Hypercomplex analysis and integration of systems of ordinary differential equations

We review the theory of hypercomplex numbers and hypercomplex analysis with the ultimate goal of applying them to issues related to the integration of systems of ordinary differential equations (ODEs). We introduce the notion of hypercomplexification, which allows the lifting of some results known for scalar ODEs to systems of ODEs. In particular, we provide another approach to the construction of superposition laws for some Riccati‐type systems, we obtain invariants of Abel‐type systems, we derive integrable Ermakov systems through hypercomplexification, we address the problem of linearization by hypercomplexification, and we provide a solution to the inverse problem of the calculus of variations for some systems of ODEs. Copyright © 2016 John Wiley & Sons, Ltd.     

带凹性生产成本运输问题的新随机规划模型及其求解

提出了一种新的能反映决策者满意度的随机变量序关系,并据此研究了随机不等式的确定性等价类,方法被称为满意度方法.最后将其应用于带凹性生产成本运输问题的求解中,并将方法与常用的机会约束方法进行比较,说明满意度法不仅合理可行,而且当决策者对约束条件的要求越高时,它所得最优值越优于机会约束法所得最优值.     

广义黏性逼近方法及其应用

黏性逼近方法在非扩张映射不动点问题的研究中扮演着重要的角色。提出了一类广义黏性逼近方法，在一定条件下，证明了该算法的收敛性.作为应用，将所得的收敛性结果应用于求解约束凸优化问题与双层优化问题。     

Modern information technologies in construction of kinetic models for reactions of metal complex catalysis

For detailed study of complex chemical reactions mechanisms experiment is conducted for selected private reactions. This causes a problem of kinetic parameters getting—the same set of rate constants must describe both public and private reaction stages, and also a general mechanism. In this paper, solution of this problem for a reaction of olefins hydroalumination is proposed. To optimize the computational process a methodology of parallelization is elaborated. On the base of parallel computations, a kinetic model for the reaction assigned is constructed, and on its base, the physical and chemical conclusions about reaction mechanism are done.     

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and suppose that there exists ε 0 such that if f ∈ F, then |(f 2 ) (ξ)|≤4-ε for all fixed points ξ of the second iterate f 2 . We show that then F is normal. This is deduced from a result which says that if p is a polynomial of degree at least 2, then p 2 has a fixed point ξ such that |(p 2 ) (ξ)|≥4. The results are motivated by a problem posed by Yang Lo.     

Weak coupling of a Reynolds model and a Stokes model for hydrodynamic lubrication

The Reynolds model is a reduced Stokes model, valid for narrow lubrication regions. In order to be able to handle locally non‐narrow regions such as pits or grooves, often displaying rapid geometrical variations, there is a need to be able to transit to the more accurate Stokes model. A fundamental problem is how to couple the two models in a numerical simulation, preferably allowing for different meshes in the different domains. In this paper, we present a weak coupling method for Reynolds and Stokes models for lubrication computations, including the possibility of cavitation in the different regions. The paper concludes with a numerical example. Copyright © 2010 John Wiley & Sons, Ltd.     

The contact Yamabe flow on K-contact manifolds

We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds.     

Parallel Schwarz alternating methods for anisotropic diffusion of speckled medical images

This paper deals with ultrasound medical image processing, particularly to filter the noise while preserving the edges and structures of information. The mathematical processing consists in solving by a numerical way a nonlinear evolutive boundary value problem. Several numerical semi-implicit time marching schemes are considered and analyzed. At each time step, parallel synchronous or asynchronous Schwarz alternating methods are used to solve the linear system and its convergence is studied. Lastly, the results of sequential and parallel simulations are presented.      

基于COSM的三维显微图像复原算法研究

光学分层显微成像技术(COSM)不仅可用于去除非聚焦层杂散光的影响以及噪声的干扰,而且能复原样本的清晰三维像,将成为提取微流体的三维温度和速度场分布信息的有效工具.本文研究了基于已知点扩展函数的6种COSM成像算法,详细讨论了6种COSM成像算法的原理和实现,构造了三维样本图像和点扩展函数模型,并对复原结果进行了分析....