In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

Let φ be a w-continuous homomorphism from a dual Banach algebra to C. The notion of φ-Connes amenability is studied and some characterizations is given. A type of diagonal for dual Banach algebras is dened. It is proved that the existence of such a diagonal is equivalent to φ-Connes amenability. It is also shown that φ-Connes amenability is equivalent to so-called φ-splitting of a certain short...

Finding the best weights of the state variables and the control variables in the objective function of a linear-quadratic control problem is considered. The weights of these variables are considered as two diagonal matrices with appropriate size and so the objective function of the control problem becomes a function of the diagonal elements of these matrices. The optimization problem which is d...

Recent prior studies with argumentation systems have shown that, unfortunately, with larger learner groups using argumentation software over longer periods of time, argument maps inevitably increase greatly in size and complexity, often leading to learner confusion. To help users understand and navigate within large and complex argument maps, we implemented an initial version of mini maps withi...

A classical result of Schur and Horn [Sc, Ho] states that the set of diagonal elements of all n x n Hermitian matrices with fixed eigenvalues is a convex set in IRn. Kostant [Kt] has generalized this result to the case of any semisimple Lie group. This is often referred to as the linear convexity theorem of Kostant: picking up the diagonal of a Hermitian matrix is a linear operation. This resul...

Reasoning with hypothetical cases helps decision-makers evaluate alternate hypotheses for deciding a case. The hypotheticals demonstrate the sensitivity of a hypothesis to apparently small factual differences that may require different results because they shift the tradeoffs among conflicting underlying principles. By anticipating variations, the decision-maker seeks to formulate as general an...

Argument & Computation (A&C) enters its seventh year, renewed in two respects: • A new access policy with a new publisher: the journal adopts a full open access policy with no fees for authors who submit a paper during coming two years at least. We are indebted to the new publisher IOS Press for its enthusiastic support in enabling and promoting this important transition; • A renewed editorial ...

This paper reports progress in realizing human-agent argumentation, which we argue will be part of future Computer-Supported Collaborative Argumentation (CSCA) tools. With a particular interest in argument mapping, we present two investigations demonstrating how a particular agent-oriented language and architecture can augment CSCA: (i) the use of the IBIS formalism enabling Brahms agents to si...

Rapid growth in the area of argument mining has resulted in an ever increasing volume of analysed argument data. Being able to store information about arguments people make in favour or against different opinions, decisions and actions is a highly valuable resource, yet extremely challenging for sense-making. How, for example, can an analyst quickly check whether in a corpus of citizen dialogue...