Euclid of Alexandria is one of those among the mathematicians of ancient Greek culture about whom little biographically is known. The date and city of his birth are not preserved for posterity, although modern historians assign approximate dates based on the extant literature of the period in which he worked. Archimedes of Syracuse mentions Euclid during the reign of Ptolemy I of Egypt (306-283...

This is a chapter from the book System Design, Modeling, and Simulation using Ptolemy II This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License. To view a copy of this license, visit: http://creativecommons.org/licenses/by-sa/3.0/, or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA. Permissions beyond t...

Recent opinions that Israel’s covenants and promises are missing in Rev 20:1-10 have rested on poor hermeneutical foundations. Three major OT covenants with Israel are prominent throughout the Apocalypse and therefore are foundational to what John writes in chapter 20. God promised Abraham a people who are quite visible in Revelation 7, 12, and 14, and in 2:9 and 3:9, where physical descendants...

This is a chapter from the book System Design, Modeling, and Simulation using Ptolemy II This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License. To view a copy of this license, visit: http://creativecommons.org/licenses/by-sa/3.0/, or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA. Permissions beyond t...

We review the main scientific pictures of universe developed from ancient times to Albert Einstein and underline that all them treated as a stationary system with unchanged physical properties. In contrast this, 100 years ago Alexander Friedmann predicted expands starting point infinitely large energy density. briefly discuss meaning this prediction its experimental confirmation consisting disc...

Dataflow process networks are a special case of Kahn process networks (PN). In dataflow process networks, each process consists of repeated firings of a dataflow actor, which defines a quantum of computation. Using this quantum avoids the complexities and context switching overhead of process suspension and resumption incurred in most implementations of Kahn process networks. Instead of context...

We construct frieze patterns of type DN with entries which are numbers of matchings between vertices and triangles of corresponding triangulations of a punctured disc. For triangulations corresponding to orientations of the Dynkin diagram of type DN , we show that the numbers in the pattern can be interpreted as specialisations of cluster variables in the corresponding Fomin-Zelevinsky cluster ...

The Ptolemy project studies heterogeneous modeling and design of concurrent systems. The focus is on embedded systems, particularly those that mix technologies, including for example analog and digital electronics, hardware and software, and electronics and mechanical devices (including MEMS, microelectromechanical systems). The focus is also on systems that are complex in the sense that they m...