利用GM(1,1)模型预测曲线波形

针对给出的函数y=f(x),x∈[a,b],将其值域进行n等分,设yi为其中任一分点,对应x=xi(i=1,2,…,m),用GM(1,1)模型对序列{x1,x2,…,xm}进行预测,得到曲线y=f(x)在下一段时间与直线y=yi的交点位置.当GM(1,1)模型的误差较大时,可利用带有残差修正的GM(1,1)模型进行残差修正,以提高GM(1,1)模型预测值的精确度.     

An L p -theory of Stochastic PDEs of Divergence Form on Lipschitz Domains

Stochastic partial differential equations of divergence form are considered on Lipschitz domains. Existence and uniqueness results are given in weighted Sobolev spaces. It is allowed that the coefficients of the equations substantially oscillate or blow up near the boundary.      

Ring-opened Crystal Structure and Photochromism of 2,2-Bis（4-tertiary butyl phenyl）-3H-naphtho[2,1-b]pyran

The title compound, 2,2-bis（4-tertial butyl phenyl） naphthopyran, has been prepared and characterized by means of IR, ^1H NMR and elemental analysis, and its crystal structure was determined with X-ray diffraction in the ring-opened form after hydrolyzation. It belongs to monoclinic, space group P21/c, with a = 14.358（3）, b = 7.6725（15）, c = 24.470（5） А, β= 97.147（4）°, C_33H_36O2, Mr=464.62, V= 2674.8（9）А^3, Z = 4, Dc = 1.154 g/cm^3,μ= 0.070 mm^-1, F（000） = 1000, the final R = 0.0514 and wR = 0.1272 for 5444 observed reflections （I 〉 2σ（I））. X-ray analysis revealed that the C（13）-O（1） bond of the title compound cracks after UV irradiation, the six-membered heterocycles are destroyed, and zwitterionic intermediates come into being. The molecular structure in the ring-opened form is obtained after hydrolyzation. It is infrequent that the single-crystal structure is determined in a ring-opened form. A two-dimensional framework is formed by O-H…O and CAr-H…O hydrogen bonds. The UV-vis spectra show that the title compound exhibits excellent photochromic properties in solutions and polymers.     

矩阵形式二次修正Maxwell-Dirac系统的多尺度算法

带二次修正项的Dirac方程在拓扑绝缘体、石墨烯、超导等新材料电磁光特性分析中有着十分广泛的应用.本文工作的创新点有：一是首次提出了矩阵形式带有二次修正项的Dirac方程,它是比较一般的数学框架,涵盖了上述材料体系很多重要的物理模型,具体见附录A;二是针对上述材料体系的电磁响应问题,提出了有界区域Weyl规范下具有周期间断系数矩阵形式带二次修正项Maxwell-Dirac系统的多尺度渐近方法,结合Crank-Nicolson有限差分方法和自适应棱单元方法,发展了一类多尺度算法.数值试验结果验证了多尺度渐近方法的正确性和算法的有效性.     

Gravitational radiation and the evolution of gravitational collapse in cylindrical symmetry

Using the Sparling form and a geometric construction adapted to spacetimes with a 2-dimensional isometry group, we analyse a quasi-local measure of gravitational energy. We then study the gravitational radiation through spacetime junctions in cylindrically symmetric models of gravitational collapse to singularities. The models result from the matching of collapsing dust fluids interiors with gravitational wave exteriors, given by the Einstein–Rosen type solutions. For a given choice of a frame adapted to the symmetry of the matching hypersurface, we are able to compute the total gravitational energy radiated during the collapse and state whether the gravitational radiation is incoming or outgoing, in each case. This also enables us to distinguish whether a gravitational collapse is being enhanced by the gravitational radiation.     

Multiple rogue wave solutions for a (3+1)-dimensional Hirota bilinear equation

In this paper, we considered the multiple rogue wave solutions of a (3+1)-dimensional Hirota bilinear equation by using a symbolic computation approach. Based on the bilinear form of this equation, the first-order rogue waves, the second-order rogue waves and the third-order rogue waves are presented. Moreover, some basic properties of multiple rogue waves and their collision structures are explained by drawing the three dimensional plot.     

Bilinear form and new interaction solutions for the sixth-order Ramani equation

By using the Hirota’s bilinear method, the bilinear form of the sixth-order Ramani equation is succinctly obtained. With the aid of the obtained bilinear form, some new interaction solutions which include interaction solutions between exponential and trigonometric functions, interaction solutions between exponential and hyperbolic functions, and interaction solutions between trigonometric and hyperbolic functions are also presented by employing the three wave method.     

Unitary groups and ramified extensions

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated unitary groups, including their orders when the ring in question is finite.     

Bifurcations and spatiotemporal patterns in a ratio‐dependent diffusive Holling‐Tanner system with time delay

In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics.     

Superconvergence analysis of finite element method for Poisson–Nernst–Planck equations

This article concerns with the superconvergence analysis of bilinear finite element method (FEM) for nonlinear Poisson–Nernst–Planck (PNP) equations. By employing high accuracy integral identities together with mean value technique, the superclose estimates in H¹‐norm are derived for the semi‐discrete and the backward Euler fully‐discrete schemes, which improve the suboptimal error estimate in L²‐norm in the previous literature. Furthermore, the global superconvergence results in H¹‐norm are obtained through interpolation postprocessing approach. Finally, a numerical example is provided to confirm the theoretical analysis.