基于非线性项变号的p-Laplacian方程两点边值问题正解的存在性

该文利用不动点指数理论,考虑了边值问题(BVP)(φ_p(u′(t)))′+a(t)f(t,u(t))=0,0t1,u′(0)=u(1)=0或u(0)=u(1)=0在非线性项f(t,u)可变号的情况下两个正解存在的充分条件,推广和改进了现有文献的结果.     

Multiplicity Results for Periodic Solutions to Second-Order Difference Equations

By using the Z _p geometrical index theory, some sufficient conditions on the multiplicity results of periodic solutions to the second-order difference equations

渐近线性二阶Hamilton系统解的存在性和多重性

在实际问题中存在着Neumann边值情形.为实际需要,运用指标理论和Morse理论研究了渐近线性二阶Hamilton系统在这种情形下解的存在性和多重性问题。     

Morse指标和闭测地线的稳定性

令ind(c)为n+1维Riemann流形M上闭测地线c的Morse指标.我们证明:对于闭测地线c,如果它是定向的且n+ind(c)是奇数,或它是非定向的且n+ind(c)为偶数,则c不稳定.Poincaré的一个著名定理说Riemann面上的极小闭测地线是不稳定的,我们的结果是该结论的一个推广.     

Eighth-order methods with high efficiency index for solving nonlinear equations

In this paper, we derive a new family of eighth-order methods for solving simple roots of nonlinear equations by using weight function methods. Per iteration these methods require three evaluations of the function and one evaluation of its first derivative, which implies that the efficiency indexes are 1.682. Numerical comparisons are made to show the performance of the derived methods, as shown in the illustration examples.     

The nonidealness index of rank-ideal matrices

A polyhedron is integral if all its extreme points have 0, 1 components and in this case the matrix M is called ideal. When Q has fractional extreme points, there are different ways of classifying how far M is away from being ideal, through the polyhedral structure of Q. In this sense, Argiroffo, Bianchi and Nasini (2006) [1] defined a nonidealness index analogous to an imperfection index due to Gerke and McDiarmid (2001) [10].In this work we determine the nonidealness index of rank-ideal matrices (introduced by the authors (2008)). It is known that evaluating this index is NP-hard for any matrix. We provide a tractable way of evaluating it for most circulant matrices, whose blockers are a particular class of rank-ideal matrices, thereby following similar lines as done for the imperfection ratio of webs due to Coulonges, Pêcher and Wagler (2009) [7].Finally, exploiting the properties of this nonidealness index, we identify the facets of the set covering polyhedron of circulant matrices, having maximum strength with respect to the linear relaxation, according to a measure defined by Goemans (1995) [9].     

Decompositions for edge-coloring join graphs and cobipartite graphs

An edge-coloring is an association of colors to the edges of a graph, in such a way that no pair of adjacent edges receive the same color. A graph G is Class 1 if it is edge-colorable with a number of colors equal to its maximum degree Δ(G). To determine whether a graph G is Class 1 is NP-complete [I. Holyer, The NP-completeness of edge-coloring, SIAM J. Comput. 10 (1981) 718-720]. First, we propose edge-decompositions of a graph G with the goal of edge-coloring G with Δ(G) colors. Second, we apply these decompositions for identifying new subsets of Class 1 join graphs and cobipartite graphs. Third, the proposed technique is applied for proving that the chromatic index of a graph is equal to the chromatic index of its semi-core, the subgraph induced by the maximum degree vertices and their neighbors. Finally, we apply these decomposition tools to a classical result [A.J.W. Hilton, Z. Cheng, The chromatic index of a graph whose core has maximum degree 2, Discrete Math. 101 (1992) 135-147] that relates the chromatic index of a graph to its core, the subgraph induced by the maximum degree vertices.     

GL(n,K)中一类准可解子群的结构及其在Fuchsian系统中的应用(英文)

本文研究了单值群的可解性与Fuchsian方程可积性之间的关系.利用可解群及GL(n,K)的性质,获得GL(n,K)中一类准可解子群的结构定理,并将之心用于Fuchsian系统的可积性研究之中.     

湍流中漫射目标偏振部分相干激光的闪烁特性

采用广义惠更斯-菲涅耳原理和矩阵光学理论,研究了湍流大气中偏振部分相干激光波束从发射机到目标和从目标到接收机双程路径的闪烁特性。将产生任意偏振光束的琼斯矩阵和ABCD传输矩阵进行结合,围绕接收机处波场四阶矩展开推导,得出双程路径下偏振部分相干激光波束在接收机处的闪烁指数表达式,数值分析了大气折射率结构常数、激光波束的波长、束宽、相干长度对接收机处光强闪烁指数的影响。结果表明:偏振部分相干激光波束的闪烁指数随着目标与发射机之间距离呈现先增大、到达峰值后逐渐减小的变化趋势;相干性差的光束产生的闪烁指数小,相干长度微小的变化将会产生较大的闪烁指数变化,相干性好的光束产生较大的闪烁指数,但是相干长度的变化对闪烁指数的影响很小。     

Effect of Alkyl Side Chain Length on Relaxation Behaviors in Poly(n-alkyl Acrylates) and Poly(n-alkyl Methacrylates)

Dynamic mechanical analysis (DMA) is used to investigate the effect of alkyl side chain length on the relaxation behavior of poly(n-alkyl acrylates) (PnAA) and poly(n-alkyl methacrylates) (PnAMA) above the glass transition temperature (T_g). Master curves and shift factors (log a_T) were obtained using the time–temperature superposition (TTS) principle. The log a_T curves of PnAA and PnAMA exhibit a dynamic crossover from one Vogel–Fulcher–Tammann–Hesse (VFTH) equation to another above T_g. The corresponding temperature was designated as the dynamic crossover temperature (T_c). It is found that T_c/T_g and the apparent activation energy (E_g) increases, e whereas the fragility index (m) decreases with increasing alkyl side chain length. Further analysis shows that m ∝ T_g, E_g∝ , and E_g∝ m² for both PnAA and PnAMA.