A Rota–Baxter algebra, also known as a Baxter algebra, is an algebra with a linear operator satisfying a relation, called the Rota–Baxter relation, that generalizes the integration by parts formula. Most of the studies on Rota–Baxter algebras have been for commutative algebras. Two constructions of free commutative Rota–Baxter algebras were obtained by Rota and Cartier in the 1970s and a third ...

objectives: the aim of present study was to evaluate some effects of crinum zeylanicum (c. zeylanicum) on central nervous system. materials and methods: c. zeylanicum methanolic bulb extract (250-1000 mg/kg orally), 2 mg chlorpromazine and 4 mg diazepam /kg body weight intraperitoneally respectively were tested in mice using irwin test, pentobarbitone-induced sleep test, spontaneous motor activ...

Trapping of interventional devices used to treat in-stent restenosis is rarely reported in the literature. Among those is a trapped rota ablation wire causing longitudinal stent deformation, sometime requiring another stent deployment onto the collapse stent. A Rota ablator getting stuck into the stent is very rare, and a lethal complication. We report a case of 79-year-old gentleman who underw...

Rota-Baxter algebras appeared in both the physics and mathematics literature. It is of great interest to have a simple construction of the free object of this algebraic structure. For example, free commutative Rota-Baxter algebras relate to double shuffle relations for multiple zeta values. The interest in the non-commutative setting arised in connection with the work of Connes and Kreimer on t...

Doctors take many forms of leave to further career training. Many hospital rotas omit these and are not updated frequently to reflect swaps in on-call duties. As a result, confusion arises with reduced staffing levels leading to sub-optimal patient care. Using Google Sheets, rota's can be modified to be team specific, remotely accessed, and edited by any device with an internet connection and w...

In this paper, we establish the Composition-Diamond lemma for λ-differential associative algebras over a field K with multiple operators. As applications, we obtain Gröbner-Shirshov bases of free λ-differential Rota-Baxter algebras. In particular, linear bases of free λ-differential Rota-Baxter algebras are obtained and consequently, the free λ-differential Rota-Baxter algebras are constructed ...

The central nervous system (CNS) depressant and anticonvulsant activities of iso-6-spectaline (SPEC) were investigated in animal models. The SPEC from Senna spectabilis var. excelsa (Schrad) (0.1, 0.5 and 1.0 mg/ kg) injected by oral route (p.o.) in mice caused a significant decrease in the motor activity up to 30 days after the administration and in the dose of 1.0 mg/kg significantly reduced ...

Most of the studies on Rota–Baxter algebras (also known as Baxter algebras) have been for commutative algebras. Free commutative Rota–Baxter algebras were constructed by Rota and Cartier in the 1970s. A later construction was obtained by Keigher and one of the authors in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the...

Most of the studies on Rota–Baxter algebras (also known as Baxter algebras) have been for commutative algebras. Free commutative Rota–Baxter algebras were constructed by Rota and Cartier in the 1970s. A later construction was obtained by Keigher and one of the authors in terms of mixable shuffles. Recently, noncommutative Rota–Baxter algebras have appeared both in physics in connection with the...

An expression in the exterior algebra of a Peano space yielding Pappus' theorem was originally given by Doubilet, Rota, and Stein [Doubilet, P., Rota, G.-C. & Stein, J. (1974) Stud. Appl. Math. 8, 185-216]. Motivated by an identity of Rota, I give an identity in a Grassmann-Cayley algebra of step 3, involving joins and meets alone, which expresses the theorem of Pappus.