Modelling the Pulsating Process

We continue research on machine-oracle modelling of second-order arithmetic. The pulsating process described in [1, 2] is simulated using oracles of so-called autonomous hierarchies. The outcome is constructing a generalized constructive model for a fragment of second-order arithmetic described in [2].     

Modelling the Process of Multiattribute Choice

In most of the multiattribute utility models it is assumed that the analytical forms of partial and overall utility functions are known, and hence the problem becomes one of estimating the values of model parameters. This assumption is rather restrictive since one may not possess prior knowledge as to the analytical forms of such functions. The present paper is an attempt to eliminate some of the shortcomings of the existing models by proposing two new formulations of the multiattribute choice problem without a priori limitation to any strict form of partial utility function.     

Modelling and Simulation of Degassing Process

This work deals with the modelling and simulation of a degassing process mainly used for extruders in polymer industry. The numerical simulations are done with finite-volume method using OpenFOAM for a 2D single screw extruder. The material parameters have been all chosen for a PDMS-Pentane polymer mixture so that the results could be compared with the available experiments already performed for this mixture [1]. In addition to experiments, the numerical results will be compared with an analytical solution derived from Danckwerts' model [2][3]. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Modelling of the Adoption of Process Innovations

An alternative view on the modelling of diffusion processesof process innovations has been introduced by Nooteboom (1989). Thebasic idea in that paper is to model the process of adoption ofprocess innovations as a gambling model with odds in favourdepending on expected returns and odds against depending on risk.In this paper it is investigated under which theoretical conditions posed on the expected return function the usual adopted assumptions Nooteboom (1989) with respect to the parameters of the gambling model are in fact reasonable. It is shown that only under certainconditions the assumptions made on the gambling model are true ontheoretical grounds. In all other cases a nonexample shows that theresults as mentioned in literature are in general not true.     

Modelling and Simulation of Heat and Mass Transfer,via Symbolic Computation

This basically tutorial/case study paper illustrates the application of symbolic computation for two classical cases of chemical engineering, namely the modelling and simulation of a heat transfer process intensified by fin-covered surface, and a convective mass transport with first order irreversible chemical reaction. It has been shown that computer algebra provides a comfortable and elegant way to solve such technical problems in fully analytical form, with standard mathematical knowledge.     

Process Modelling under Uncertainty: Simulation Analysis of Indian Steel

The process model of the Indian iron and steel industry is presented, with particular focus on energy use and conservation possibilities. Uncertainty problems in the industry are analysed by using probabilistic Monte-Carlo simulations, where model parameters are assumed to be stochastic and distributed normally. Instead of the usual random sampling methods for generating inputs into the simulations, a stratified (Latin hypercube) sampling method is used. Statistical analysis of the output results shows that, for the steel industry in India, energy-conservation technologies would have insignificant impact on performance. A further contribution of the paper is the use of a microcomputer for large-scale Monte-Carlo simulations.     

Statistical Analysis of a Spatial Counting Process Modelling Crystallization of Polymers

The nucleation phase of the crystallization of polymers is described in terms of a stochastic spatial counting process, whose intensity depends upon the available volume. Estimation of the relevant parameters of the process are obtained via the maximum likelihood method [6]. The asymptotic properties of the estimators (proved in [6]) are applied to study their qualitative behaviour, as a function of the available volume and time. In this paper, a goodness of fit of the stochastic model proposed has been carried out via a Kolmogorov-Smirnov approach. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modelling,Synthesis, and Simulation of Supervisory Process Control Systems

Modelling, synthesis, and simulation issues of the supervisory systems in process control are investigated in the paper. Petri nets are used as a basic modelling framework for the supervisory part of the system. It is shown how the final verification effort can be minimised by applying formal synthesis methods. A straightforward approach to the industrial implementation of the developed solutions is suggested by means of sequential function chart representation. A batch process cell case study is used to illustrate the described concepts. Corresponding continuous and discrete event models of the process cell units are developed and a co-ordinating supervisor is designed by the method of place invariants. The system is simulated by the continuous simulation tool Matlab-Simulink, which is enhanced for simulation of the sequential control logic represented by sequential function chart.     

Newton—Riemann时空中的动力学（Ⅲ）

讨论了Newton-Riemann时空中的动力学－－Hamilton力学及其在流体力学中的应用。     

Modelling with the Novel INAR(1)-PTE Process

Methodology and Computing in Applied Probability - In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced....     

The Stochastically Subordinated Poisson Normal Process for Modelling Financial Assets

The method of stochastic subordination, or random time indexing, has been recently applied to Wiener process price processes to model financial returns. Previous emphasis in stochastic subordination models has involved explicitly identifying the subordinating process with an observable quantity such as number of trades. In contrast, the approach taken here does not depend on the specific identification of the subordinated time variable, but rather assumes a class of time models and estimates parameters from data. In addition, a simple Markov process is proposed for the characteristic parameter of the subordinating distribution to explain the significant autocorrelation of the squared returns. It is shown, in particular, that the proposed model, while containing only a few more parameters than the commonly used Wiener process models, fits selected financial time series particularly well, characterising the autocorrelation structure and heavy tails, as well as preserving the desirable self-similarity structure, and the existence of risk-neutral measures necessary for objective derivative valuation. Also, it will be shown that the model proposed fits financial times series data better than the popular generalised autoregressive conditional heteroscedasticity (GARCH) models. Additionally, this paper will develop a skew model by replacing the normal variates with Lévy stable variates.     

Causal Properties of Fibered Space-Time

Mathematical Notes - On the space of a principal bundle, a Lorentzian metric and a time orientation are given that are invariant with respect to the action of the structure group. These objects...     

Modelling a Multitype Branching Brownian Motion: Filtering of a Measure-Valued Process

In the framework of marked trees, a multitype branching brownian motion, described by measure-valued processes, is studied. By applying the strong branching property, the Markov property and the expression of the generator are derived for the process whose components are the measure-valued processes associated to each type particles. The conditional law of the measure-valued process describing the whole population observing the cardinality of the subpopulation of a given type particles is characterized as the unique weak solution of the Kushner‐Stratonovich equation. An explicit representation of the filter is obtained by Feyman–Kac formula using the linearized filtering equation.     

Boundary Control of the Heat Transfer Process in the Space

Russian Mathematics - We consider the simplest mathematical model of the following problem. On a part of the border of a region D ? ?2 there is a heater having the adjustable...     

Newton—Riemann时空中的动力学（Ⅱ）

讨论了Newton-Riemann时空中运动的相对性及运动方程的协变性,N－R时空中Newton力学与广义相对论的某些关系及其异同。     

Modelling of Heat Transfer and Vehicle Dynamics for Thermal Load Reduction by Hypersonic Flight Optimization

Heat input reduction by appropriate, optimal trajectory control is considered for the range cruise and the return-to-base cruise of a hypersonic vehicle propelled by a turbo/ram jet engines combination. A mathematical model is developed for describing the unsteady heat transfer through the thermal protection system. This model is coupled to the model of the dynamics of the vehicle. An efficient optimization technique is applied for constructing a solution for the two cruise problems. The results show that significant heat input reductions can be achieved with only a small penalty in fuel consumption.     

Maintenance Decision Support: Analysing Crankcase Lubricant Condition by Markov Process Modelling

The probabilistic changes in certain measurable physical parameters of a lubricant are used to develop a mathematical model of the physical-chemical deterioration process taking place in the crankcase of locomotive diesel engines. A seven-state Markov chain is formulated with actual data taken from the year 1985. Statistical inference is used to establish that the chain is of the first order and that it is applicable across the fleet of locomotives in the study. The Markov model is shown to have the twin advantages of enhancing one's understanding of the deterioration process and of providing a means for predicting future changes. The model also lends itself to the specification of input data.     

Modelling of Marginally Regular Bivariate Counting Process and its Application to Shock Model

In this paper, we develop a new class of bivariate counting processes that have ‘marginal regularity’ property. But, the ‘pooled processes’ in the developed class of bivariate counting processes are not regular. Therefore, the proposed class of processes allows simultaneous occurrences of two types of events, which can be applicable in practical modeling of counting events. Initially, some basic properties of the new class of bivariate counting processes will be discussed. Based on the obtained properties, the joint distributions of the numbers of events in time intervals will be derived and the dependence structure of the bivariate process will be discussed. Furthermore, the marginal and conditional processes will be studied. The application of the proposed bivariate counting process to a shock model will also be considered. In addition, the generalization to the multivariate counting processes will be discussed briefly.     

Space-Time Localisation for the Dynamic Model

We prove an a priori bound for solutions of the dynamic equation. This bound provides a control on solutions on a compact space-time set only in terms of the realisation of the noise on an enlargement of this set, and it does not depend on any choice of space-time boundary conditions. We treat the large- and small-scale behaviour of solutions with completely different arguments. For small scales we use bounds akin to those presented in Hairer's theory of regularity structures. We stress immediately that our proof is fully self-contained, but we give a detailed explanation of how our arguments relate to Hairer's. For large scales we use a PDE argument based on the maximum principle. Both regimes are connected by a solution-dependent regularisation procedure. The fact that our bounds do not depend on space-time boundary conditions makes them useful for the analysis of large-scale properties of solutions. They can, for example, be used in a compactness argument to construct solutions on the full space and their invariant measures. © 2020 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC