Pruned discrete random samples

Let $X_i,i\in \mathbb{N}$, be independent and identically distributed random variables with values in ${\mathbb{N}}_0$. We transform (‘prune’) the sequence $\{X_1,\dots ,X_n\},n\in \mathbb{N}$, of discrete random samples into a sequence $\{0,1,2,\dots ,Y_n\},n\in \mathbb{N}$, of contiguous random sets by replacing $X_{n+1}$ with $Y_n+1$ if $X_{n+1}>Y_n$. We consider the asymptotic behaviour of $Y_n$ as $n\to \infty$. Applications include path growth in digital search trees and the number of tables in Pitmanʼs Chinese restaurant process if the latter is conditioned on its limit value.     

Modelling and simulation of steam turbine processes: individual models for individual tasks

Within power plants, several physical, chemical and mechanical processes are conducted to transfer the energy, stored in fossil fuel, into electrical energy. This energy conversion is divided into several stages. Hitherto, the largest conventional power plants employ steam turbines as prime movers to drive a generator. Hence, a steam turbine is one module to convert heat energy into mechanical energy. And thus it is one link in the chain of energy conversions with the aim of generating electrical energy. Today, steam turbine industry faces numerous challenges concerning efficiency, commissioning time, start-up times, operation, availability, safety, cost-effectiveness, etc. Many of these tasks can be supported by simulating the transient operational behaviour of the turbine in advance. For example, the commissioning time can be shortened if the turbine controllers are initialized with well-tuned pre-set parameters; cost-effectiveness can be increased by setting aside unnecessary devices and exactly determining material specifications; safety may be increased by predicting the impacts of failures and thus taking the necessary precautions. Different tasks require different details regarding the employed turbine simulation model. Thus, the turbine controller may be well tuned with less complex simulation models of turbine, generator and electrical grid, whereas detailed studies of failures, mainly the transient behaviour which may lead to serious damages, may require detailed modelling of the turbine-internal thermodynamic processes. Here, a brief overview of models which simulate the transient thermodynamic behaviour of a steam turbine is presented. Three different approaches will be introduced and compared with respect to different operating situations. Also, special attention is directed towards the time dependence of critical states, mainly turbine speed and pressure development in certain areas. The first model is based on a simple, linear approach and is suitable of giving a quick overview. The second one incorporates more details and is useful if the operating point is close to the design point. Finally, the last model incorporates mass and energy balances as well as the major non-linearities. Hence it depicts the turbine behaviour over a large range of operating points.     

Lyapunov Type Integral Inequalities for Certain Differential Equations

In the present paper we establish Lyapunov type integral inequalities related to the zeros of solutions of certain second-order differential equations by using elementary analysis. We also present some immediate applications of our results to study the asymptotic behavior of solutions of the corresponding differential equations.     

Existence and asymptotic behaviour of solutions of a nonlinear evolution problem

We prove existence and asymptotic behaviour of a weak solutions of a mixed problem for where A is the pseudo-Laplacian operator.     

Global existence and asymptotic behaviour for systems of nonlinear hyperbolic equations

We consider the initial-boundary value problem for a class of nonlinear hyperbolic equations system in a bounded domain. Using the potential well theory, the existence of global solutions is investigated. We also established the asymptotic behaviour of global solutions as t?→?+?∞ by applying the multiplier method.     

On the asymptotic behaviour of a pantograph–type difference equation

In this paper we study the asymptotic behaviour of solutions of the pantograph-type differnce equation, and obtain aymptotic estimates, which can imply asymptotic stability or stability of solutions     

具有局部阻尼的热弹性问题的渐近行为和指数稳定性

一个关于具有局部阻尼的半线性热弹性问题,是材料科学中最重要的数学模型之一．这个问题的解的存在性和齐次问题解的指数衰竭于零的性质被得到了．进而,也得到了对非齐次问题吸收集的存在性．结果显示了所研究的系统是渐近稳定的．     

GM(1,1)建模方法的改进及其应用

应用微分方程的两种数值解法估计GM(1,1)模型中的待辩参数a、u,并对模型的边界条件做了改进,建立了灰微分方程的时间响应表达式,讨论了由此建立的GM(1,1)模型的适用范围和预测精度.通过实例的分析计算,证明改进的模型具有良好的预测精度,满足工程实际需要,拓广了GM(1,1)模型的适用范围.