Let T (X) be the tensor bialgebra over an alphabet X. It is a graded connected cocommutative bialgebra, canonically isomorphic to the envelopping bialgebra of the free Lie algebra over X, Lie(X). The subalgebra of its convolution algebra generated by the projections arising from the graduation is also an algebra for the composition of morphisms and is anti-isomorphic as such with the direct sum...

Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various familiar vector spaces. Several examples are given. The motivating example is the directed self assembly of a large number of particles for technological purposes...

Causal and non-causal observability are discussed in this paper for nonlinear timedelay systems. By extending the Lie derivative for time-delay systems in the algebraic framework introduced by Xia et al. (2002), we present a canonical form and give sufficient condition in order to deal with causal and non-causal observations of state and unknown inputs of time-delay systems.

Here I = [-Ji (a2j-l,a2J) and XI(Y) is the characteristic function of the set I . In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to v(a). Also v(a) is a tau-function and we present a new simplified derivation of the system of nonlinear completely integrable equations (the aj's a r e the independent variables) that were first derived by Jimbo, Miwa, ...

The complete 3D nonlinear dynamic problem of extensible, flexible risers conveying fluid is considered. For describing the dynamics of the system, the Newtonian derivation procedure is followed. The velocity field inside the pipe formulated using hydrostatic and Bernoulli equations. The hydrodynamic effects of external fluids are taken into consideration through the nonlinear drag forces in var...

In commutative algebra, a Weitzenböck derivation is a nonzero triangular linear derivation of the polynomial algebra K[x1, . . . , xm] in several variables over a field K of characteristic 0. The classical theorem of Weitzenböck states that the algebra of constants is finitely generated. (This algebra coincides with the algebra of invariants of a single unipotent transformation.) In this paper ...

In this paper we provide an algebraic derivation of the explicit Witten volume formulas for a few semi-simple Lie algebras by combining a combinatorial method with the ideas used by Gunnells and Sczech in the computation of higher-dimensional Dedekind sums.