Managing temporary workers in higher education: still at the margin?

Purpose – To evaluate whether “numerical flexibility” – specifically a form of temporary and precarious employment – hourly-paid part-time teaching in the UK higher education sector – adds strategic value and demonstrates good practice. Design/methodology/approach – The study is based on new evidence drawn from five case study organisations in which a range of managers was interviewed in depth. Findings – Analysis identifies a continuum of strategies from integration into the main workforce through to “deepened differentiation”. Although integration is somewhat problematic when applied to a diverse group, differentiation seems predicated on a defensive, risk management approach designed to further marginalise this activity. Also, differentiation fails to address the aspirations of many employees, creating tensions between institutional strategy and the needs of academic heads. Research limitations/implications – The number of case studies is limited. These case studies were selected because they had the most proactive strategies on this issue, which infers that the majority of employers in HE have not been rather less strategic or proactive. Practical implications – The paper is of particular value to HR professionals considering the use of numerical flexibility approaches. It also contributes to the academic debate on the strategic value of such approaches. Originality/value – The paper explores a neglected but important area of the workforce. The paper notes that some supposed benefits of numerical flexibility might be illusory, such as the deployment of allegedly “cheap and disposable” substitute workers which may be offset by unintentional consequences including rigidities in an organisation's human resource systems

An extension of Chebfun to two dimensions

An object-oriented MATLAB system is described that extends the capabilities of Chebfun to smooth functions of two variables defined on rectangles. Functions are approximated to essentially machine precision by using iterative Gaussian elimination with complete pivoting to form “chebfun2” objects representing low rank approximations. Operations such as integration, differentiation, function evaluation, and transforms are particularly efficient. Global optimization, the singular value decomposition, and rootfinding are also extended to chebfun2 objects. Numerical applications are presented

Equivalence Theorems in Numerical Analysis : Integration, Differentiation and Interpolation

We show that if a numerical method is posed as a sequence of operators acting on data and depending on a parameter, typically a measure of the size of discretization, then consistency, convergence and stability can be related by a Lax-Richtmyer type equivalence theorem -- a consistent method is convergent if and only if it is stable. We define consistency as convergence on a dense subspace and stability as discrete well-posedness. In some applications convergence is harder to prove than consistency or stability since convergence requires knowledge of the solution. An equivalence theorem can be useful in such settings. We give concrete instances of equivalence theorems for polynomial interpolation, numerical differentiation, numerical integration using quadrature rules and Monte Carlo integration.Comment: 18 page

Moments of spectral functions: Monte Carlo evaluation and verification

The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable against time whenever the potential function is arbitrarily smooth. Here, I demonstrate that the numerical differentiation of the estimating functionals can be more successfully implemented by means of pseudospectral methods (e.g., exact differentiation of a Chebyshev polynomial interpolant), which utilize information from the entire interval $(-\beta \hbar / 2, \beta \hbar/2)$. The algorithmic detail that leads to robust numerical approximations is the fact that the path integral action and not the actual estimating functional are interpolated. Although the resulting approximation to the estimating functional is non-linear, the derivatives can be computed from it in a fast and stable way by contour integration in the complex plane, with the help of the Cauchy integral formula (e.g., by Lyness' method). An interesting aspect of the present development is that Hamburger's conditions for a finite sequence of numbers to be a moment sequence provide the necessary and sufficient criteria for the computed data to be compatible with the existence of an inversion algorithm. Finally, the issue of appearance of the sign problem in the computation of moments, albeit in a milder form than for other quantities, is addressed.Comment: 13 pages, 2 figure

Computing with functions in spherical and polar geometries I. The sphere

A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian elimination together with the double Fourier sphere method. We show that this procedure allows for stable differentiation, reduces the oversampling of functions near the poles, and converges for certain analytic functions. Operations such as function evaluation, differentiation, and integration are particularly efficient and can be computed by essentially one-dimensional algorithms. A highlight is an optimal complexity direct solver for Poisson's equation on the sphere using a spectral method. Without parallelization, we solve Poisson's equation with $100$ million degrees of freedom in one minute on a standard laptop. Numerical results are presented throughout. In a companion paper (part II) we extend the ideas presented here to computing with functions on the disk.Comment: 23 page

Problems in fluid dynamics

A scheme was developed for the parametric differentiation and integration of gas dynamics equations. A numerical integration of the gas dynamics equations is necessarily performed for a specific set of parameter values. The linear variational equations are obtained by differentiating the exact equations with respect to each of the relevant parameters. The resulting matrix of flow quantities is referred to as the Jacobi matrix. The subsequent procedure is then straightforward. The method was tested for two dimensional supersonic flow past an airfoil, with airfoil thickness, camber, and angle of attack varied. This approach has great potential value for rapidly assessing the effect of design changes. The other focus of the work was on problems in fluid stability, bifurcations, and turbulence

Numerical differentiation for local and global tangent operators in computational plasticity

CIMNE - PI 144In this paper, numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators. The deriva- tivesoftheconstitutive equationsareapproximatedbymeansofdifferenceschemes. These derivatives are needed to achieve quadratic convergence in the integration at Gauss-point level and in the solution of the boundary value problem. Numerical differentiation is shown to be a simple, robust and competitive alternative to an- alytical derivatives. Quadratic convergence is maintained, provided that adequate schemes and stepsizes are chosen. This point is illustrated by means of some nu- merical examples.Peer ReviewedPreprin