Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuoustime and discrete-time systems. A necessary and sufficient condition for a linear system on a time scale to be positive is presented. Properties of positive reachable sets are investigated and characterizations of various controllability pr...

In this paper, we use the interior-outer-set model to calculate the risk of crop flood and order farming alternatives for Huarong County, China, where only a small sample of eight observations is available. Any risk assessment from the data must be imprecise. The risk calculated by this suggested model is a particular case among imprecise probabilities, called possibility–probability distributi...

Maximum entropy discrimination (MED) is a general framework for discriminative estimation which integrates the principles of maximum entropy and maximum margin. In this paper, we propose a novel approach named multi-kernel MED (MKMED) for multi-view learning (MVL), which takes advantage of the complementary principle for MVL. Multiple kernels encode the similarities in different views. We obtai...

Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation solutions these help their delayed Mittag–Leffler matrix functions is used to obtain controllability Hyers–Ulam stability results. By introducing a Gramian matrix, we establish some sufficient necessary conditions for systems. In addition, by applyin...

This paper introduces a novel mathematical and computational framework, namely Log-Hilbert-Schmidt metric between positive definite operators on a Hilbert space. This is a generalization of the Log-Euclidean metric on the Riemannian manifold of positive definite matrices to the infinite-dimensional setting. The general framework is applied in particular to compute distances between covariance o...

The plane wave solutions of the three-wave resonant interaction in the plane are considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space gives solutions of the three-wave resonant interaction that can be understood as a Darboux transformation of the plane wave solutions. The method is extended further to obtain general Da...

For a general class of dynamical systems (of which the canonical continuous and uniform discrete versions are but special cases), we prove that there is a state feedback gain such that the resulting closed-loop system is uniformly exponentially stable with a prescribed rate. The methods here generalize and extend Gramian-based linear state feedback control to much more general time domains, e.g...

For each positive even integer j there is an infinite arithmetic sequence of dimensions d for which we construct a j -simplex of maximum volume in the d-dimensional unit cube. For fixed d, all of these maximal j -simplices have the same Gram matrix, which is a multiple of I+J. For j even, a new upper bound for the volume of a j -simplex in the d-dimensional unit cube is given. 1997 Academic Press

Fractional control systems with the Caputo derivative are considered. The modified controllability Gramian and the minimum energy optimal control problem are investigated. Construction of minimizing steering controls for the modified energy functional are proposed.