Cesar A. Gómez

Exact Solutions for the Generalized BBM Equation with Variable Coefficients

The variational iteration algorithm combined with the exp-function method is suggested to solve the generalized Benjamin-Bona-Mahony equation (BBM) with variable coefficients. Periodic and soliton solutions are formally derived in a general form. Some particular cases are considered.

The variational iteration method combined with improved generalized tanh–coth method applied to Sawada–Kotera equation

Abstract We obtain new exact solutions to generalized Sawada–Kotera equation. Using the variational iteration method combined with the improved generalized tanh–coth method, we construct new traveling wave solutions for the standard Sawada–Kotera equation and, by means of scaling, we obtain new solutions to general Sawada–Kotera equation. Periodic and soliton solutions are formally derived for both models.

Stock loans in incomplete markets

Abstract A stock loan is a contract whereby a stockholder uses shares as collateral to borrow money from a bank or financial institution. In Xia and Zhou (2007, Stock loans, Mathematical Finance, 17(2), pp. 307–317), this contract is modelled as a perpetual American option with a time-varying strike and analysed in detail within a risk-neutral framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite, we use a time-homogeneous utility maximization problem to obtain an exact formula for the value of the loan fee to be charged by the bank. For loans of finite maturity, we characterize the fee using variational inequality techniques. In both cases, we show analytically how the fee varies with the model parameters and illustrate the results numerically.

Infinite Horizon MPC and model reduction applied to large scale chemical plant

This paper studies the application of Infinite Horizon Model predictive Control (MPC) and model reduction by means of Hankel norm to chemical process of interest in the field of control of large, complex and networked systems. In this paper we first describes the model of the complete process which is composed by three reactors and three distillation columns. Later, we show the main aspects about model reduction by means of Hankel norm and Infinite Horizon MPC and finally the model obtained through numerical linearization and model reduction is used to design centralized Infinite Horizon Model predictive Control (MPC).

An approach to stability and controllability analysis in batch processes using set theory methods

A barely approached of the topics in the area of Batch Process (BP) Control is controllability and stability analysis. This is because the dynamic characteristic of BPs makes the traditional analysis of these properties harder. Characteristics like the transitory dynamics of the states and the irreversibility of the states (from the dynamic systems point of view) are serious obstacles for the use of classic tools to make an analysis of stability and controllability in BP, therefore, other tools should be used in order to come closer to a theoretical analysis on BP control. One approach is the use of some set theorys definitions. This paper uses the Controllable Trajectories Sets (CTS) to carry out a theoretical analysis on BP control.

Hierarchical control of large scale systems: A zone control approach

Abstract A methodology for hierarchical control of large scale systems is presented. This approach uses an integration of dynamic real time optimization (DRTO) and model predictive control (MPC) with zone control (coordinator). The dynamic real time optimization problem is solved in the upper layer and addresses the overall economic objective to provide the reference trajectories for the coordinator (middle layer) that calculates hierarchical input variables and output references that are always into the designed zone, this information is taken by the subsystems controllers (lower layer) to generate the input variables that is going to be applied, and that reach the reference that the coordinator generate. This methodology is applied to a complete chemical process composed by three chemical reactors type CSTR (Continuous Stirred Tank Reactor) and three non reactive binary distillation columns.

A greener method for content sharing in mobile ad hoc networks

A mobile ad hoc network (MANET) is characterized by its dynamic and decentralized topology, which allows exchanging information between mobile nodes without any pre-existing telecommunications infrastructure. However, mobile devices have constrained resources like memory, energy, bandwidth, etc., that must be optimally used in situations where a MANET is needed. For that reason, we propose a greener method for content sharing in MANETs that reduces energy consumption of nodes. We evaluate our method through simulations using J-Sim environment. Simulation results show that our method uses more efficiently the node resources than a centralized content sharing technique.