This paper provides a solution to the problem of computing a robustly positively invariant outer approximation of the minimal robustly positively invariant set for a discretetime, linear, time-invariant system. It is assumed that the disturbance is additive and persistent, but bounded.

We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when it is not unique. Provided the approximation problem yields a set of score vectors, rather than a unique (up to a constant factor) one, the set...

In this work, a Multi-Level Artificial Bee Colony (called MLABC) for optimizing numerical test functions is presented. In MLABC, two species are used. The first species employs n colonies where each of them optimizes the complete solution vector. The cooperation between these colonies is carried out by exchanging information through a leader co lony, which contain s a set of elite bees. The sec...

Extending differential-based operations to color images is hindered by the multi-channel nature of color images. The derivatives in different channels can point in opposite directions, hence cancellation might occur by simple addition. The solution to this problem is given by the structure tensor for which opposing vectors reinforce each other. We review the set of existing tensor based feature...

It is proved that if the Schrödinger equation Lψ = λψ of CalogeroMoser-Sutherland type with L = −∆ + ∑ α∈A+ mα(mα + 1)(α, α) sin(α, x) has a solution of the product form ψ0 = ∏ α∈A+ sin −mα(α, x), then the function F (x) = ∑ α∈A+ mα(α, x) 2 log (α, x) satisfies the generalised WDVV equations. This explains the relation between these equations and the deformed CMS quantum problems observed in [7...

We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number state variables that can be communicated instantaneously. When capacities are small compared to dimensionality vectors, it not possible instantaneously communicate full information every edge. how (small steady variance states) achie...

Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in u...

The SST decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. In this topic we are going to consider vectors as fuzzy vectors. We have considered a numerical example and tried to find out solution vector x in fuzzified form using method of SST decomposition.

one of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. in this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. we also devote to characterizing bijective morphisms on quantum effects leaving the witness...

We show that the Duffin-Kemmer-Petiau equation, minimally coupled to an Abelian gauge field, can be regarded as a matrix equation for potential produced internally from matter fields. This solved rational expression in terms of currents bilinear wave function, together with similar field strength tensor, thus providing invariant formulation self-interacting DKP equations. give derivation this r...