We study the combinatorics of fully commutative elements in Coxeter groups of type H n for any n > 2. Using the results, we construct certain canonical bases for non-simply-laced generalized Temperley–Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.

We address the attainability of the Hashin-Shtrikman bounds for multiphase composite materials. We demonstrate that the Hashin-Shtrikman bounds are not always attainable and give new restrictions on the attainable Hashin-Shtrikman bounds in terms of the conductivities and volume fractions of the constituent phases. New optimal microstructures are also constructed to attain the Hashin-Shtrikman ...

In the present paper, we investigate two new subclasses 〖AR〗_(Σ_m ) (δ,λ;α) and (δ,λ;β) of Σ_m consisting m-fold symmetric holomorphic bi-univalent functions in open unit disk Δ. For from classes described here, obtain estimates on initial bounds |d_(m+1) | |d_(2m+1) |. addition, get special cases for our results.

In the present work, by making use of Gegenbauer polynomials, we introduce and study a certain family λ -pseudo bistarlike id="M2"> biconvex functions with respect to symmetrical points defined in open unit disk. We obtain estimates for initial coefficients solve Fekete–Szeg id="M3"> o ...