2013 No. 1
Display Method:
2013, (1): 1-6.
Abstract(
PDF 195KB
Abstract:
A necessary and sufficient condition for the adjoint equivalence of two graphs with the adjoint minimum real root at least $-$4 was given. Based on this result, a necessary and sufficient condition of the chromatic equivalence for the complement graphs of these graphs can be naturally obtained.
A necessary and sufficient condition for the adjoint equivalence of two graphs with the adjoint minimum real root at least $-$4 was given. Based on this result, a necessary and sufficient condition of the chromatic equivalence for the complement graphs of these graphs can be naturally obtained.
2013, (1): 7-10, 23.
Abstract:
The linear arboricity of a graph $G$ is the minimum number of linear forests which partition the edges of $G$. This paper proved that if $G$ can be embedded on a surface of large genus without 4-cycle and $\Delta(G)\geq (\sqrt{45-45\varepsilon}+10)$, then its linear arboricity is $\lceil \frac{\Delta}{2}\rceil$, where $\varepsilon=2-2h$ if the orientable surface with genus \,$h(h1)$\,or $\varepsilon=2-k$ if the nonorientable surface with genus \,$k(k2)$. It improves the bound obtained by J. L. Wu. As an application, the linear arboricity of a graph with fewer edges were concluded.
The linear arboricity of a graph $G$ is the minimum number of linear forests which partition the edges of $G$. This paper proved that if $G$ can be embedded on a surface of large genus without 4-cycle and $\Delta(G)\geq (\sqrt{45-45\varepsilon}+10)$, then its linear arboricity is $\lceil \frac{\Delta}{2}\rceil$, where $\varepsilon=2-2h$ if the orientable surface with genus \,$h(h1)$\,or $\varepsilon=2-k$ if the nonorientable surface with genus \,$k(k2)$. It improves the bound obtained by J. L. Wu. As an application, the linear arboricity of a graph with fewer edges were concluded.
2013, (1): 11-16.
Abstract:
This paper showed that the number of the shortest cycles in a planar graph of order $n$ is at most $O(n^{2})$ and the bound is the best possible (subject to the power of $n$) since $K_{n-2,n}$ contains exactly $\frac{(n-2)(n-3)}{2}$ many 4-cycles.
This paper showed that the number of the shortest cycles in a planar graph of order $n$ is at most $O(n^{2})$ and the bound is the best possible (subject to the power of $n$) since $K_{n-2,n}$ contains exactly $\frac{(n-2)(n-3)}{2}$ many 4-cycles.
2013, (1): 17-23.
Abstract:
Using tools of spherical harmonics and Hamburger's moment, we proved that an origin-symmetric convex body containing a sphere of radius $\delta$ in its interior is determined in ${\mathbb{R}}^{n}$ by the volume of its polar bodies with respect to all the points near the sphere.
Using tools of spherical harmonics and Hamburger's moment, we proved that an origin-symmetric convex body containing a sphere of radius $\delta$ in its interior is determined in ${\mathbb{R}}^{n}$ by the volume of its polar bodies with respect to all the points near the sphere.
2013, (1): 24-29, 53.
Abstract:
It was proved that the Bayesian linear unbiased estimator of the unknown parameters in a general linear model under the quadratic loss function is also the Bayesian linear unbiased estimator under the matrix loss function. The robustness of the Bayesian linear unbiased estimator of the unknown parameter in terms of error distributions was also discussed; moreover, the necessary and sufficient conditions are obtained, under which the Bayesian linear unbiased estimator of the unknown parameters hold its optimality.
It was proved that the Bayesian linear unbiased estimator of the unknown parameters in a general linear model under the quadratic loss function is also the Bayesian linear unbiased estimator under the matrix loss function. The robustness of the Bayesian linear unbiased estimator of the unknown parameter in terms of error distributions was also discussed; moreover, the necessary and sufficient conditions are obtained, under which the Bayesian linear unbiased estimator of the unknown parameters hold its optimality.
2013, (1): 30-40.
Abstract:
Firstly the relation between the credibility premium under balanced loss function and quadratic loss function was given. Then the linear regression credibility premium with correlation risk under balanced loss function was derived. At last the credibility premium was expressed in balanced loss function when the target estimator was specialized, meanwhile the regression credibility model with equal correlation and common effect risk under balanced loss function was discussed.
Firstly the relation between the credibility premium under balanced loss function and quadratic loss function was given. Then the linear regression credibility premium with correlation risk under balanced loss function was derived. At last the credibility premium was expressed in balanced loss function when the target estimator was specialized, meanwhile the regression credibility model with equal correlation and common effect risk under balanced loss function was discussed.
2013, (1): 41-46, 75.
Abstract:
The common fixed points of two finite families of set-valued asymptotically nonexpansive mappings were studied in real uniformly convex Banach spaces. A finite-step iteration process for these two families was introduced, and some strong convergence theorems for this scheme were proved. The results improve and extend some recent relative results.
The common fixed points of two finite families of set-valued asymptotically nonexpansive mappings were studied in real uniformly convex Banach spaces. A finite-step iteration process for these two families was introduced, and some strong convergence theorems for this scheme were proved. The results improve and extend some recent relative results.
2013, (1): 47-53.
Abstract:
Based on the results by HAN Mao-an, et al. for computing some focus values of non-smooth Li\'{e}nard systems, the number of limit cycles bifurcated from the origin of some more general non-smooth Li\'{e}nard systems were given by using maple process.
Based on the results by HAN Mao-an, et al. for computing some focus values of non-smooth Li\'{e}nard systems, the number of limit cycles bifurcated from the origin of some more general non-smooth Li\'{e}nard systems were given by using maple process.
2013, (1): 54-60, 75.
Abstract:
Let $\F$ be a family of meromorphic functions on a domain $D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$ not positive integer). If for every $f \in \F$, $f(z) = a \Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$ is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon 0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.
Let $\F$ be a family of meromorphic functions on a domain $D$, $a$ and $b$ be two nonzero finite complex numbers($\frac{a}{b}$ not positive integer). If for every $f \in \F$, $f(z) = a \Rightarrow f^{(k)}(z) = a$, and the zeros multiplicity of $f - a$ is at least $k$, and $|f(z) - a| \geq \varepsilon$ ($\varepsilon 0)$ whenever $f^{(k)}(z) = b$, then $\F$ is normal on $D$.
2013, (1): 61-75.
Abstract:
The affine Weyl group $(\widetilde{C}_4,\,S)$ can be considered as the fixed point set of the affine Weyl group $(\widetilde{A}_7,\,\widetilde{S})$ under a certain group automorphism $\alpha$. Let $\widetilde{l}:\widetilde{A}_7\longrightarrow \mathbf{\mathbf{N}}$ be the length function of\,$\widetilde{A}_7$. The restriction of $\widetilde{l}$ on $\widetilde{C}_4$, denoted by $L$, is a weighted function on $\widetilde{C}_4$. This paper classified the cells in weighted Coxteger group\,$(\widetilde{C}_4,\,L)$.
The affine Weyl group $(\widetilde{C}_4,\,S)$ can be considered as the fixed point set of the affine Weyl group $(\widetilde{A}_7,\,\widetilde{S})$ under a certain group automorphism $\alpha$. Let $\widetilde{l}:\widetilde{A}_7\longrightarrow \mathbf{\mathbf{N}}$ be the length function of\,$\widetilde{A}_7$. The restriction of $\widetilde{l}$ on $\widetilde{C}_4$, denoted by $L$, is a weighted function on $\widetilde{C}_4$. This paper classified the cells in weighted Coxteger group\,$(\widetilde{C}_4,\,L)$.
2013, (1): 76-90.
Abstract:
We showed that all the left cells in the Weyl group $E_{6}$ were left-connected, verifying a conjecture of Lusztig in our case.
We showed that all the left cells in the Weyl group $E_{6}$ were left-connected, verifying a conjecture of Lusztig in our case.
2013, (1): 91-103, 114.
Abstract:
The fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under a certain group automorphism $\alpha$ with $\alpha\,(\widetilde{S}) = \widetilde{S}$ can be considered as the affine Weyl group ($\widetilde{C}_n,S$). Then the left and two-sided cells of the weighted Coxeter group ($\widetilde{C}_n,\widetilde{\ell}$), where $\widetilde{\ell}$ is the length function of $\widetilde{A}_{2n}$, can be given an explicit description by studying the fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under $\alpha$. We describe the cells of ($\widetilde{C}_n,\widetilde{\ell}$) corresponding to the partitions $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$ with $1\leqslant k \leqslant 2n+1$ and $(2n-1,2)$.
The fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under a certain group automorphism $\alpha$ with $\alpha\,(\widetilde{S}) = \widetilde{S}$ can be considered as the affine Weyl group ($\widetilde{C}_n,S$). Then the left and two-sided cells of the weighted Coxeter group ($\widetilde{C}_n,\widetilde{\ell}$), where $\widetilde{\ell}$ is the length function of $\widetilde{A}_{2n}$, can be given an explicit description by studying the fixed point set of the affine Weyl group ($\widetilde{A}_{2n},\widetilde{S}$) under $\alpha$. We describe the cells of ($\widetilde{C}_n,\widetilde{\ell}$) corresponding to the partitions $\textbf{k}\textbf{1}^{\textbf{2n+1-k}}$ with $1\leqslant k \leqslant 2n+1$ and $(2n-1,2)$.
2013, (1): 104-114.
Abstract:
null
null
2013, (1): 115-120.
Abstract:
The amorphous wires of nominal compositions Fe73.0Cu1.0Nb2.0Si13.5B9.0 were prepared by glass-coating melt-spinning method. Then, the wires were annealed at 480~650 ℃ for 30 min in nitrogen atmosphere. The composite wires with copper layer using electroless deposition were produced, a thin layer of copper deposited onto the microwires annealed at 570 ℃. The morphology of composite microwires was observed using SEM. The giant magnetoimpedance effect on the samples was investigated. The results show that soft magnetic properties of the specimen can improve its MI ratio. The electromagnetic interactions between the ferromagnetic core and the copper layer can also affect MI ratio.
The amorphous wires of nominal compositions Fe73.0Cu1.0Nb2.0Si13.5B9.0 were prepared by glass-coating melt-spinning method. Then, the wires were annealed at 480~650 ℃ for 30 min in nitrogen atmosphere. The composite wires with copper layer using electroless deposition were produced, a thin layer of copper deposited onto the microwires annealed at 570 ℃. The morphology of composite microwires was observed using SEM. The giant magnetoimpedance effect on the samples was investigated. The results show that soft magnetic properties of the specimen can improve its MI ratio. The electromagnetic interactions between the ferromagnetic core and the copper layer can also affect MI ratio.
2013, (1): 121-127, 138.
Abstract:
Methyl methacrylate-styrene copolymer/multiwalled carbon nanotubes (P(MMA-St)/MWNTs) composites were prepared via situ emulsion polymerization and the influence of temperature modification on the conductivity of the composites was studied. The results indicated that the conductivity of the composite in the threshold value was increased by 2 orders of magnitude after temperature modification at 200 ℃ for 1 h. The relationship between the structure, interaction and properties of the composites were initiated by FTIR, XPS and XRD. After temperature modification some ester and acid in the PMMA change into anhydride. The change can prolong the effective conjugation and enhance the interaction between copolymers and MWNTs that the conductivity of composites improved.
Methyl methacrylate-styrene copolymer/multiwalled carbon nanotubes (P(MMA-St)/MWNTs) composites were prepared via situ emulsion polymerization and the influence of temperature modification on the conductivity of the composites was studied. The results indicated that the conductivity of the composite in the threshold value was increased by 2 orders of magnitude after temperature modification at 200 ℃ for 1 h. The relationship between the structure, interaction and properties of the composites were initiated by FTIR, XPS and XRD. After temperature modification some ester and acid in the PMMA change into anhydride. The change can prolong the effective conjugation and enhance the interaction between copolymers and MWNTs that the conductivity of composites improved.
2013, (1): 128-138.
Abstract:
A method based on capillary electrophoresis coupled with amperometric detection (CE-AD) was developed for the simultaneous determination of phenols: 2,4-dichlorophenol, p-nitrophenol, o-cresol, m-cresol and p-cresol. The effects of working electrode potential, pH and concentration of running buffer, separation voltage and injection time on CE-AD were investigated. Under the optimum conditions, the aim analytes could be separated in buffer solution of Na2HPO4-NaOH at pH 11.38 within 25 min. A 300 m diameter carbon disk electrode generated good current responses at +0.78 V ( vs SCE) for all analytes. The current responses were linear with concentrations over three orders of magnitude with detection limits at 10-7mol/L (S/N=3) and the recoveries were in the range of 94.0%～107.0%. This method could be successfully applied to the analysis of actual sample from coking plants with satisfactory results.
A method based on capillary electrophoresis coupled with amperometric detection (CE-AD) was developed for the simultaneous determination of phenols: 2,4-dichlorophenol, p-nitrophenol, o-cresol, m-cresol and p-cresol. The effects of working electrode potential, pH and concentration of running buffer, separation voltage and injection time on CE-AD were investigated. Under the optimum conditions, the aim analytes could be separated in buffer solution of Na2HPO4-NaOH at pH 11.38 within 25 min. A 300 m diameter carbon disk electrode generated good current responses at +0.78 V ( vs SCE) for all analytes. The current responses were linear with concentrations over three orders of magnitude with detection limits at 10-7mol/L (S/N=3) and the recoveries were in the range of 94.0%～107.0%. This method could be successfully applied to the analysis of actual sample from coking plants with satisfactory results.
2013, (1): 139-144.
Abstract:
A newly exotic genus Kickxia Dumort.(Scrophulariaceae) is recorded in Shanghai and China. And 11 newly recorded species are found in Shanghai, namely, Kickxia elatine (L.) Dumort., Amaranthus polygonoides L., Ampelopsis japonica (Thunb.) Makino, Asarum forbesii Maxim., Ammannia multiflora Roxb., Elymus shandongensis B. Salomon, Rorippa dubia (Pers.) H. Hara, Cardamine scutata Thunb., Corydalis sheareri S. Moore, Basella alba L. and Melochia corchorifolia L. respectively.
A newly exotic genus Kickxia Dumort.(Scrophulariaceae) is recorded in Shanghai and China. And 11 newly recorded species are found in Shanghai, namely, Kickxia elatine (L.) Dumort., Amaranthus polygonoides L., Ampelopsis japonica (Thunb.) Makino, Asarum forbesii Maxim., Ammannia multiflora Roxb., Elymus shandongensis B. Salomon, Rorippa dubia (Pers.) H. Hara, Cardamine scutata Thunb., Corydalis sheareri S. Moore, Basella alba L. and Melochia corchorifolia L. respectively.