Inversion of some series of free quasi-symmetric functions

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

Analytical D’Alembert Series Solution for Multi-Layered One-Dimensional Elastic Wave Propagation with the Use of General Dirichlet Series

A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

This article is essentially an appendix to [4]. We gather here some useful properties of the algebra FQSym of free quasi-symmetric functions which were overlooked in [4]. Recall that FQSym is a subalgebra of the algebra of noncommutative polynomials in infinitely many variables ai which is mapped onto Gessel’s algebra of quasi-symmetric functions QSym by the commutative image ai 7→ xi of K〈A〉. ...

Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder

An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are u...

The primitives of the Hopf algebra of noncommutative symmetric functions

Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theore...