On null isotropy in spacetimes

Null isotropy in a spacetime is defined. The relation of null isotropy to the constant curvature and infinitesimal spatial isotropy is investigated. The influence of null isotropy on conjugate points along null geodesics and curvature singularities is investigated.     

Equilibrium points of the tilted perfect fluid Bianchi VI<Subscript><Emphasis Type="Italic">h</Emphasis></Subscript> state space

We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI_h filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is found that only when the group parameter satisfies h > –1 a self-similar solution exists. In particular we show that for h > – there exists a self-similar equilibrium point provided that whereas for h < – the state parameter belongs to the interval (1, . This family of new exact self-similar solutions belongs to the subclass n = 0 having non-zero vorticity. In both cases the equilibrium points have a six-dimensional stable manifold and may act as future attractors at least for the models satisfying n = 0. Also we give the exact form of the self-similar metrics in terms of the state and group parameter. As an illustrative example we provide the explicit form of the corresponding self-similar radiation model ( = ), parametrised by the group parameter h. Finally we show that there are no tilted self-similar models of type III and irrotational models of type VI_h.     

Powerful arithmetic progressions

We give a complete characterization of so-called powerful arithmetic progressions, i.e. of progressions whose kth term is a kth power for all k. We also prove that the length of any primitive arithmetic progression of powers can be bounded both by any term of the progression different from 0 and ±1, and by its common difference. In particular, such a progression can have only finite length.     

On diameter perfect constant-weight ternary codes

From cosets of binary Hamming codes we construct diameter perfect constant-weight ternary codes with weight n-1 (where n is the code length) and distances 3 and 5. The class of distance 5 codes has parameters unknown before.     

Statistical aspects of the identification of material parameters for elasto-plastic models

Summary The presented method to identify material parameters for inelastic deformation laws is based on the numerical analysis of inhomogeneous stress and strain fields received from suitable experiments. Tensile and bending tests were carried out to obtain elastic and hardening parameters. The deformation law for small elasto-plastic strains is presented as a system of nonlinear differential and algebraic equations (DAE) consisting of the stress–strain relation, evolution equations for the internal variables and the yield condition. Different rules for the evolution equations of isotropic, kinematic and distorsional hardening are proposed. The DAE are discretized using an implicit Euler method, and the resulting system of nonlinear algebraic equations is solved using the Newton method. Deterministic optimization procedures are preferred to identify material parameters from a least-squares functional of numerical and measured comparative quantities. The gradient of the objective function was calculated using a semianalytical sensitivity analysis. Due to measurement errors, the optimal sets of material parameters are non unique. The approximate estimation of confidence regions and the calculation of correlation coefficients is presented. The results of several optimization processes for material parameters of elasto-plastic deformation laws show a good agreement between measured and calculated values, but they show also problems which may occur if systematic errors will not be recognized and deleted. Received 30 September 1999; accepted for publication 8 March 2000     

On The Maximum Friction Law for Rigid/Plastic,Hardening Materials

For a rigid/plastic, hardening material model, it is shown that the velocity fields adjacent to surfaces of maximum friction must satisfy the sticking condition. This means that the stress boundary condition, the maximum friction law, may be replaced by the velocity boundary condition. Axisymmetric flows without rotation and planar flows are considered.     

Batch processing with interval graph compatibilities between tasks

We analyze batch-scheduling problems that arise in connection with certain industrial applications. The models concern processing on a single max-batch machine with the additional feature that the tasks of the same batch have to be compatible. Compatibility is a symmetric binary relation—the compatible pairs are described with an undirected “compatibility graph”, which is often an interval graph according to some natural practical conditions that we present. We consider several models with varying batch capacities, processing times or compatibility graphs. We summarize known results, and present a min-max formula and polynomial time algorithms.     

Skew partitions in perfect graphs

We discuss some new and old results about skew partitions in perfect graphs.     

Building nonredundant adaptive wavelets by update lifting

In this paper, we propose a technique for building adaptive wavelets by means of an extension of the lifting scheme. Our scheme comprises an adaptive update lifting step and a fixed prediction lifting step. The adaptivity consists hereof that the system can choose between two different update filters, and that this choice is triggered by the local gradient of the original signal. If the gradient is large (in some seminorm sense) it chooses one filter, if it is small the other. We derive necessary and sufficient conditions for the invertibility of such an adaptive system for various scenarios. Furthermore, we present some examples to illustrate our theoretical results.     

Finding more perfect matchings in leapfrog fullerenes

We use some recent results on the existence of long cycles in leapfrog fullerenes to establish new exponential lower bounds on the number of perfect matchings in such graphs. The new bounds are expressed in terms of Fibonacci numbers.