Describing the topology of real algebraic curves is a classical problem in computational algebraic geometry. It is usually based on algebraic techniques applied directly to the curve equation. We use the implicit support function representation for this purpose which can in certain cases considerably simplify this task. We describe possible strategies and demonstrate them on a simple example. W...

This paper serves as a broad introduction to the theory and application of Angle-Systems. Angle-Systems are defined as an algebraic structure, and their basic properties are introduced. The correspondence between AngleSystems and embeddings of graphs upon an orientable surface is discussed, and various graph theoretic results are formalized as properties of algebraic structures. Symmetry patter...

We discuss parabolic versions of Euler’s identitye = cos t + i sin t.A purely algebraic approach based on dual numbers is known to produce a verytrivial relation e = 1 + εt. Therefore we use a geometric setup of parabolicrotations to recover the corresponding non-trivial algebraic framework. Our maintool is Möbius transformations which turn out to be closely related to induc...

We give algebraic characterizations for expansiveness of algebraic actions of countable groups. The notion of p-expansiveness is introduced for algebraic actions, and we show that for countable amenable groups, a finitely presented algebraic action is 1-expansive exactly when it has finite entropy. We also study the local entropy theory for actions of countable amenable groups on compact groups...

We develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has quantifiers that are interpreted using a refinement relation. A refinement relation is like a bisimulation, except that from the three relational requirements only ‘atoms’ and ‘back’ have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of ...

We introduce the Poincaré series for a divisorial valuation v and prove that this series is an equivalent algebraic datum to the dual graph of v. We give an explicit computation of the Poincaré series.

In this short note, we describe one of the long-standing open problems in algebraic coding theory, i.e., whether there exists a binary self-dual [72, 36, 16] code.

In an attempt to create an algebraic framework for dual canonical bases and total positivity in semisimple groups, we initiate the study of a new class of commutative algebras.

Using the dual of Bousfield-Friedlander localization we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful to study realization and moduli problems in algebraic topology.

A solution is presented to a doubly mixed boundary value problem of the torsion of an elastic layer, partially resting on a rigid circular base by a circular rigid punch attached to its surface. This problem is reduced to a system of dual integral equations using the Boussinesq stress functions and the Hankel integral transforms. With the help of the Gegenbauer expansion formula of the Bessel f...