2010 No. 5
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2010, (5): 1-13.
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Abstract:
Research developments on maximum genus of graphs in graph embedding theory since 1971 were reviewed, including the following aspects: the relationships between maximum genus and other graph invariants such as connectivity, diameter, girth, chromatic number and z-factors; maximum genus and embedded graphs; and number of maximum genus embeddings.
Research developments on maximum genus of graphs in graph embedding theory since 1971 were reviewed, including the following aspects: the relationships between maximum genus and other graph invariants such as connectivity, diameter, girth, chromatic number and z-factors; maximum genus and embedded graphs; and number of maximum genus embeddings.
2010, (5): 14-19.
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This paper considered the following problem: Among all the complements of unicyclic graphs with order n, which one has the maximum spectral radius? It was showed that the extremal graph is S_n^3, where S_n^3 is obtained from a 3-cycle by attaching n-3 pendant vertices to a vertex.
This paper considered the following problem: Among all the complements of unicyclic graphs with order n, which one has the maximum spectral radius? It was showed that the extremal graph is S_n^3, where S_n^3 is obtained from a 3-cycle by attaching n-3 pendant vertices to a vertex.
2010, (5): 20-26.
Abstract:
By applying discharging method and using the properties of critical graphs, we proved that every simple planar graph G with Delta =6 is of class 1, if any two k-cycles of length at most 6 are not adjacent.
By applying discharging method and using the properties of critical graphs, we proved that every simple planar graph G with Delta =6 is of class 1, if any two k-cycles of length at most 6 are not adjacent.
2010, (5): 27-32，5.
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In this paper, the inverse eigenvalue problem of anti-reflexive matrices with a submatrix constraint was discussed. The sufficient and necessary conditions under which the problem was solvable were obtained by using the matrix decompositions, and the general expression of the solution was given.
In this paper, the inverse eigenvalue problem of anti-reflexive matrices with a submatrix constraint was discussed. The sufficient and necessary conditions under which the problem was solvable were obtained by using the matrix decompositions, and the general expression of the solution was given.
2010, (5): 33-37,4.
Abstract:
By using theory of bounded linear operators on Hilbert spaces, the Shermen-Morrison-Woodbury (SMW) formula's Moore-Penrose inverse was presented. The formula obtained can be used to compute certain perturbation of A^+ and the Moore--Penrose inverses of some operator matrices.
By using theory of bounded linear operators on Hilbert spaces, the Shermen-Morrison-Woodbury (SMW) formula's Moore-Penrose inverse was presented. The formula obtained can be used to compute certain perturbation of A^+ and the Moore--Penrose inverses of some operator matrices.
2010, (5): 38-48.
Abstract:
Statistical inference procedures were proposed in assessing product reliability based on EM algorithm. The general formulae to estimate parameters were derived in the degradation model when its random effects follow an exponential family, and sensitivity of the choice of the distributions of the random effects was assessed via simulation. Two real data sets were analyzed.
Statistical inference procedures were proposed in assessing product reliability based on EM algorithm. The general formulae to estimate parameters were derived in the degradation model when its random effects follow an exponential family, and sensitivity of the choice of the distributions of the random effects was assessed via simulation. Two real data sets were analyzed.
2010, (5): 49-55.
Abstract:
This paper explicitly computed the variance-optimal hedging strategy in discrete time for binary options and European call option on Dividend-paying Stock. An example of prediction of dividend was given.
This paper explicitly computed the variance-optimal hedging strategy in discrete time for binary options and European call option on Dividend-paying Stock. An example of prediction of dividend was given.
2010, (5): 56-66.
Abstract:
In 1966, O. A. Ladyzhenskaya proposed a kind of modified Navier-Stokes equations to describe the three-dimensional nonstationary flows of viscous incompressible fluids without assuming small gradients of the velocities. This paper considered large time behavior of a solution for the modified Navier-Stokes equations in a bounded domain and showed that decay of the solution is exactly of exponential type when force term is equal to zero.Moreover the ratio of the enstrophy over the energy has a limit as time tends to infinity, and the limit is an eigenvalue of the Stokes operator.
In 1966, O. A. Ladyzhenskaya proposed a kind of modified Navier-Stokes equations to describe the three-dimensional nonstationary flows of viscous incompressible fluids without assuming small gradients of the velocities. This paper considered large time behavior of a solution for the modified Navier-Stokes equations in a bounded domain and showed that decay of the solution is exactly of exponential type when force term is equal to zero.Moreover the ratio of the enstrophy over the energy has a limit as time tends to infinity, and the limit is an eigenvalue of the Stokes operator.
2010, (5): 67-72, .
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The peakons are peaked solitary wave solutions of a certain nolinear dispersive equation that is a model in shallow water theory. In this paper, the author showed that the peaked solitons to the DGH equation were orbital stable in H^1 norm by constructing a functional and conservation laws. The stability theorem indicates that, if a wave is close to the peakons at the beginning, it will remain close to some translate of it at any time later.
The peakons are peaked solitary wave solutions of a certain nolinear dispersive equation that is a model in shallow water theory. In this paper, the author showed that the peaked solitons to the DGH equation were orbital stable in H^1 norm by constructing a functional and conservation laws. The stability theorem indicates that, if a wave is close to the peakons at the beginning, it will remain close to some translate of it at any time later.
2010, (5): 73-83.
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A concrete nonlinear system with degree two and the least dimension (=3) was firstly given, and it was shown that the system has a heterodimensional cycle with double orbit flips. Then, by using Silnikov coordinates and moving frame, the bifurcation of the cycle was studied under the perturbation of degree three. The method given here provides a useful reference for constructing homoclinic, heteroclinic and heterodimensional cycles with various other kinds of degeneracy.
A concrete nonlinear system with degree two and the least dimension (=3) was firstly given, and it was shown that the system has a heterodimensional cycle with double orbit flips. Then, by using Silnikov coordinates and moving frame, the bifurcation of the cycle was studied under the perturbation of degree three. The method given here provides a useful reference for constructing homoclinic, heteroclinic and heterodimensional cycles with various other kinds of degeneracy.
2010, (5): 84-90.
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This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbitwas deduced for quadratic system.
This paper derived the necessary and sufficient condition for the existence of invariant real irreducible algebraic curve of a polynomial differential system. Using this result and quadratic polynomials of quadratic system, we established some criteria to determine whether equilibrium was circled by a closed orbit. Finally, a property of the equilibrium enclosed in a periodic orbitwas deduced for quadratic system.
2010, (5): 91-95.
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Let C be the Cantor ternary set. The condition of the intersection C\cap (C+t)\cap (C+s)\neq\emptyset was considered and the Hausdorff dimension of (t,s) was computed when the intersection was nonempty. A conclusion was proved: dim_H C\cap (C+t)\cap (C+s)=0 for a.e. (t,s)\in{\bf R}\times {\bf R}. Then by a related result of Moran set, the expression of dim_H C\cap (C+t)\cap (C+s) was investigated.
Let C be the Cantor ternary set. The condition of the intersection C\cap (C+t)\cap (C+s)\neq\emptyset was considered and the Hausdorff dimension of (t,s) was computed when the intersection was nonempty. A conclusion was proved: dim_H C\cap (C+t)\cap (C+s)=0 for a.e. (t,s)\in{\bf R}\times {\bf R}. Then by a related result of Moran set, the expression of dim_H C\cap (C+t)\cap (C+s) was investigated.
2010, (5): 96-102.
Abstract:
This paper proposed a new tree alignment algorithm for determining the optimal matching structure of the input web pages, in order to extract web data automatically. Based on the alignment, the trees were merged into one union tree whose nodes record statistical information obtained from multiple web pages. The algorithm detects repeating patterns on the union tree, and a wrapper built on the most probable content block and the repeating patterns extracts data from web pages. Experimental results showed that the proposed algorithm achieves high extraction accuracy and has steady performance.
This paper proposed a new tree alignment algorithm for determining the optimal matching structure of the input web pages, in order to extract web data automatically. Based on the alignment, the trees were merged into one union tree whose nodes record statistical information obtained from multiple web pages. The algorithm detects repeating patterns on the union tree, and a wrapper built on the most probable content block and the repeating patterns extracts data from web pages. Experimental results showed that the proposed algorithm achieves high extraction accuracy and has steady performance.
2010, (5): 103-109.
Abstract:
Polystyrene photonic crystal and a series of two-dimensional (2D) photonic crystals based on polystyrene template were prepared, including two-dimensional photonic crystal of α-Fe2O3 bowls and two-dimensional photonic crystal of ZnO pillars. Large-area specular reflectance measurements showed the presence of photonic stop band. Self-assembled PS is a simple, low cost and repeatability method to fabricate large-area two-dimensional photonic crystal. It offers a new idea on preparing two-dimensional photonic crystal.
Polystyrene photonic crystal and a series of two-dimensional (2D) photonic crystals based on polystyrene template were prepared, including two-dimensional photonic crystal of α-Fe2O3 bowls and two-dimensional photonic crystal of ZnO pillars. Large-area specular reflectance measurements showed the presence of photonic stop band. Self-assembled PS is a simple, low cost and repeatability method to fabricate large-area two-dimensional photonic crystal. It offers a new idea on preparing two-dimensional photonic crystal.
2010, (5): 110-117.
Abstract:
Br2 doped PANI was synthesised by chemical oxidation method and absorption of bromine vapor. MWNTs/PANI and MWNTs/Br2 doped PANI composites were prepared by mechanical blending method, The new composite exhibits as high electrical conductivity as that of pure MWNTs. 5~10 S·m^-1. Fourier transform infrared spectroscopy (FTIR), thermo gravimetric (TG), ultraviolet-visible absorption spectra (UV-Vis), X-ray powder diffraction (XRD) and X-ray spectroscopy (XPS) were used to study the electrical conductivity properties and mechanism. The results showed that π-π and p-π system is formed between MWNTs and doped PANI . MWNTs combined with the Br2 doped PANI to form charge transfer composites, then form individual conductive units, which play a critical role in forming the conducting net of composites. With the increase of conductive units, conducting system is formed by conductive unit connection and the conductivity of composites reaches the maximum.
Br2 doped PANI was synthesised by chemical oxidation method and absorption of bromine vapor. MWNTs/PANI and MWNTs/Br2 doped PANI composites were prepared by mechanical blending method, The new composite exhibits as high electrical conductivity as that of pure MWNTs. 5~10 S·m^-1. Fourier transform infrared spectroscopy (FTIR), thermo gravimetric (TG), ultraviolet-visible absorption spectra (UV-Vis), X-ray powder diffraction (XRD) and X-ray spectroscopy (XPS) were used to study the electrical conductivity properties and mechanism. The results showed that π-π and p-π system is formed between MWNTs and doped PANI . MWNTs combined with the Br2 doped PANI to form charge transfer composites, then form individual conductive units, which play a critical role in forming the conducting net of composites. With the increase of conductive units, conducting system is formed by conductive unit connection and the conductivity of composites reaches the maximum.
2010, (5): 118-125.
Abstract:
The electrical conductivity of polyphenylacetylene (PPA) was enhaced by eleven orders of magnitude after absorption of bromine vapor. TG, UV-Vis spectra, and XPS spectra were used to study the interaction among bromine, nano-graphite and PPA. According to the results, bromine played a major role to enhance the conductivity of the composites when the weight percentage of bromine doped graphite was low. When the weight percentage of bromine doped graphite was high, the doping effect formed by bromine doped nanographite and bromine doped PPA, was the main point to enhance the conductivity. When the weight percentage of bromine doped nano-graphite was higher, the conductive network formed by bromine doped nano-graphite, played a major role.
The electrical conductivity of polyphenylacetylene (PPA) was enhaced by eleven orders of magnitude after absorption of bromine vapor. TG, UV-Vis spectra, and XPS spectra were used to study the interaction among bromine, nano-graphite and PPA. According to the results, bromine played a major role to enhance the conductivity of the composites when the weight percentage of bromine doped graphite was low. When the weight percentage of bromine doped graphite was high, the doping effect formed by bromine doped nanographite and bromine doped PPA, was the main point to enhance the conductivity. When the weight percentage of bromine doped nano-graphite was higher, the conductive network formed by bromine doped nano-graphite, played a major role.
2010, (5): 126-133.
Abstract:
Monodisperse polystyrene (PS) colloidal particles were prepared by a quick emulsifier-free emulsion polymerization (EFEP) method, and their highly ordered colloidal crystals were fabricated by both centrifugal method and vertical surface method. Scanning Electron Microscope (SEM) and VIS-UV were used to study the topography, structure and optical properties of the colloidal crystals. The resulting planar samples by centrifugal method were distinctly thicker than that by vertical surface method. PS colloidal crystals by centrifugal method with a velocity of 1 000 r/min and a temperature of 40 ℃ exhibited a highly ordered three-dimensional structure. The optimized assembly conditions were discussed via samples’ optical properties and the transmission spectra showed the peak wavelength suffered a shift with the change of the PS spheres’ diameter.
Monodisperse polystyrene (PS) colloidal particles were prepared by a quick emulsifier-free emulsion polymerization (EFEP) method, and their highly ordered colloidal crystals were fabricated by both centrifugal method and vertical surface method. Scanning Electron Microscope (SEM) and VIS-UV were used to study the topography, structure and optical properties of the colloidal crystals. The resulting planar samples by centrifugal method were distinctly thicker than that by vertical surface method. PS colloidal crystals by centrifugal method with a velocity of 1 000 r/min and a temperature of 40 ℃ exhibited a highly ordered three-dimensional structure. The optimized assembly conditions were discussed via samples’ optical properties and the transmission spectra showed the peak wavelength suffered a shift with the change of the PS spheres’ diameter.
2010, (5): 134-141,.
Abstract:
Poly-γ-glutamic acid (γ-PGA) produced by fermentation of Bacillus sp was studied as a potential novel green scale inhibitor. The effects of γ-PGA concentration, molecular weight of γ-PGA, temperature, pH and Ca2+concentration on the scale inhibiting rate of γ-PGA were respectively analyzed using static anti-scaling method, and the structural characterization of scale inhibiting products and possible mechanism were investigated. The results reveal that both large molecular γ-PGA and small molecular γ-PGA have inhibiting efficiency. More specifically, small molecular γPGA shows the better inhibiting efficiency with their lowest concentration to get 100% inhibiting efficiency from scale of CaSO4 and CaCO3 being 4 mg/L and 2 mg/L respectively, while large molecular γ-PGA to get the same efficiency in the same condition is 20 mg/L respectively.
Poly-γ-glutamic acid (γ-PGA) produced by fermentation of Bacillus sp was studied as a potential novel green scale inhibitor. The effects of γ-PGA concentration, molecular weight of γ-PGA, temperature, pH and Ca2+concentration on the scale inhibiting rate of γ-PGA were respectively analyzed using static anti-scaling method, and the structural characterization of scale inhibiting products and possible mechanism were investigated. The results reveal that both large molecular γ-PGA and small molecular γ-PGA have inhibiting efficiency. More specifically, small molecular γPGA shows the better inhibiting efficiency with their lowest concentration to get 100% inhibiting efficiency from scale of CaSO4 and CaCO3 being 4 mg/L and 2 mg/L respectively, while large molecular γ-PGA to get the same efficiency in the same condition is 20 mg/L respectively.
2010, (5): 142-148.
Abstract:
The goal of this study is to investigate the effects of glucose fluctuation on cultured human L02 hepatocytes in vitro and discuss its possible mechanism. Cultured cells were randomly divided into 4 groups: normal (N), high glucose (HG), glucose fluctuation (GF) and osmotic pressure (OP). After 72 hours, alanine transferase (ALT), aspartate amino transferase (AST) and lactate dehydrogenase (LDH) in the medium were measured. In the cells, glycogen, glutathione (GSH), superoxide dismutase (SOD), malondialdehyde (MDA), Na+K+-ATP and Ca2+Mg2+-ATP enzyme activities were detected. In addition, cell membrane fluidity was also detected. Compared with the N group, the activities of ALT，AST and LDH in the HG and GF groups increased markedly, while the activities of GSH, SOD, Na+K+-ATP and Ca2+ Mg2+-ATP enzymes were decreased significantly. The contents of glycogen and MDA in the cells of HG and GF groups were increased obviously, while cell membrane fluidity was decreased markedly (all p＜0.01). There are also significantly statistical differences between the HG and GF groups(all p＜0.01). Our results demonstrate that glucose fluctuation can change the permeability of cell membrane, lead to the leakage of enzymes and cause marked oxidative damage and cell toxicity in human L02 hepatocytes. Moreover, the deleterious effects of GF on the L02 cells are significantly higher than that of the HG group.
The goal of this study is to investigate the effects of glucose fluctuation on cultured human L02 hepatocytes in vitro and discuss its possible mechanism. Cultured cells were randomly divided into 4 groups: normal (N), high glucose (HG), glucose fluctuation (GF) and osmotic pressure (OP). After 72 hours, alanine transferase (ALT), aspartate amino transferase (AST) and lactate dehydrogenase (LDH) in the medium were measured. In the cells, glycogen, glutathione (GSH), superoxide dismutase (SOD), malondialdehyde (MDA), Na+K+-ATP and Ca2+Mg2+-ATP enzyme activities were detected. In addition, cell membrane fluidity was also detected. Compared with the N group, the activities of ALT，AST and LDH in the HG and GF groups increased markedly, while the activities of GSH, SOD, Na+K+-ATP and Ca2+ Mg2+-ATP enzymes were decreased significantly. The contents of glycogen and MDA in the cells of HG and GF groups were increased obviously, while cell membrane fluidity was decreased markedly (all p＜0.01). There are also significantly statistical differences between the HG and GF groups(all p＜0.01). Our results demonstrate that glucose fluctuation can change the permeability of cell membrane, lead to the leakage of enzymes and cause marked oxidative damage and cell toxicity in human L02 hepatocytes. Moreover, the deleterious effects of GF on the L02 cells are significantly higher than that of the HG group.