Wondering how to use Lyapunov in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning .
Lyapunov in a sentence
Lyapunov meaning
A transliteration of the Russian surname Ляпуно́в (Ljapunóv)
Using Lyapunov
- The main meaning on this page is: A transliteration of the Russian surname Ляпуно́в (Ljapunóv)
- In the example corpus, lyapunov often appears in combinations such as: aleksandr lyapunov, the lyapunov, of lyapunov.
Context around Lyapunov
- Average sentence length in these examples: 23.6 words
- Position in the sentence: 5 start, 8 middle, 1 end
- Sentence types: 14 statements, 0 questions, 0 exclamations
Corpus analysis for Lyapunov
- In this selection, "lyapunov" usually appears in the middle of the sentence. The average example has 23.6 words, and this corpus slice is mostly made up of statements.
- Around the word, aleksandr, maximal, see, exponents, exponent and developed stand out and add context to how "lyapunov" is used.
- Recognizable usage signals include above the lyapunov condition can and aleksandr lyapunov and jules. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "lyapunov" sits close to words such as aat, abhorrence and abms, which helps place it inside the broader word index.
Example types with lyapunov
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Aleksandr Lyapunov developed many important approximation methods. (7 words)
In more mathematical terms, the Lyapunov exponent measures the sensitivity to initial conditions. (13 words)
Without the perturbations from the terrestrial planets the Lyapunov time would be close to 10,000 years. (17 words)
It was not until the nineteenth century was at an end that the importance of the central limit theorem was discerned, when, in 1901, Russian mathematician Aleksandr Lyapunov defined it in general terms and proved precisely how it worked mathematically. (40 words)
This stretching-and-folding does not just produce a gradual divergence of the sequences of iterates, but an exponential divergence (see Lyapunov exponents ), evidenced also by the complexity and unpredictability of the chaotic logistic map. (35 words)
Bernstein presents a historical discussion focusing on the work of Pafnuty Chebyshev and his students Andrey Markov and Aleksandr Lyapunov that led to the first proofs of the CLT in a general setting. (33 words)
Example sentences (14)
Aleksandr Lyapunov and Jules Henri Poincaré worked on the foundations of chaos theory without any computer at all.
Aleksandr Lyapunov developed many important approximation methods.
Bernstein presents a historical discussion focusing on the work of Pafnuty Chebyshev and his students Andrey Markov and Aleksandr Lyapunov that led to the first proofs of the CLT in a general setting.
For example, the maximal Lyapunov exponent (MLE) is most often used because it determines the overall predictability of the system.
In more mathematical terms, the Lyapunov exponent measures the sensitivity to initial conditions.
It was not until the nineteenth century was at an end that the importance of the central limit theorem was discerned, when, in 1901, Russian mathematician Aleksandr Lyapunov defined it in general terms and proved precisely how it worked mathematically.
Lindeberg CLT main In the same setting and with the same notation as above, the Lyapunov condition can be replaced with the following weaker one (from Lindeberg in 1920).
Non-linear control systems use specific theories (normally based on Aleksandr Lyapunov 's Theory) to ensure stability without regard to the inner dynamics of the system.
Scholars like Rudolf E. Kalman and Aleksandr Lyapunov are well-known among the people who have shaped modern control theory.
Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond; weather systems, a few days (unproven); the solar system, 50 million years.
The number of Lyapunov exponents is equal to the number of dimensions of the phase space, though it is common to just refer to the largest one.
The rate of separation depends on the orientation of the initial separation vector, so a whole spectrum of Lyapunov exponents exist.
This stretching-and-folding does not just produce a gradual divergence of the sequences of iterates, but an exponential divergence (see Lyapunov exponents ), evidenced also by the complexity and unpredictability of the chaotic logistic map.
Without the perturbations from the terrestrial planets the Lyapunov time would be close to 10,000 years.
Common combinations with lyapunov
These word pairs occur most frequently in English texts: