Authentication codes were introduced by Simmons in [1]. A good survey of the current status can be found in [3]. We start by explaining what authentication codes, with and without arbitration, are and mention some important properties of them. We illustrate these concepts by showing some known schemes. Next we discuss generalised dual arcs, since they can serve as a tool to construct authentica...

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In the part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also...

In this paper, we firstly show that the $N$-dual operation of the right residual implication, which is induced by a left-conjunctive right arbitrary $vee$-distributive left semi-uninorm, is the right residual coimplication induced by its $N$-dual operation. As a dual result, the $N$-dual operation of the right residual coimplication, which is induced by a left-disjunctive right arbitrary $wedge...

We show that several families of polynomials defined via fillings of diagrams satisfy linear recurrences under a natural operation on the shape of the diagram. We focus on key polynomials, (also known as Demazure characters), and Demazure atoms. The same technique can be applied to Hall–Littlewood polynomials and dual Grothendieck polynomials. The motivation behind this is that such recurrences...

when two species of animals overlap geographically, the differences between them are accentuated in the zone of sympatry and weakened or lost entirely in the parts of their ranges outside this zone. The characters involved in this dual divergence-convergence pattern may be morphological, ecological, behavioral, or physiological. [The SCI® indicates that this paper has been cited in over 255 pub...

We provide a systematic approach to obtain formulas for characters and Kostant u-homology groups of the oscillator modules of the finite dimensional general linear and ortho-symplectic superalgebras, via Howe dualities for infinite dimensional Lie algebras. Specializing these Lie superalgebras to Lie algebras, we recover, in a new way, formulas for Kostant homology groups of unitarizable highes...

Given a lattice Λ in a locally compact abelian group G and a measurable subset Ω with finite and positive measure, then the set of characters associated to the dual lattice form a frame for L2(Ω) if and only if the distinct translates by Λ of Ω have almost empty intersections. Some consequences of this results are the wellknown Fuglede theorem for lattices, as well as a simple characterization ...

In this paper we obtain the discrete integrable self-dual network hierarchy associated with a spectral problem. On basis of theory algebraic curves, continuous flow and related to are straightened using Abel-Jacobi coordinates. The meromorphic function Baker-Akhiezer introduced on hyperelliptic curve. Quasi-periodic solutions constructed help asymptotic properties algebra-geometric characters f...