To some Hecke symmetries (i.e. Yang-Baxter braidings of Hecke type) we associate ”noncommutative varieties” called braided spheres. An example of such a variety is the Podles’ nonstandard quantum sphere. On any braided sphere we introduce and compute an ”equivariant” analogue of Connes’ noncommutative index. In contrast with the Connes’ construction our version of equivariant NC index is based ...

We introduce a notion of " freely braided element " for simply laced Cox-eter groups. We show that an arbitrary group element w has at most 2 N (w) com-mutation classes of reduced expressions, where N(w) is a certain statistic defined in terms of the positive roots made negative by w. This bound is achieved if w is freely braided. In the type A setting, we show that the bound is achieved only f...

Fiber-reinforced polymer (FRP) rods are advanced composite materials with high strength, light weight, non-corrosive properties, and superior durability properties. Under severe environmental conditions, for concrete structures, the use of glass-fiber-reinforced (GFRP) is a cost-effective alternative to traditional steel reinforcement. This study compared flexural behavior an OPC slab high-volu...