Modelling and Simulation of Food Foams

The rheological behaviour of protein solutions containing bubbles at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. Protein foams have a great importance in food production because of their special sensory properties. A suspension that contains bubbles in a Newtonian liquid exhibits inherently a complex rheological behaviour, such as elastic effects, a shear- and time-dependent viscosity and normal stress differences. The deformation state of the bubbles in a suspension subjected to a steady shear is a function of the gas volume fraction ϕ and the capillary number N_Ca. In the present article, material equations for protein solutions with gas volume fractions ϕ ≤ 0.75 and small bubble deformations, i. e. N_Ca ≪ 1, are analysed and further developed. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micro‐Mechanical Modelling of the Constitutive Behaviour of NiTi Shape Memory Alloys

The superelasticity and shape memory effect in NiTi alloys are examined on the basis of micromechanics within the energy minimization framework. We describe the behaviour of polycrystalline shape‐memory alloys via orientation‐distribution of the various martensite‐variants (domains) present in the material. Stress‐strain curves are presented and special attention is payed to the volume fraction of martensite for specific NiTi alloys (Nitinol) specimen under uniaxial tension. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of the Transport of Protein Foams

The behaviour of foams at rest, but particularly during fluid mechanical transport is not sufficiently investigated yet. The present article deals with protein foams as they have a great importance in food production. In the first part, the foaming process of a highly viscous liquid due to gaseous materials dispersed under pressure in the liquid and mass transport of volatile components dissolved in the liquid is considered. The aim is to calculate the foam volume and the concentration of the dissolved, volatile components as a function of the material and process parameters. In the second part, material equations for bubble suspensions with gas volume fractions ϕ ≤ 0.6 and small bubble deformations (i.e. N_Ca ≪ 1) are presented. The basics form two constitutive laws which are used for describing a steady shear flow. If the rates of work of the two models are compared, material equations for the shear viscosity and the normal stress differences can be derived. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oscillatory Behaviour of a Higher Order Nonlinear Neutral Delay Type Functional Differential Equation with Oscillating Coefficients

In this paper we are concerned with the oscillation of solutions of a certain more general higher order nonlinear neutral type functional differential equation with oscillating coefficients. We obtain two sufficient criteria for oscillatory behaviour of its solutions.     

Graded Meshes for Higher Order FEM

A singularly perturbed one-dimensional convection-diffusion problem is solved numerically by the finite element method based on higher order polynomials. Numerical solutions are obtained using S-type meshes with special emphasis on meshes which are graded (based on a mesh generating function) in the fine mesh region. Error estimates in the ε-weighted energy norm are proved. We derive an 'optimal' mesh generating function in order to minimize the constant in the error estimate. Two layer-adapted meshes defined by a recursive formulae in the fine mesh region are also considered and a new technique for proving error estimates for these meshes is presented. The aim of the paper is to emphasize the importance of using optimal meshes for higher order finite element methods. Numerical experiments support all theoretical results.     

Asymptotics of Higher Order Ospt-Functions for Overpartitions

In this paper we obtain asymptotic formulas for positive crank and rank moments for overpartitions. Moreover, we show that crank and rank moments are asymptotically equal while the difference is asymptotically positive. This indicates that there exist analogous higher ospt-functions for overpartitions, which we define.     

Higher Order Fractional Differentiability for the Stationary Stokes System

This paper focuses on the higher order fractional differentiability of weak solution pairs to the following nonlinear stationary Stokes system■In terms of the difference quotient method,our first result reveals that if F ∈ B_p,q.loc^β(Ω,Rⁿ) for p=2 and 1≤q≤2n/n-2β,then such extra Besov regularity can transfer to the symmetric gradient Du and its pressure π with no losses under a suitable fractional differentiability assumption on x■A(x,ξ).Furthermore,when the vecto...     

Regularization for Higher Order Singular Integral Equations

By means of the definition of Hadamard principal value permutation formula and composition formula for higher order singular integrals developing in [5], the regularization problems for higher order singular integral equations with variable coefficients are discussed, and the higher order singular integral equations with constant coefficient are solved. It is the first time to treat the high order singular integral equations of arbitrary degree in the theory of singular integral equations.      

高阶导数的一个极限表达式

通过对二阶微分问题的求解与推广,给出求解高阶导数的极限表达式．这也是差分法的一个推广．     

Global Behaviour of a Reaction-Diffusion System Modelling Chemotaxis

Using Lyapunov functionals the global behaviour of the solutions of a reaction-diffusion system modelling chemotaxis is studied for bounded piecewise smooth domains in the plane. Geometric criteria can be given so that this dynamical system tends to a (not necessarily trivial) stationary state.     

Gibbs Measure for the Higher Order Modified Camassa-Holm Equation

This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial data and periodic boundary condition.Motivated by the works of Thomann and Tzvetkov(Nonlinearity,23(2010),2771–2791),Tzvetkov(Probab.Theory Relat.Fields,146(2010),4679–4714),Burq,Thomann and Tzvetkov(Ann.Fac.Sci.Toulouse Math.,27(2018),527–597),the authors first construct the Borel measure of Gibbs type in the Sobolev spaces with lower regularity,and then establish the existence of global solution to the equation with the helps of Prokhorov compactness theorem,Skorokhod convergence theorem and Gibbs measure.     

极大高阶交换子的端点估计

该文主要确立了当b∈BMO 时, 极大高阶奇异积分算子交换子T_{b, m}* 满足如下不等式 |{y∈Rⁿ:T_{b, m}*f(y)>λ}|≤C||b||^m_BMO∫_Rⁿ|f(y)|/λ (1+log⁺|f(y)|/λ)^mdy 且T_{b, m}* 在L^p(Rⁿ)(1 < p <∞上有界.     

Admissible Domains for Higher Order Differential Equations

This paper analyzes the geometric structure of certain domains in the complex plane which arise in the asymptotic theory of linear ordinary differential equations containing a parameter. These domains, called admissible, are domains in which an asymptotic representation of the solution of the differential equation may be found and across whose boundaries these representations may undergo a rapid change of asymptotic behavior (the Stokes phenomenon). A knowledge of the disposition of those domains associated with a particular differential equation is necessary for a satisfactory asymptotic theory of the equation. The main analysis gives necessary and sufficient conditions for identifying admissible domains and gives a procedure for obtaining particular admissible subdomains of a given domain. Sufficient conditions are established to determine the maximality of admissible domains. A section of examples is included to highlight the salient features of this theory. In all of the results, criteria involving only purely local properties of the boundary are needed to determine the global properties of admissibility and maximal admissibility .     

高阶马尔可夫链的降阶模型及其应用

本文通过对传统高阶马尔可夫链模型的状态空间进行阶数重构,导出一个在重构状态空间上的降阶马尔可夫模型。理论分析证明,降阶马尔可夫链模型不但可以描述传统高阶马尔可夫链模型的全部性态,更能表达较传统模型细微的随机结构。然后,应用降阶模型对我国股票指数的动态变化进行实证分析,讨论了阶数的选取和高阶马尔可夫性检验,分析了股票市场内在波动结构。最后,对股指序列作出短期与长期的预测分析。     

Non-Oscillatory Solutions for Higher Order Dynamic Equations

A new non-oscillatory theory is presented for higher order delayand neutral equations. The results include both singular andnonsingular problems.     

Higher Order Derivative Characterization for Fock-Type Spaces

In this paper, we give a characterization for the Fock-type space \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) in terms of higher order derivatives of f and behaviors of local integral means of those derivatives. The space \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) has the closed subspace \({\mathcal{F}_{\alpha, 0}^{\infty}(\mathbb{C}^N)}\). We also characterize this subspace via higher order derivatives. As an application we study the boundedness and compactness of the extended Cesaro operator T _g on \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) and \({\mathcal{F}_{\alpha, 0}^{\infty}(\mathbb{C}^N)}\).     

Modelling Joint Behaviour of Asset Prices Using Stochastic Correlation

Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation models, two goodness-of-fit procedures are proposed based on the copula of Wiener increments. One uses the confidence domain for the centered Kendall function, and the other relies on strong and weak tail dependence. The constant correlation model and two different stochastic correlation models, given by Jacobi and hyperbolic tangent transformation of Ornstein-Uhlenbeck (HtanOU) processes, are compared by analyzing daily close prices for Apple and Microsoft stocks. The constant correlation, i.e., the Gaussian copula model, is unanimously rejected by the methods, but all other two are acceptable at a 95% confidence level. The analysis also reveals that even for Wiener processes, stochastic correlation can create tail dependence, unlike constant correlation, which results in multivariate normal distributions and hence zero tail dependence. Hence models with stochastic correlation are suitable to describe more dangerous situations in terms of correlation risk.

     

The Higher Order Approximation of Solution of Quasilinear Second Order Systems for Singular Perturbation

In this paper, using the theory of invariant region, the author considers the existence and the asymptotic behavior of solution of vector second order quasi-linear boundary value problem: $\epsilon y''=f(x,y,\epsilon)y''+g(x,y,\epsilon)$ $y(0,\epsilon)=A(\epsilon),y(1,\epsilon)=B(\epsilon)$ as the positive perturbation parameter e tends to zero, where y, g, A and B are vector-valued and f is a matrix function. Under the appropriate assumptions the author obtains, involving the boundary layer, uniformly valid asymptotic solution of higher order approximation.