Some properties for the largest component of random geometric graphs with applications in sensor networks

In this paper we consider the standard Poisson Boolean model of random geometric graphs G（Hλ,s; 1） in Rd and study the properties of the order of the largest component L1 （G（Hλ,s; 1）） . We prove that ElL1 （G（Hλ,s; 1））] is smooth with respect to A, and is derivable with respect to s. Also, we give the expression of these derivatives. These studies provide some new methods for the theory of the largest component of finite random geometric graphs （not asymptotic graphs as s - co） in the high dimensional space （d 〉 2）. Moreover, we investigate the convergence rate of E[L1（G（Hλ,s; 1））]. These results have significance for theory development of random geometric graphs and its practical application. Using our theories, we construct and solve a new optimal energy-efficient topology control model of wireless sensor networks, which has the significance of theoretical foundation and guidance for the design of network layout.     

Positive solutions for one-dimensional -Laplacian boundary value problems with sign changing nonlinearity

This paper deals with the existence of positive solutions for the one-dimensional p-Laplacian

subject to the boundary value conditions:

where _p(s)=|s|^p−2s,p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term f is involved with the first-order derivative explicitly and f may change sign.     

Some fixed point theorems and existence of positive solutions of two-point boundary-value problems

Three theorems are obtained for the existence of at least one or three fixed points for a completely continuous mapping, which extend the Krasnoselskii’s compression–expansion theorem in cones. Based on them two theorems for the existence of positive solutions of two-point boundary-value problems are proved under a quite relaxed condition compared with the existing literature.     

Existence result of second-order differential equations with integral boundary conditions at resonance

By using Mawhin's continuation theorem, some sufficient conditions for the existence of solution for a class of second-order differential equations with integral boundary conditions at resonance are established, which are complement of previously known results. The interesting point is that we shall deal with the case dimKerL=2, which will cause some difficulties in constructing the projector Q. Since all the existence results obtained in previous papers are for the case dimKerL=1, our work is new.     

Symplectic synchronization of different chaotic systems

In this paper, a new symplectic synchronization of chaotic systems is studied. Traditional generalized synchronizations are special cases of the symplectic synchronization. A sufficient condition is given for the asymptotical stability of the null solution of an error dynamics. The symplectic synchronization may be applied to the design of secure communication. Finally, numerical results are studied for a Quantum-CNN oscillators synchronized with a Rössler system in three different cases.     

N=2 超对称KdV 方程的双线性形研究

利用双线性方法研究$N=2$超对称KdV方程. 通过适当的相关变换, 将$N=2, a=4$和$N=2, a=1$超对称KdV方程转化成双线性形式, 由此构造了相应方程的解. 对于$N=2, a=1$ 超对称KdV方程, 还得到了它的双线性B\"acklund变换和Lax 表示.     

On equalities for BLUEs under misspecified Gauss-Markov models

This paper studies relationships between the best linear unbiased estimators （BLUEs） of an estimable parametric functions Kβunder the Gauss-Markov model {y, Xβ, σ^2]E} and its misspecified model {y, X0β,σ^2∑0}. In addition, relationships between BLUEs under a restricted Gauss Markov model and its misspecified model are also investigated.     

Quality evaluation of cortex moutan by high performance liquid chromatography coupled with diode array detector and electrospary ionization tandem mass spectrometry

An high performance liquid chromatography (HPLC) coupled with diode array detector (DAD) and electrospray ionization tandem mass spectrometry (ESI/MS(n)) method was developed for quality evaluation of Cortex Moutan through identification of common constituents based on chromatographic fingerprints and determination of key pharmacological compounds. The representative chromatographic fingerprints of Cortex Moutan were obtained by analyzing 10 batches of samples under the optimized HPLC conditions and the results showed that the chromatographic profiles of the analyzed samples were very similar. Total of nineteen common peaks were detected and seventeen of them were identified rapidly by their characteristic UV profile and the information of molecular structure provided by ESI/MS(n) experiments. Simultaneously, five key pharmacological compounds, namely gallic acid, oxypaeoniflorin, paeoniflorin, benzoylpaeoniflorin and paeonol, were determined by the validated HPLC-DAD method. The linear calibration curves were acquired with correlation coefficients higher than 0.999. The precisions of intra-day and inter-day were not exceeding 3.1%, and the recoveries of five analytes were from 92.86 to 99.35%. This developed method that combined the chromatographic fingerprints and quantification assay ensured the phytoequivalence and pharmacological effects of Cortex Moutan and was successfully applied to the quality control of Cortex Moutan.     

Variation analysis of affinity-membrane model based on Freundlich adsorption

The variation analysis of membrane properties including membrane thickness and pore-size was carried out theoretically by using affinity-membrane model based upon the Freundlich adsorption equation. As the percentage variation of membrane thickness and distribution of pore-size increase, we find that (1) the time of total saturation is delayed; (2) the loading capacity at the point of breakthrough are decreased; (3) solute recovery efficiency and ligand utilization efficiency is decreased; (4) the thickness of unused membrane is increased. The results show that even small variations of thickness and distribution of pore size may severely degrade the membrane performance.