Indeed, the new contradictions not only affected the conception of set and logical concepts, they also came to include the notion of definability and its relation with a fundamental issue: the structure of the mathematical continuum and in particular whether the continuum can be well-ordered and whether Cantor's Continuum Hypothesis (CH) holds.
The range of validity of the effective continuum obtained by the discrete homogenization has been assessed by comparing the frequency band structure of this continuum with that obtained by a Floquet-Bloch analysis.
The mechanical structure of the proposed continuum robot is shown in Fig. 2.
Comparing the frequency band structure of the effective continuum with that obtained by Floquet Bloch analysis extended to a 3D context shows that the wave propagation characteristics can be directly obtained from the homogenized continuum at low frequencies.
One possible explanation for this is that the structure of the synthetic continua affected the results.
Blue, green, yellow, and so on do not exist as distinct colours in nature, waiting to be labelled differently, as it were, by different languages; they come into existence, for the speakers of particular languages, by virtue of the fact that those languages impose structure upon the continuum of colour and assign to three of the areas thus recognized the words "blue," "green," "yellow".
The higher-order gradient continuum theory is employed to study the structural parameters and elastic properties of single-walled carbon nanocones (SWCNCs), where the higher-order Cauchy Born rule is used to link the deformation of the carbon atomic structure to that of the continuum level.
In these models, the fine scale is proposed to describe the real behavior of crystalline structure wherever the continuum description fails.
However, we feel that to highlight the significance of sequence and structure in the continuum and to better understand the dynamics of protein DNA interactions it is instructive to distinguish between these two conceptually distinct landscapes, even though transitions between the two are smoothly connected in time.
A thoroughgoing synechist, he maintained that physical reality is a continuous plenum, and that the structure of a continuum, common to space, time and motion, is not reducible to anything else.
