We derive a new four-dimensional partial differential equation with the isospectral Lax representation by shrinking symmetry algebra of reduced quasi-classical self-dual Yang–Mills and applying technique twisted extensions to obtained Lie algebra. Then we find recursion operator for symmetries construct Bäcklund transformation between this Martínez Alonso–Shabat equation. Finally, integrable hi...

In this paper, we study the duals of some finite dimensional pointed Hopf algebras working over an algebraically closed field k of characteristic 0. In particular, we study pointed Hopf algebras with coradical k[Γ] for Γ a finite abelian group, and with associated graded Hopf algebra of the form B(V )#k[Γ] where B(V ) is the Nichols algebra of V = ⊕iV χi gi ∈ k[Γ] k[Γ]YD. As a corollary to a ge...

The k-Schur functions were first introduced by Lapointe, Lascoux and Morse [18] in the hopes of refining the expansion of Macdonald polynomials into Schur functions. Recently, an alternative definition for k-Schur functions was given by Lam, Lapointe, Morse, and Shimozono [17] as the weighted generating function of starred strong tableaux which correspond with labeled saturated chains in the Br...

Keywords: Linear codes MDS-codes AMS Subject classiication (1985) 94B05 Summary: We give several bounds for the length, dimension or minimum distance of linear block codes whose dimension equals the minimum distance of their dual codes. Zusammenfassung: Wir geben verschiedene Schranken f ur die L ange, die Dimension und den Minimalabstand linearer Blockcodes, deren Dimension gleich dem Mini-mal...