in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

In this paper we completed the classification of the phase portraits in the Poincaré disc of uniform isochronous cubic and quartic centers previously studied by several authors. There are three and fourteen different topological phase portraits for the uniform isochronous cubic and quartic centers respectively.

Most data centers deploy fixed network topologies. This brings difficulties to traffic optimization and network management, because bandwidth locked up in fixed links is not adjustable to traffic needs, and changes of network equipments require cumbersome rewiring of existing links. We believe the solution is to introduce topological flexibility that allows dynamic cable rewiring in the network...

Define a topological Lie group to be a group object in the category of topological manifolds. Until stated otherwise G is assumed finite-dimensional. Theorem 1.1. LetG be a compact, simple Hausdorff group. Then eitherG is a finite simple group or it is Lie. The latter are much easier to classify: they are U(n), O(n), U(n,H) mod their centers, or one of five special cases (of dimensions ≤ 248), ...

Exciton scattering theory attributes excited electronic states to standing waves in quasi-one-dimensional molecular materials by assuming a quasi-particle picture of optical excitations. The quasi-particle properties at branching centers are described by the corresponding scattering matrices. Here, we identify the topological invariant of a scattering center, referred to as its winding number, ...

We study the problem of coexistence of a countable number of periodic orbits of different topological types (saddles, saddle–centers, and elliptic) in the case of four-dimensional symplectic diffeomorphisms with a homoclinic trajectory to a saddle–focus fixed point.

Nonlinear Schrödinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schrödinger equation describes coherent states. Such modes are also named topological because the solutions corresponding to different spectral levels have principally different spatial dependences. The theory of resonant e...