A necessary and sufficient condition for the existence of positive solutions to a kind of singular three-point boundary value problem

In this paper, we are concerned with the following three point boundary value problem

     

Ricci flow on surfaces with cusps

We consider the normalized Ricci flow ? _t g = (ρ ? R)g with initial condition a complete metric g ₀ on an open surface M where M is conformal to a punctured compact Riemann surface and g ₀ has ends which are asymptotic to hyperbolic cusps. We prove that when χ(M) < 0 and ρ < 0, the flow g(t) converges exponentially to the unique complete metric of constant Gauss curvature ρ/2 in the conformal class.     

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.     

Ordered tournaments and ordered triplewhist tournaments with the three person property

It is well known that an ordered tournament OWh(v) exists if and only if v ≡ 1 (mod 4), v ≥ 5. An ordered triplewhist tournament on v players is said to have the three person property if no two games in the tournament have three common players. We briefly denote such a design as a 3POTWh(v). In this article, we show that a 3POTWh(v) exists whenever v>17 and v ≡ 1 (mod 4) with few possible exceptions. We also show that an ordered whist tournament on v players with the three person property, denoted 3POWh(v), exists if and only if v ≡ 1 (mod 4), v ≥ 9. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 39–52, 2009     

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.