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How do you use Pontryagin in a sentence? See 5 example sentences showing how this word appears in different contexts.

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Pontryagin in a sentence

Using Pontryagin

  • In the example corpus, pontryagin often appears in combinations such as: the pontryagin, pontryagin duality.

Context around Pontryagin

  • Average sentence length in these examples: 20.4 words
  • Position in the sentence: 4 start, 1 middle, 0 end
  • Sentence types: 5 statements, 0 questions, 0 exclamations

Often before:

precisely 1×

Often after:

duality 3× maximum 1× dual 1×

Sentence patterns with Pontryagin

These short patterns come directly from the example sentences and show how the word is often embedded:

also the pontryagin duality for 1× more precisely pontryagin duality defines 1× see also pontryagin duality notes 1× the pontryagin dual of 1× using the pontryagin maximum principle 1×

Sentence openings and endings

Common sentence openings:

in particular there 1× more precisely pontryagin 1× see also pontryagin 1× see also the 1× the pontryagin dual 1×

Common sentence endings:

and co 1953 1× compact abelian groups 1× dynamic programming method 1× is locally compact 1× the fourier transform 1×

Words around Pontryagin

Just before it in the word index:

pontrilas 4 pontotoc 6 pontos 2 pontoons 16 pontoon 63 ponton 6

Just after it in the word index:

ponts 3 pontus 26 ponty 27 pontyclun 2 pontymister 2 pontypool 25

Similar in corpus frequency:

aadujeevitham 7 aani 7 aarne 7 aasb 7 aasen 7 aashiqui 7

Corpus analysis for Pontryagin

  • In this selection, "pontryagin" usually appears near the start of the sentence. The average example has 20.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, precisely, duality, maximum and dual stand out and add context to how "pontryagin" is used.
  • Recognizable usage signals include also the pontryagin duality for and more precisely pontryagin duality defines. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "pontryagin" sits close to words such as aadujeevitham, aani and aarne, which helps place it inside the broader word index.

Example types with pontryagin

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

See also the Pontryagin duality for the generalized underpinnings of the Fourier transform. (13 words)

More precisely, Pontryagin duality defines a self- duality of the category of locally compact abelian groups. (16 words)

The Pontryagin dual of a topological abelian group A is locally compact if and only if A is locally compact. (20 words)

Longer example sentences

In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method. (32 words)

See also * Pontryagin duality Notes Further reading * Lynn Loomis, An Introduction to Abstract Harmonic Analysis, D. van Nostrand and Co., 1953. (21 words)

The Pontryagin dual of a topological abelian group A is locally compact if and only if A is locally compact. (20 words)

Example sentences (5)

In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method.

More precisely, Pontryagin duality defines a self- duality of the category of locally compact abelian groups.

See also * Pontryagin duality Notes Further reading * Lynn Loomis, An Introduction to Abstract Harmonic Analysis, D. van Nostrand and Co., 1953.

See also the Pontryagin duality for the generalized underpinnings of the Fourier transform.

The Pontryagin dual of a topological abelian group A is locally compact if and only if A is locally compact.

Common combinations with pontryagin

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "pontryagin" in a sentence?
An example: "In particular, there are two types of strategies: the open-loop strategies are found using the Pontryagin maximum principle while the closed-loop strategies are found using Bellman's Dynamic Programming method." This page contains 5 example sentences with the word "pontryagin" from authentic English texts.
How many example sentences with "pontryagin" are there?
Voorbeeldzinnen.info contains 5 example sentences with "pontryagin", drawn from a database of millions of English sentences.