We introduce an addition law for the usual quantummatrices A(R) by means of a coaddition ∆t = t⊗ 1 + 1⊗ t. It supplements the usual comultiplication ∆t = t⊗ t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m × n quantum matrices. As an application, we construct leftinvariant vector ...

Let k be an integer with id="M2"> 4 ≤ 6 and id="M3"> η any real number. Suppose that id="M4"> λ 1 , 2 … 5 are nonzero numbers, not all of them have the same sign, id="M5"> / is irrational. It p...

BACKGROUND The Scottish Government set out its policy on addressing the poor oral health of Scottish children in 2005. This led to the establishment of Childsmile, a national programme designed to improve the oral health of children in Scotland. One element of the programme promotes daily tooth brushing in all nurseries in Scotland (Childsmile Core). A second targeted component (Childsmile Nurs...

Most youth psychotherapy research involves conditions quite unlike the clinical practice it is designed to strengthen. Most studies have not tested interventions with clinically referred youths and practicing clinicians in clinical care settings, nor have they tested whether new treatments produce better outcomes than usual practice. Limited exposure to real-world conditions and questions may p...

Polyethylene’s application for insulating is highly advanced but due to thermoplastic properties, its application confronts constraints such as the limited 70°C temperature of the conductor. Polyethylene thermosetting procedure in which molecules are knotted and a 3D-molecular-network formed is developed to conquer the mentioned problem and to raise the applicable temperature of the i...