可压缩流动的Fourier谱-有限元解法

本文考虑n维(n=2,3)可压缩流动的带有单向周期边值条件问题的数值解.我们在周期方向采用Fourier谱方法,在非周期方向采用有限元方法,从而构造了一类谱-有限元格式.文中严格分析了计算误差,得到了收敛阶的估计.     

“自我融资”的数学表达和Black-Scholes方程的推导

对L aw rence C.Evans提出的B lack-Scho les偏微分方程的一种基于“自我融资(self-financing)”的概念的推导方法进行改进和补充.我们采用离散时间模型对“自我融资”进行系统的分析,并给出直观的金融阐释和一个新的数学推导方法.我们的推导方法与L aw rence C.Evans的论述相辅相成,二者结合在一起,为“自我融资”的概念提供了一个完整的数学刻划.     

求解一般非线性互补问题的光滑化方法

在利用Fischer-Burmeister函数将非线性互补问题转化为非线性方程组的基础上,本文通过将信赖域方法与线性搜索方法结合起来,提出了求解一般非线性互补问题的光滑化方法.算法中我们给出了一个特定条件,条件满足时,采用信赖步,条件不满足时.采用梯度步.我们证明了算法具有全局收敛性.在解是R-正则的条件下,收敛速度是Q-超线性/Q-二阶收敛的.     

马尔科夫模型下的股票大宗交易中的清算问题数值算法（英文）

采用马尔科夫链逼近的方法研究了在股票交易中的最佳清算准则的数值算法.与现有文献相比,文章具有以下特点:首先,不同于基于布朗运动的股票模型,我们采用由连续时间马尔科夫链驱动的动态模型.其次,我们着重解决大宗股票的交易问题.和我们之前文章中通过动态规划把相应的问题转化为带状态约束的HJB(Hamilton-Jacobi-Bellman)方程的方法略有不同,我们采取马尔科夫链逼近的方法,对数值算法的收敛性进行了论证.此外,我们进一步提供了相应的数值实例用以演示说明.     

Cohen-Grossberg神经网络的全局指数稳定性分析

本文研究了CohenGrossberg神经网络模型的指数稳定性.为避免构造Lyapunov函数的困难,我们采用广义相对Dalquist数方法来分析神经网络的稳定性.借助这一方法,我们不但得到了CohenGrossberg神经网络模型平衡解的存在性、唯一性和全局指数稳定性的新的充分条件,而且给出了神经网络的指数衰减估计.所获结论改进了已有文献的相关结果.     

基于Huber正则化的红外与可见光图像融合

图像融合通常是指从多源信道采集同一目标图像,将互补的多焦点、多模态、多时相和/或多视点图像集成在一起,形成新图像的过程.在本文中,我们采用基于Huber正则化的红外与可见光图像的融合模型.该模型通过约束融合图像与红外图像相似的像素强度保持热辐射信息,以及约束融合图像与可见光图像相似的灰度梯度和像素强度保持图像的边缘和纹理等外观信息,同时能够改善图像灰度梯度相对较小区域的阶梯效应.为了最小化这种变分模型,我们结合增广拉格朗日方法(ALM)和量身定做有限点方法(TFPM)的思想设计数值算法,并给出了算法的收敛性分析.最后,我们将所提模型和算法与其他七种图像融合方法进行定性和定量的比较,分析了本文所提模型的特点和所提数值算法的有效性.     

带跳随机波动率模型的高阶ADI分裂格式

针对带跳随机波动率模型满足的偏积分微分方程,提出一种新的高阶交替方向隐式（ADI）有限差分格式,该模型是一个具有混合导数和非常数系数的对流扩散型初边值问题.我们将不同的高阶空间离散与时间步ADI分裂格式相结合,得到了一种空间四阶精度、时间二阶精度的有效方法,并采用Fourier方法分析了高阶ADI格式的稳定性.最后,通过对欧式看跌期权定价模型进行数值实验证实了数值方法的高阶收敛性.     

用导数求极值的方法提高病毒检测的效率

在进行大规模新冠检测时,我国采用先对样本分组、再将样本混合检测的策略取得了很好的检测效率.但是在对样本进行分组时,单组的样本数量选择多少是最好呢?我们对此问题进行了数学建模分析:以降低总检测次数为优化目标,找出总检测次数与单组样本数量之间的函数关系,采用导数求极值的计算方法,获得了最优的单组样本数量取值.     

质量工程试验的数据分析(上)

引言 本文介绍质量工程试验中的数据分析方法.所谓质量工程试验是为优化生产工序而进行的试验;这里,只讨论有确定目标值的.我们提出了一整套数据分析方法,它分为三个阶段:探索阶段,模型化阶段,优化阶段.在这三个阶段,我们都强调用图示法来指导分析及对结果作出解释.我们讨论了数据变换以及变换后数据的分析与田口的信噪比分析的关系.我们的介绍将按使用者易于接受的方式进行,并通过一个实例来解释. 结构数据方法 试验设计方法传统上总是致力于找出影响生产工序水平的因子.这里,我们还需要来找出影响生产工序变异性的因子.这在日本,特别是田…     

函数型部分线性复合分位数回归模型的估计（英文）

本文研究函数型部分线性复合分位数回归模型的估计问题.我们采用函数型主成分分析方法分析斜率函数,回归样条逼近非参数函数.在相当宽松的条件下给出斜率函数和非参数函数的收敛速度.最后通过理论模拟和实例分析来评价我们提出的方法.     

Composition of binary integral quadratic forms via integral 2 × 2 matrices and composition of matrix classes

A treatment by integral matrices is given for composition of pairs of integral quadratic forms with the same discriminant. The forms are associated with a pair of similar 2 × 2 matrices AB with irrational eigen values which generate the maximal order. The most general integral similarity between AB is given by a matrix whose entries are linear forms in two indeterminates with integral coefficients. This matrix is a "compositum" of two factors of the same nature. By equating determinants a composition of two quadratic forms results. The method can be generalized to n × n matrices.     

On equivalence of binary forms

In this paper the question of equivalence of two binary forms is related to certain properties of the roots. A method is given to determine whether or not two forms are equivalent. This method applies to a wide class of forms, though not all.     

Rankin–Cohen brackets on Siegel modular forms and special values of certain Dirichlet series

Given a fixed Siegel cusp form of genus two, we consider a family of linear maps between the spaces of Siegel cusp forms of genus two by using the Rankin–Cohen brackets and then we compute the adjoint maps of these linear maps with respect to the Petersson scalar product. The Fourier coefficients of the Siegel cusp forms of genus two constructed using this method involve special values of certain Dirichlet series of Rankin type associated to Siegel cusp forms. This is a generalisation of the work due to Kohnen (Math Z 207:657–660, 1991) and Herrero (Ramanujan J 36:529–536, 2015) in the case of elliptic modular forms to the case of Siegel cusp forms which is also considered earlier by Lee (Complex Var Theory Appl 31:97–103, 1996) for a special case.     

The geometry of a quasilinear system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables

The geometry of a system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using the Cartan method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasil’ev (for infinite groups). Systems of quasilinear equations with the first and second partial derivatives of two functions u and v in two independent variables x and y are classified.     

Comparison of Two Methods for Superreplication

Abstract

We compare two methods for superreplication of options with convex pay-off functions. One method entails the overestimation of an unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear Black–Scholes BS-type equation. In the second method, the choice of quadratic form is made pointwise. This leads to a fully non-linear equation, the so-called Black–Scholes–Barenblatt (BSB) equation, for the value of the superreplicating portfolio. In general, this value is smaller for the second method than for the first method. We derive estimates for the difference between the initial values of the superreplicating strategies obtained using the two methods.     

The geometry of a quasilinear system of two partial differential equations containing the first and the second partial derivatives of two functions in two independent variables

The geometry of the system of two partial differential equations containing the first and second partial derivatives of two functions in two independent variables is studied by using Élie Cartan’s method of invariant forms and the group-theoretic method of extensions and enclosings due to G. F. Laptev (for finite groups) and A. M. Vasil’ev (for infinite groups). Systems of quasilinear equations with the first and second partial derivatives of two functions u and v in two independent variables x and y are classified.     

Ideal composition in quadratic fields: from Bhargava to Gauss

Recent work of Bhargava has described higher composition laws that, among other things, subsume the composition of binary quadratic forms first given by Gauss. Bhargava??s presentation, however, does not provide an algorithmic method for compounding forms in the manner of Arndt??s classical composition method. In this paper, we will show, given two binary quadratic forms, how to find the Bhargava cube that represents their composition, and we will show that this can be done by what is essentially Arndt??s classical method.     

Curved flats,pluriharmonic maps and constant curvature immersions into pseudo-Riemannian space forms

We study two aspects of the loop group formulation for isometric immersions with flat normal bundle of space forms. The first aspect is to examine the loop group maps along different ranges of the loop parameter. This leads to various equivalences between global isometric immersion problems among different space forms and pseudo-Riemannian space forms. As a corollary, we obtain a non-immersibility theorem for spheres into certain pseudo-Riemannian spheres and hyperbolic spaces. The second aspect pursued is to clarify the relationship between the loop group formulation of isometric immersions of space forms and that of pluriharmonic maps into symmetric spaces. We show that the objects in the first class are, in the real analytic case, extended pluriharmonic maps into certain symmetric spaces which satisfy an extra reality condition along a totally real submanifold. We show how to construct such pluriharmonic maps for general symmetric spaces from curved flats, using a generalised DPW method.      

On the Krylov subspace methods based on tensor format for positive definite Sylvester tensor equations

This paper deals with studying some of well‐known iterative methods in their tensor forms to solve a Sylvester tensor equation. More precisely, the tensor form of the Arnoldi process and full orthogonalization method are derived by using a product between two tensors. Then tensor forms of the conjugate gradient and nested conjugate gradient algorithms are also presented. Rough estimation of the required number of operations for the tensor form of the Arnoldi process is obtained, which reveals the advantage of handling the algorithms based on tensor format over their classical forms in general. Some numerical experiments are examined, which confirm the feasibility and applicability of the proposed algorithms in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Normal form theory for reversible equivariant vector fields

We give a method to obtain formal normal forms of reversible equivariant vector fields. The procedurewe present is based on the classical method of normal forms combined with tools from invariant theory. Normal forms of two classes of resonant cases are presented, both with linearization having a 2-dimensional nilpotent part and a semisimple part with purely imaginary eigenvalues.