LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM

In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.     

Finite <Emphasis Type="Italic">p</Emphasis>-groups with a class of complemented normal subgroups

Assume G is a finite group and H a subgroup of G. If there exists a subgroup K of G such that G = HK and H ∩ K = 1, then K is said to be a complement to H in G. A finite p-group G is called an NC-group if all its proper normal subgroups not contained in Φ(G) have complements. In this paper, some properties of NC-groups are investigated and some classes of NC-groups are classified.     

The Value Distribution and Normality Criteria of a Class of Meromorphic Functions

In this article, we use Zalcman Lemma to investigate the normal family of meromorphic functions concerning shared values, which improves some earlier related results.     

Besov空间中双参数Volterra型重分数过程的弱逼近

In this paper, we prove that two-parameter Volterra multifractional process can be approximated in law in the topology of the anisotropic Besov spaces by the family of processes{B_n(s,t)},n∈N defined by B_n(s,t)=∫_0~s ∫_0~tk_(a(s))(s,u)K_(β(t))(t,u)θ_(n(u,v))dudv,here {θ_n(u, v)}n∈N is a family of processes, converging in law to a Brownian sheet as n→∞,based on the well known Donsker's theorem.     

Reconstruction of the Linear Ordinary Differential System Based on Discrete Points

In this paper, we discuss an inverse problem, i.e., the reconstruction of a linear differential dynamic system from the given discrete data of the solution. We propose a model and a corresponding algorithm to recover the coefficient matrix of the differential system based on the normal vectors from the given discrete points, in order to avoid the problem of parameterization in curve fitting and approximation. We also give some theoretical analysis on our algorithm. When the data points are taken from the solution curve and the set composed of these data points is not degenerate, the coefficient matrix $A$ reconstructed by our algorithm is unique from the given discrete and noisefree data. We discuss the error bounds for the approximate coefficient matrix and the solution which are reconstructed by our algorithm. Numerical examples demonstrate the effectiveness of the algorithm.     

重氮化制备钯(0)催化剂及其用于合成芳香胺研究

以2,3-二氨基萘为配体,K_2PdCl_4为金属前驱体,经重氮化制备出一种Pd(0)纳米催化剂(Pd-NPs),其结构经TEM、 XPS、 XRD、 EA和ICP-OES表征,并将催化剂应用于芳香醛类化合物直接还原胺化反应中.在常温常压下以苯甲醛为底物,水为溶剂,H_2为还原剂,探究了胺源、溶剂pH、催化剂用量、反应时间等变量对芳香伯胺产率的影响.实验结果表明芳香伯胺产率高达99%,且该催化剂能多次使用而不失活.     

数理统计在地球化学样品分析质量控制中的应用

使用Excel2013和Minitab两种常用软件对地球化学样品中CaO含量分布情况进行了研究,运用描述性统计、正态分布、背景值与异常方法对实验室分析的广西某地地球化学样品的分析数据进行了质量评价,结果表明:综合运用计算机软件和数理统计方法,能快速找到分析数据的详细信息和数据特征,判别地球化学样品实验室分析数据的准确性,找出元素的背景值和异常值并剔除异常值,比较发现,样品中CaO含量分析数据对数转换后比原始数据的分布更趋于正态分布,相比于X射线荧光光谱方法,用电感耦合等离子体发射光谱法测定的结果更符合正态分布。方法对地球化学调查样品的分析数据质量评价作了有益的尝试,揭示了数理统计方法是地球化学样品分析质量控制的有效手段。