Plotkin’s dual characterization of strongly algebraic domains – by sets of minimal upper bounds and by sequences of finite posets – is stated and proved in the topical setting.

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.

We show that every self-orthogonal code over $\mathbb F_q$ of length $n$ can be extended to a self-dual code, if there exists self-dual codes of length $n$. Using a family of Galois towers of algebraic function fields we show that over any nonprime field $\mathbb F_q$, with $q\geq 64$, except possibly $q=125$, there are self-dual codes better than the asymptotic Gilbert--Varshamov bound.

In the first part of this paper, we implement the multiplier algebra of the dual of an algebraic quantum group (A, ∆) (see [13]) as a subset of the space of linear functionals on A. In a second part, we construct the universal corepresentation and use it to prove a bijective corespondence between corepresentations of (A, ∆) and homomorphisms on its dual.

In this paper, we show that the moving directions of the primal-affine scaling method (with logarithmic barrier function), the dual-affine scaling method (with logarithmic barrier function), and the primal-dual interior point method are merely the Newton directions along three different algebraic "paths" that lead to a solution of the Karush-Kuhn-Tucker conditions of a given linear programming ...

We discuss a class of binary cyclic codes and their dual codes. The minimum distance is determined using algebraic geometry, and an application of Weil’s theorem. We relate the weights appearing in the dual codes to the number of rational points on a family of genus 2 curves over a finite field.

We apply algebraic and vertex operator techniques to solve two dimensional reduced vacuum Einstein's equations. This leads to explicit expressions for the coefficients of metrics solutions of the vacuum equations as ratios of determinants. No quadratures are left. These formulas rely on the identification of dual pairs of vertex operators corresponding to dual metrics related by the Kramer-Neug...

In this article, a differential construction for the dual of an algebraic-geometric code on a projective surface is given. Afterwards, this result is used to lower bound the minimum distance of this dual code. The found bounds involve intersection numbers of some particular divisors on the surface. AMS Classification: 14J20, 94B27, 11G25.