We consider when the quaternion matrix equation AXB+CXD=E has a reflexive (or anti-reflexive) solution with respect to given generalized reflection matrix. adopt real representation method derive solutions it is solvable. Moreover, we obtain explicit expressions of least-squares solutions.

The goal of achieving powerful problem solving capabilities leads to the “advice taker” form of program and the associated problem of control. This proposal outlines an approach to this problem based on the construction of problem solvers with advanced self-knowledge and introspection capabilities. 1 The Problem of Control Self-reverence, self-knowledge, self-control, These three alone lead lif...

Many efforts have been made in recent years to construct formal systems for mechanizing general mathematical reasoning. Most of these systems are based on logics which are stronger than first-order logic (FOL). However, there are good reasons to avoid using full second-order logic (SOL) for this task. In this work we investigate a logic which is intermediate between FOL and SOL, and seems to be...

Throughout the sequel, E denotes a reflexive real Banach space and E∗ its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with ‖x‖ = 1, and each > 0, there exists δ > 0 such that, for every y ∈ E satisfying ‖y‖ = 1 and ‖x− y‖ ≥ , one has ‖x + y‖ ≤ 2(1 − δ). Recall that any reflexive Banach space admits an equivalent norm with which it is loca...

In this paper, we obtain a complete description of the invariant subspace structure of an interesting new class of algebras which we call free semigroup algebras. This enables us to prove that they are reflexive, and moreover to obtain a quantitative measure of the distance to these algebras in terms of the invariant subspaces. Such algebras are called hyper-reflexive. This property is very str...

BACKGROUND Cough reflex testing is a validated tool for identifying patients at risk of silent aspiration. However, inter- and intra-rater reliabilities of perceptual judgements of cough strength are sub-optimal. Although there are clinically established methods for measuring volitional cough strength, no similar methods are identified for reflexive cough strength. This study evaluated three me...

The gender information in written Chinese third person pronouns is not symmetrically encoded: the character for "he" (, with semantic radical , meaning human) is used as a default referring to every individual, while the character for "she" (, with semantic radical , meaning woman) indicates females only. This critical feature could result in different patterns of processing of gender informati...

We extend Kozen’s theory KA of Kleene Algebra to axiomatize parts of the equational theory of context-free languages, using a least fixed-point operator μ instead of Kleene’s iteration operator ∗. Although the equational theory of context-free languages is not recursively axiomatizable, there are natural axioms for subtheories KAF ⊆ KAR ⊆ KAG: respectively, these make μ a least fixed point oper...

In a recent paper in Journal of Convex Analysis the authors studied, in non-reflexive Banach spaces, a class of maximal monotone operators, characterized by the existence of a function in Fitzpatrick’s family of the operator which conjugate is above the duality product. This property was used to prove that such operators satisfies a restricted version of Brøndsted-Rockafellar property. In this ...

Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the ...