Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modal...

Quadratic residue codes have been one of the most important classes of algebraic codes. They have been generalized into duadic codes and quadratic double circulant codes. In this paper we introduce a new subclass of double circulant codes, called duadic double circulant codes, which is a generalization of quadratic double circulant codes for prime lengths. This class generates optimal self-dual...

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

It is the aim of this paper to compute the category of Eilenberg-Moore algebras for the monad arising from the dual unit-ball functor on the category of (semi)normed spaces. We show that this gives rise to a stronger algebraic structure than the totally convex one obtained from the closed unit ball functor on the category of Banach spaces.

We explicitly construct the twistor spaces of some self-dual metrics with torus action given by D. Joyce. Starting from a fiber space whose fibers are compact singular toric surfaces, we apply a number of birational transformations to obtain the desired twistor spaces. Especially an important role is played by flops, a useful operation in algebraic geometry.

Using methods from algebraic topology and group cohomology, I pursue Grothendieck’s question on equality of geometric and cohomological Brauer groups in the context of complex-analytic spaces. The main result is that equality holds under suitable assumptions on the fundamental group and the Pontrjagin dual of the second homotopy group. I apply this to Lie groups, Hopf manifolds, and complex-ana...

We devise a new criterion for linear independence over function fields. Using this tool in the setting of dual t-motives, we find that all algebraic relations among special values of the geometric Γ-function over Fq[T ] are explained by the standard functional equations.

In this paper, we built a family of 4d-dimensional two-step nilpotent Lie algebras (gd)d≥2 so that the cortex of the dual of each gd is a projective algebraic set. We also give a complete description of the cortex of the exponential connected and simply connected Lie group G = R o R.

For proving linear independence of real numbers, Hermite [6] considered simultaneous approximation to these numbers by algebraic numbers. The point of view introduced by Siegel in 1929 [14] is dual (duality in the sense of convex bodies): he considers simultaneous approximation by means of independent linear forms. We define the height of a linear form L = a0X0 + · · · + amXm with complex coeff...