The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. ...

In this paper we find, for n ≤ 16, the maximum number of edges in a 4-uniform hypergraph which does not have the complete 4-uniform hypergraph on five vertices,K4 5 , as a subgraph. Equivalently, we find all optimal (n, n−4, n−5) covering designs for n ≤ 16. Using these results we find a new upper bound for the Turán density ofK4 5 . π(K4 5 ) ≤ 1753 2380 = 0.73655 . . . . Finally wemake some no...

Extremal regularization finds a model fitting the data to a specified tolerance, and additionally minimizing an auxiliary criterion. It provides relative model/data space weights when no statistical information about the model or data is available other than an estimate of noise level. A version of the Moré-Hebden algorithm using conjugate gradients to solve the various linear systems implement...

Non-extremal overlapping p-brane supergravity solutions localised in their relative transverse coordinates are constructed. The construction uses an algebraic method of solving the bosonic equations of motion. It is shown that these non-extremal solutions can be obtained from the extremal solutions by means of the superposition of two deformation functions defined by vacuum solutions of M-theor...

Abstract: The relation between extremal values of the error and the coefficients of its differential equations is one of the central problems of control systems in chemical industry, because extremal values of the error sometimes cause serious damages to the environment or to the system itself. Analytical formulae for the determination of these values are known only for the second-order systems...

We investigate the five and six-dimensional black strings within EinsteinMaxwell theory. The extremal black strings are endowed with the null Killing symmetry. We study the propagation of Einstein-Maxwell modes in the extremal black string background by using this symmetry. It turns out that one graviton is a propagating mode, while both the Maxwell(F) and three-form (H) fields are non-propagat...

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

This paper applies Pontryagin’s Maximum Principle to the time optimal control of differential drive mobile robots with velocity bounds. The Maximum Principle gives necessary conditions for time optimality. Extremal trajectories are those which satisfy these conditions, and are thus a superset of the time optimal trajectories. This paper derives a compact geometrical structure for extremal traje...

For lengths 8, 16 and 24, it is known that there is an extremal Type II Z2k-code for every positive integer k. In this paper, we show that there is an extremal Type II Z2k-code of lengths 32, 40, 48, 56 and 64 for every positive integer k. For length 72, it is also shown that there is an extremal Type II Z4k-code for every positive integer k with k ≥ 2.

In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying curves are not the extremal curves and giv...