The triple phase transitions or simultaneous of three different phases, namely, topological, parity-time $(\mathcal{P}\mathcal{T})$ symmetry breaking, and metal-insulator transitions, are observed in an extension the $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian Aubry-Andr\'e-Harper model. In this model, besides complex quasiperiodic on-site potential, non-Hermiticity is also included neares...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Background: Helicobacter pylori (H. pylori) infection has become a remarkable worldwide health problem. The eradication of H. challenge. Probiotics have proven beneficial in reducing the side effects and increases patient compliance. Lactobacillus reuteri (L. reuteri) is frequently used probiotic considered safe for human consumption. aim this study was to compare effectiveness conventional ant...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Treatment of TiCl(NMe(2))(3) with H(3)N·B(C(6)F(5))(3) results in N-H activation and ligand exchange to yield the structurally characterised salt [TiCl(NMe(2))(2)(NMe(2)H)(2)](+)[Ti[triple bond]NB(C(6)F(5))(3)(Cl)(2)(NMe(2)H)(2)](-). Cation exchange with [Me(4)N]Cl, [Ph(4)P]Cl and [(PhCH(2))Ph(3)P]Cl yields the respective ammonium and phosphonium salts of the [Ti[triple bond]NB(C(6)F(5))(3)(Cl)...