Rolling mill performance

A rolling mill may be modelled as a number of inertial masses coupled by torsional springs. The question considered by the Study Group was whether the parameters of the system could be determined from measurements of the torques and accelerations at a number of points in the system. A number of related aspects such as resonances, torque amplification factors and parameter identification were also examined. The group concluded that frequency analysis and lumped mass models were potentially useful for the analysis of rolling mill performance

A simple model for the cold rolling of metal foil

The flow of perfectly plastic material between elastic rolls is examined as a model for rolling of foils. Key non-dimensional parameters are identified and the potential for approximate solutions, based on an asymptotic analysis, is examined

Flows in gas pipelines

Safe and efficient use of compressors in a pipeline network is quite complex since high pressures and pressure fluctuations may damage the pipeline. As a consequence, the problem posed to the Study Group was to examine to what extent mathematical modelling can be used to provide guidance for the operation of compressor stations

New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit

In this paper we define a new coherence index, named the global 2-coherence, of a given dictionary and study its relationship with the traditional mutual coherence and the restricted isometry constant. By exploring this relationship, we obtain more general results on sparse signal reconstruction using greedy algorithms in the compressive sensing (CS) framework. In particular, we obtain an improved bound over the best known results on the restricted isometry constant for successful recovery of sparse signals using orthogonal matching pursuit (OMP).Comment: arXiv admin note: substantial text overlap with arXiv:1307.194

High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels

The solution of the Volterra integral equation, $$( * )\qquad x(t) = g_1 (t) + \sqrt {t}g_2 (t) + \int _0^t \frac {K(t,s,x(s))} {\sqrt {t - s} } ds, \quad 0 \leqq t \leqq T,$$ where $g_1 (t)$, $g_2 (t)$ and $K(t,s,x)$ are smooth functions, can be represented as $x(t) = u(t) + \sqrt {t}v(t)$,$0 \leqq t \leqq T$, where $u(t)$, $v(t)$ are, smooth and satisfy a system of Volterra integral equations. In this paper, numerical schemes for the solution of (*) are suggested which calculate $x(t)$ via $u(t)$, $v(t)$ in a neighborhood of the origin and use (*) on the rest of the interval $0 \leqq t \leqq T$. In this way, methods of arbitrarily high order can be derived. As an example, schemes based on the product integration analogue of Simpson's rule are treated in detail. The schemes are shown to be convergent of order $h^{{7 / 2}}$. Asymptotic error estimates are derived in order to examine the numerical stability of the methods

On the Micro-Dynamics of a Cash-in-Advance Economy (revised version of WP 04-12)

The purpose of this paper is to develop a general equilibrium model with money and trade taking place at disequilibrium prices. There are multiple markets being visited sequentially and transactions occur along the adjustment path. This implies quantity rationing to clear the market and we assume that there are cash-in-advance constraints on the transactions. The updating of the prices and cash balances along the way makes it necessary for agents to reconsider their trading plans subject to new information due to substitution and spill-over effects. The dynamics of this disequilibrium re-optimization process are shown to depend crucially on the exchange mechanisms that are imposed. One of the results is that the introduction of a cash-in-advance constraint does not help in stabilizing the fluctuations of cash balances, even though it does prevent debts from occurring outside of equilibrium.