for certain classes of graphs. An analogue of Whitney's theorem on connectivity is obtained. Parameters are also defined for minimal separating sets consisting of a mixture of vertices and edges, and these are shown to depend on the maximum and minimum values of the vertex and edge connectivity parameters. 相似文献
92.
93.
For positive integersr ands, f′(r, s) is defined as the smallest positive integerp such that every connected (ordinary) graph of orderp contains eitherr mutually adjacent lines ors mutually disjoint lines. It is found thatf’(r,s) =(r−1) (s−1)+2 unlessr=2 and s ≠ 1, in which casef′(2,s)=3.
Definitions not given here can be found in [7, 8]. 相似文献
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95.
In this work, Abel’s integral operator is represented based on Alpert’s multiwavelets as a sparse matrix and then a non-linear Abel’s integral equation of the second kind is solved by multiwavelets Galerkin method. Nonlinearity and singularity make the numerical procedure more challenging. But the proposed scheme overcomes these problems. Convergence analysis is investigated and some numerical examples validated this analysis.
相似文献96.
In this Note, we prove that every m-th root Finsler metric with isotropic Landsberg curvature reduces to a Landsberg metric. Then, we show that every m-th root metric with almost vanishing H-curvature has vanishing H-curvature. 相似文献
97.
Citric acid was used to crosslink whey proteins and sugar beet pectin at 50°C with the aid of sodium hydroxide as catalyst. The effects of the pH of biopolymers mixed solution and the duration of the crosslinking process on various characteristics of generated particles were studied. Although the majority of the generated aggregates were of submicron size, particles as small as 59 nm were present. The crosslinking duration did not affect the size of aggregates; however, the samples crosslinked at pH 4.2 were greater than those obtained at pH 7.0. Scanning electron microscopy images revealed that aggregates were not uniformly shaped; differential scanning calorimetry indicated that conjugate whey protein–pectin aggregates had greater thermal stabilities than their parent individual biopolymers. The occurrence of crosslinkages was confirmed by the results of Fourier transform infrared spectroscopy. 相似文献
98.
Behzad Koozegar Kaleji 《Journal of Sol-Gel Science and Technology》2013,67(2):312-320
The thin films of TiO2 doped by Sn or Nb were prepared by sol–gel method under process control. The effects of Sn and Nb doping on the structural, optical and photo-catalytic properties of applied thin films have been studied by X-ray diffraction (XRD) high resolution transmission electron microscopy and UV–Vis absorption spectroscopy. Surface chemical state of thin films was examined by atomic X-ray photoelectron spectroscopy. XRD results suggest that adding impurities has a great effect on the crystallinity and particle size of TiO2. Titania rutile phase formation in thin film was promoted by Sn4+ addition but was inhibited by Nb5+ doping. The activity of the photocatalyst was evaluated by photocatalytic degradation kinetics of aqueous methylene blue under UV and Visible radiation. The results show that the photocatalytic activity of the Sn-doped TiO2 thin film have a larger degradation efficiency than Nb-doped TiO2 under visible light, but under UV light photocatalytic activity of the Nb-doped TiO2 thin film is better. 相似文献
99.
Behzad Zeynizadeh Mohammad Mehdi Baradarani Ronak Eisavi 《Phosphorus, sulfur, and silicon and the related elements》2013,188(11):2208-2215
Abstract Solvent-free conversion of various epoxides to the corresponding thiiranes was carried out efficiently with immobilized thiourea on CaCO3. The reactions were completed within 1–12 min under oil bath (60 °C–70 °C) conditions to afford thiiranes in 88%–98% yields. [Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: Figures S1–S3.] GRAPHICAL ABSTRACT 相似文献
100.
We report on an inorganic–organic hybrid nanocomposite that represents a novel kind of fiber coating for solid-phase microextraction (SPME) of polycyclic aromatic hydrocarbons (PAHs). The material is composed of ZnO nanoparticles, polythiophene and hexagonally ordered silica, and displays good extraction capability due to its nanostructure. The nanocomposite was synthesized by an in-situ polymerization technique, and the ZnO nanoparticles were anchored to the pores in the walls. The ZnO/polythiophene/hexagonally ordered silica (ZnO/PT/SBA-15) nanocomposite was then deposited on a stainless steel wire to obtain the fiber for SPME of PAHs. Optimum conditions include an extraction temperature of 85 °C (for 30 min only), a desorption temperature of 260 °C (for 2 min), and a salt concentration (NaCl) of 20 % (w/v). The detection limits are between 8.2 and 20 pg mL?1, and the linear responses extend from 0.1 to 10 ng mL?1. The repeatability for one fiber (for n?=?5), expressed as relative standard deviation, is between 4.3 and 9.1 %. The method offers the advantage of being simple to use, rapid, and low-cost (in terms of equipment). The thermal stability of the fiber and high relative recovery (compared to conventional methods) represent additional attractive features. Figure
We report on an inorganic–organic hybrid nanocomposite that represents a novel kind of fiber coating with thermal stability and high relative recovery for solid-phase microextraction (SPME) of polycyclic aromatic hydrocarbons (PAHs). The method is simple to use, rapid and low-cost. 相似文献