A LieYRep pair consists of a Lie-Yamaguti algebra and its representation. In this paper, we establish the cohomology theory pairs characterize their linear deformations by second group. Then introduce notion relative Rota-Baxter-Nijenhuis structures on pairs, investigate properties, prove that structure gives rise to compatible Rota-Baxter operators under certain condition. Finally, show equiva...

background and aims. the aim of this study was to compare shear bond strength (sbs) of metal and ceramic brackets bonded to enamel using acid versus er:yag laser etching. materials and methods. eighty premolars were divided into 4 groups: am (acid etching/ metal brackets), ac (acid etching/ ceramic brackets), lm (laser etching/ metal brackets) and lc (laser etching/ ceramic brackets). enamel co...

The infinite limit of Matrix Theory in 4 and 10 dimensions is described in terms of Moyal Brackets. In those dimensions there exists a Bogomolni’y bound to the Euclideanized version of these equations, which guarantees that solutions of the first order equations also solve the second order Matrix Theory equations. A general construction of such solutions in terms of a representation of the targ...

We prove a property of the Poisson-Nijenhuis manifolds which yields new proofs of the bihamiltonian properties of the hierarchy of modular vector fields defined by Damianou and Fernandes.

We study two sums involving the Stirling numbers and binomial coefficients. We find their closed forms, and discuss the connection between these sums. Dedicated to the memory of our mentors, Professors Leonard Carlitz and Albert Nijenhuis