We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two dual sets of generalized reflection equations with associated consistent fusion procedures. Products of their respective solutions yield commuting quantum traces.

We prove that the commuting probability of a finite ring is no larger than the commuting probabilities of its subrings and quotients, and characterize when equality occurs in such a comparison.

We formulate a systematic construction of commuting quantum traces for reflection algebras. This is achieved by introducing two dual sets of generalized reflection equations with associated consistent fusion procedures. Products of their respective solutions yield commuting quantum traces.

Let G be a group and X a subset of G. The commuting graph on X, denoted C(G,X), has vertex set X and an edge joining x, y ∈ X whenever xy = yx. If in addition X is a set of involutions, then C(G,X) is called a commuting involution graph. Commuting graphs have been investigated by many authors. Sometimes they are tools used in the proof of a theorem, or they may be studied as a way of shedding l...

The commutant lifting theorem of Sz.Nagy and Foiaş [22, 21] is a central result in the dilation theory of a single contraction. It states that if T ∈ B(H) is a contraction with isometric dilation V acting on K ⊃ H, and TX = XT , then there is an operator Y with ‖Y ‖ = ‖X‖, V Y = Y V and PHY = XPH. This result is equivalent to Ando’s Theorem that two commuting contractions have a joint (power) d...

while fasting has been practiced for centuries, its beneficial effects was unknown until recently. this review tries to analyze the current literature of how fasting and intermittent fasting (if) could affect clinical pathological parameters, learning, mood and brain plasticity. the effects of different ways of fasting on metabolism and stress were also explored. animal experiments have elucida...

A stressful nature of exposure to traffic congestion in automobile commuting has been demonstrated in previous quasi-experimental research that has been measurement-intensive but conducted with relatively small samples. The present study examined commuting stress in automobile travel with a large representative sample (N = 2591) in southern California through telephone survey° Commuting stress ...

Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the DrinfeldSokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld-Sokolov construction can be used to deduce the existence of commuting charges in these and in wider classes of sigma-models, including those whose target manifolds are e...

Three variants of R-weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R-weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and D...

We first show that every γ-contractive commuting multioperator is unitarily equivalent to the restriction of S⊕W to an invariant subspace, where S is a backwards multi-shift and W a γ-isometry. We then describe γ-isometries in terms of (γ, 1)-isometries, and establish that under an additional assumption on T , W above can be chosen to be a commuting multioperator of isometries. Our methods prov...