In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets instead of frames. Then we characterize the po...

The server-centric datacenter network architecture can accommodate a wide variety of network topologies. Newly proposed topologies in this arena often require several rounds of analysis and experimentation in order that they might achieve their full potential as datacenter networks. We propose a family of novel routing algorithms for completely-connected recursively-defined datacenter networks ...

We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronizatio...

1. Fréchet space C∞[a, b] 2. Fréchet space of smooth functions E = C∞(Rn) 3. Fréchet space of Schwartz functions S on R 4. LF-space of test functions D on R 5. Generalized functions (distributions) D∗, S ∗, E∗ as linear functionals 6. Generalized functions D∗, S ∗, E∗ as completions of D 7. Fourier transforms of tempered distributions 8. Distributions supported at a point 9. Appendix: weak dual...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces. Every generalized metric space can be isometrically embedded in a complete function space by means of a metric version of the categorical Yoneda embedding. This simple fact gives naturally rise to: 1. a topology for generalized metric spaces which for arbitrary preorders corresponds to the Alexandroo ...