We can do so by treating the vertices one by one. Consider the intermediate situation where V1 is the set of vertices that have already got their final color (i.e., the color in X2) and V2 = V \V1. Now, pick some vertex v ∈ V2. This vertex still has the color c1 it has in state X1 and needs to be recolored to the color c2 it is supposed to have in state X2. This is only possible if the neighbor...

For centuries, storytellers and scops recited epics and national, tribal, historical, and religious stories for people, through musical speeches. Some of these narrators wrote down what they recited, and some others dictated them for scribes to be recorded. Some kings and lords also had scops in their courts to recite the stories to scribes. One of the old, oral stories of Persian literature th...

The history of the European Renaissance has been written in many versions. move from medieval to period world shows clashes between empires and human nature. contemporary scholars have variants choose form their own views about what actually transpired during historical period. most significant role Medici family was new era that witnessed art administration on Bank Florence/Italy. This paper p...

We investigate “shell structure” from Babylonian times: periodicities and beats in computer-simulated lunar data corresponding to those observed by Babylonian scribes some 2500 years ago. We discuss the mathematical similarity between the Babylonians’ recently reconstructed method of determining one of the periods of the moon with modern Fourier analysis and the interpretation of shell structur...