Solving optimal control problems with state constraints using nonlinear programming and simulation tools

This paper illustrates how nonlinear programming and simulation tools, which are available in packages such as MATLAB and SIMULINK, can easily be used to solve optimal control problems with state- and/or input-dependent inequality constraints. The method presented is illustrated with a model of a single-link manipulator. The method is suitable to be taught to advanced undergraduate and Master's level students in control engineering.

Buffon's needle problem with a twist

Some simple variations of Buffon's well-known needle problem in probability are discussed, and an interesting observation connecting the corresponding results is then made

On the principal eigenvalue of a Robin problem with a large parameter

We study the asymptotic behaviour of the principal eigenvalue of a Robin (or generalised Neumann) problem with a large parameter in the boundary condition for the Laplacian in a piecewise smooth domain. We show that the leading asymptotic term depends only on the singularities of the boundary of the domain, and give either explicit expressions or two-sided estimates for this term in a variety of situations.

Cross-layer design for multiuser MIMO MRC systems with feedback constraints

Cross-layer techniques represent efficient means to enhance throughput and increase the transmission reliability of wireless communication systems. In this paper, a cross-layer design of aggressive adaptive modulation and coding (A-AMC), truncated automatic repeat request (T-ARQ), and user scheduling is proposed for multiuser multiple-input-multiple-output (MIMO) maximal ratio combining (MRC) systems, where the impacts of feedback delay (FD) and limited feedback (LF) on channel state information (CSI) are also considered. The A-AMC and T-ARQ mechanism selects the appropriate modulation and coding schemes (MCSs) to achieve higher spectral efficiency while satisfying the service requirement on the packet loss rate (PLR), profiting from the feasibility of using different MCSs to retransmit a packet, which is destined to a scheduled user selected to exploit multiuser diversity and enhance the system's performance in terms of both transmission efficiency and fairness. The system's performance is evaluated in terms of the average PLR, average spectral efficiency (ASE), outage probability, and average packet delay, which are derived in closed form, considering transmissions over Rayleigh-fading channels. Numerical results and comparisons are provided and show that A-AMC combined with T-ARQ yields higher spectral efficiency than the conventional scheme based on adaptive modulation and coding (AMC), while keeping the achieved PLR closer to the system's requirement and reducing delay. Furthermore, the effects of the number of ARQ retransmissions, numbers of transmit and receive antennas, normalized FD, and cardinality of the beamforming weight vector codebook are studied and discussed.

A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

A semantic solution to the problem with aesthetic testimony

There is something peculiar about aesthetic testimony. It seems more difficult to gain knowledge of aesthetic properties based solely upon testimony than it is in the case of other types of property. In this paper, I argue that we can provide an adequate explanation at the level of the semantics of aesthetic language, without defending any substantive thesis in epistemology or about aesthetic value/judgement. If aesthetic predicates are given a non-invariantist semantics, we can explain the supposed peculiar difficulty with aesthetic testimony.

Periodic time series modeling of environmental proxy records with guaranteed positive growth rate estimation

Identifying a periodic time-series model from environmental records, without imposing the positivity of the growth rate, does not necessarily respect the time order of the data observations. Consequently, subsequent observations, sampled in the environmental archive, can be inversed on the time axis, resulting in a non-physical signal model. In this paper an optimization technique with linear constraints on the signal model parameters is proposed that prevents time inversions. The activation conditions for this constrained optimization are based upon the physical constraint of the growth rate, namely, that it cannot take values smaller than zero. The actual constraints are defined for polynomials and first-order splines as basis functions for the nonlinear contribution in the distance-time relationship. The method is compared with an existing method that eliminates the time inversions, and its noise sensitivity is tested by means of Monte Carlo simulations. Finally, the usefulness of the method is demonstrated on the measurements of the vessel density, in a mangrove tree, Rhizophora mucronata, and the measurement of Mg/Ca ratios, in a bivalve, Mytilus trossulus.

The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

Modelling and validation of Lactobacillus plantarum fermentations in cereal-based media with different sugar concentrations and buffering capacities

An unstructured mathematical model is proposed to describe the fermentation kinetics of growth, lactic acid production, pH and sugar consumption by Lactobacillus plantarum as a function of the buffering capacity and initial glucose concentration of the culture media. Initially the experimental data of L plantarum fermentations in synthetic media with different buffering capacity and glucose were fitted to a set of primary models. Later the parameters obtained from these models were used to establish mathematical relationships with the independent variables tested. The models were validated with 6 fermentations of L. plantarum in different cereal-based media. In most cases the proposed models adequately describe the biochemical changes taking place during fermentation and are a promising approach for the formulation of cereal-based probiotic foods. (C) 2008 Elsevier B.V. All rights reserved.