Search results for "Applied Mathematics"
showing 10 items of 4379 documents
A Calvin Bestiary
2017
This paper compares a number of mathematical models for the Calvin cycle of photosynthesis and presents theorems on the existence and stability of steady states of these models. Results on five-variable models in the literature are surveyed. Next a number of larger models related to one introduced by Pettersson and Ryde-Pettersson are discussed. The mathematical nature of this model is clarified, showing that it is naturally defined as a system of differential-algebraic equations. It is proved that there are choices of parameters for which this model admits more than one positive steady state. This is done by analysing the limit where the storage of sugars from the cycle as starch is shut d…
From a fixed bed Ag–alumina catalyst to a modified reactor design: how to enhance the crucial heterogeneous–homogeneous reactions in HC-SCR
2004
Abstract A highly active Ag/alumina catalyst for continuous reduction of NO to nitrogen with n-octane under lean conditions was prepared. It was observed in the reactor set-up experiments for optimization of the converter, that surface generated gas phase species are crucial for obtaining high conversion. EPR and matrix isolated FTIR studies at low temperature (10–18 K) were performed for identification of the radicals. Experimental data, observed at steady state conditions in the temperature range 300–550 °C, was used to produce an artificial neural network model of the catalytic converter with four catalyst beds.
Using Unfold-PCA for batch-to-batch start-up process understanding and steady-state identification in a sequencing batch reactor
2007
In chemical and biochemical processes, steady-state models are widely used for process assessment, control and optimisation. In these models, parameter adjustment requires data collected under nearly steady-state conditions. Several approaches have been developed for steady-state identification (SSID) in continuous processes, but no attempt has been made to adapt them to the singularities of batch processes. The main aim of this paper is to propose an automated method based on batch-wise unfolding of the three-way batch process data followed by a principal component analysis (Unfold-PCA) in combination with the methodology of Brown and Rhinehart 2 for SSID. A second goal of this paper is to…
Advanced stochastic control systems with engineering applications
2014
1 School of Astronautics, Harbin Institute of Technology, Harbin, Heilongjiang, China 2 School of Electrical and Electronic Engineering, The University of Adelaide, SA 5005, Australia 3 Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway 4 Institute of Automation and Complex Systems, University of Duisburg-Essen, Duisburg, Germany 5 College of Automation, Chongqing University, Chongqing 400044, China
A Fokker–Planck control framework for multidimensional stochastic processes
2013
AbstractAn efficient framework for the optimal control of probability density functions (PDFs) of multidimensional stochastic processes is presented. This framework is based on the Fokker–Planck equation that governs the time evolution of the PDF of stochastic processes and on tracking objectives of terminal configuration of the desired PDF. The corresponding optimization problems are formulated as a sequence of open-loop optimality systems in a receding-horizon control strategy. Many theoretical results concerning the forward and the optimal control problem are provided. In particular, it is shown that under appropriate assumptions the open-loop bilinear control function is unique. The res…
Solving fully randomized first-order linear control systems: Application to study the dynamics of a damped oscillator with parametric noise under sto…
2022
[EN] This paper is devoted to study random linear control systems where the initial condition, the final target, and the elements of matrices defining the coefficients are random variables, while the control is a stochastic process. The so-called Random Variable Transformation technique is adapted to obtain closed-form expressions of the probability density functions of the solution and of the control. The theoretical findings are applied to study the dynamics of a damped oscillator subject to parametric noise.
European Option Pricing and Hedging with Both Fixed and Proportional Transaction Costs
2003
Abstract In this paper we provide a systematic treatment of the utility based option pricing and hedging approach in markets with both fixed and proportional transaction costs: we extend the framework developed by Davis et al. (SIAM J. Control Optim., 31 (1993) 470) and formulate the option pricing and hedging problem. We propose and implement a numerical procedure for computing option prices and corresponding optimal hedging strategies. We present a careful analysis of the optimal hedging strategy and elaborate on important differences between the exact hedging strategy and the asymptotic hedging strategy of Whalley and Wilmott (RISK 7 (1994) 82). We provide a simulation analysis in order …
American Option Pricing and Exercising with Transaction Costs
2005
In this paper we examine the problem of finding the reservation option prices and corresponding exercise policies of American options in a market with proportional transaction costs using the utility based approach proposed by Davis and Zariphopoulou (1995). We present a model where the option holder has a constant absolute risk aversion. We discuss the numerical algorithm and propose a new characterization of the option holder's value function. We suggest original discretization schemes for computing reservation prices and exercise policies of American options. The discretization schemes are implemented for the cases of American put and call options. We present the study of the optimal tra…
Stochastic Control Problems
2003
The general theory of stochastic processes originated in the fundamental works of A. N. Kolmogorov and A. Ya. Khincin at the beginning of the 1930s. Kolmogorov, 1938 gave a systematic and rigorous construction of the theory of stochastic processes without aftereffects or, as it is customary to say nowadays, Markov processes. In a number of works, Khincin created the principles of the theory of so-called stationary processes.
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
2003
Abstract A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ. To cite this article: S. Fang, T. Zhang, C. R. Acad. Sci. Paris, Ser. I 337 (2003).