We specify the structure of completely positive operators and quantum Markov semigroup generators that are symmetric with respect to a family inner products, also providing new information on order extreme points in some previously studied cases.

For a linear map from Mm to Mn, besides the usual positivity, there are two stronger notions, complete positivity and super-positivity. Given a positive linear map φ we study a decomposition φ = φ − φ with completely positive linear maps φ (j = 1, 2). Here φ + φ is of simple form with norm small as possible. The same problem is discussed with superpositivity in place of complete positivity.

The notion of path-complete positivity is introduced as a way to generalize the property of positivity from one LTI system to a family of switched LTI systems whose switching rule is constrained by a finite automaton. The generalization builds upon the analogy between stability and positivity, the former referring to the contraction of a norm, the latter referring to the contraction of a cone (...

W hat would you estimate is the ratio of positive to negative statements in your office? Negative statements include unconstructive criticism, complaining, gossiping, blaming, and abusive language. Work environments with high levels of negative talk are often described as toxic. In a caring profession such as primary care, we hope that toxic environments are few and far between; however, even...

In this short follow-up of [3] we answer some questions posed there. In particular, we characterize two natural classes of linear operators acting on R[x1, x2, ..., xn] which (i) preserve the set of positive n-variate polynomials; (ii) either act diagonally in the monomial basis of R[x1, x2, ..., xn] or are translation-invariant.

Let ζ > e be arbitrary. In [31], the main result was the computation of p-adic topoi. We show that there exists an almost surely co-characteristic number. It was Hermite who first asked whether moduli can be classified. The work in [31] did not consider the bijective case.

An infinite matrix is called totally positive if its minors of all orders are nonnegative. A nonnegative sequence (an)n≥0 is called log-convex (logconcave, resp.) if aiaj+1 ≥ ai+1aj ( aiaj+1 ≤ ai+1aj , resp.) for 0 ≤ i < j . The object of this talk is to study various positivity properties of Riordan arrays, including the total positivity of such a matrix, the log-convexity of the 0th column an...

We propose a tutorial on relaxations and weak formulations of optimal control with their semidefinite approximations. We present this approach solely through the prism of positivity certificates which we consider to be the most accessible for a broad audience, in particular in the engineering and robotics communities. This simple concept allows to express very concisely powerful approximation c...

This paper analyses the notion of a positivity relation of Formal Topology from the point of view of the theory of Locales. It is shown that a positivity relation on a locale corresponds to a suitable class of points of its lower powerlocale. In particular, closed subtopologies associated to the positivity relation correspond to overt (that is, with open domain) weakly closed sublocales. Finall...