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Get to know Integrable better with 10+ real example sentences, the meaning.

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Integrable in a sentence

Integrable meaning

Able to be integrated.

Using Integrable

  • The main meaning on this page is: Able to be integrated.
  • In the example corpus, integrable often appears in combinations such as: integrable functions, locally integrable, be integrable.

Context around Integrable

  • Average sentence length in these examples: 21 words
  • Position in the sentence: 2 start, 11 middle, 7 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

locally 3× non 2× square 2× riemann 2× developing 1× valued 1× partially 1× kurzweil 1× lebesgue 1× besides 1×

Often after:

functions 8× function 3× software 1× hamiltonian 1×

Sentence patterns with Integrable

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

to be integrable 2× a lebesgue integrable function whose 1× all locally integrable functions satisfying 1× all square integrable functions are 1× and developing integrable software 1× and square integrable function 1× any locally integrable function has 1× be riemann integrable then this 1×

Sentence openings and endings

Common sentence openings:

if a function 2× among other things 1× conversely all locally 1× convolutions on groups 1× different initial conditions 1× differentiation suppose f 1×

Common sentence endings:

the riemann integral 2× to be integrable 2× a distributional derivative 1× are tempered distributions 1× commutative in general 1× developing integrable software 1×

Words around Integrable

Just before it in the word index:

integrability 8 integra 33 intego 3 integers 304 integer 478 intech 16

Just after it in the word index:

integrafin 3 integral 1.351 integralism 2 integrally 12 integrals 53 integrand 6

Similar in corpus frequency:

adjoint 50 affixes 50 agonisingly 50 ahn 50 ainsworth 50 airdrop 50

Corpus analysis for Integrable

  • In this selection, "integrable" usually appears in the middle of the sentence. The average example has 21 words, and this corpus slice is mostly made up of statements.
  • Around the word, locally, non, square, functions, function and software stand out and add context to how "integrable" is used.
  • Recognizable usage signals include to be integrable and a lebesgue integrable function whose. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "integrable" sits close to words such as adjoint, affixes and agonisingly, which helps place it inside the broader word index.

Example types with integrable

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

Suppose f(x) is an integrable and square-integrable function. (10 words)

In particular, any locally integrable function has a distributional derivative. (10 words)

Among other things, he showed that every piecewise continuous function is integrable. (12 words)

Longer example sentences

Convolutions on groups If G is a suitable group endowed with a measure λ, and if f and g are real or complex valued integrable functions on G, then we can define their convolution by : It is not commutative in general. (41 words)

In fact, besides integrable functions, the Laplace transform is a one-to-one mapping from one function space into another in many other function spaces as well, although there is usually no easy characterization of the range. (37 words)

If one uses the Henstock–Kurzweil integral one can have the mean value theorem in integral form without the additional assumption that derivative should be continuous as every derivative is Henstock–Kurzweil integrable. (33 words)

Example sentences (20)

If the type of partition is limited too much, some non-integrable functions may appear to be integrable.

Suppose f(x) is an integrable and square-integrable function.

Tempered distributions generalize the bounded (or slow-growing) locally integrable functions; all distributions with compact support and all square-integrable functions are tempered distributions.

The Fourier transform may be defined in some cases for non-integrable functions, but the Fourier transforms of integrable functions have several strong properties.

During the workshop discussions, developers realized they were consistently facing similar problems adapting to new computing resources and developing integrable software.

Among other things, he showed that every piecewise continuous function is integrable.

Conversely, all locally integrable functions satisfying the (volume) mean-value property are both infinitely differentiable and harmonic.

Convolutions on groups If G is a suitable group endowed with a measure λ, and if f and g are real or complex valued integrable functions on G, then we can define their convolution by : It is not commutative in general.

Advertentie

Differentiation Suppose f(x) is a differentiable function, and both f and its derivative f' are integrable.

Different initial conditions of the integrable Hamiltonian system will trace different invariant tori in phase space.

Every continuous function : is integrable (for example in the sense of the Riemann integral ).

For instance, this is the case of partially integrable and superintegrable Hamiltonian systems and non-autonomous mechanics.

Generalizing a theory of Bruns (1887), Poincaré showed that the three-body problem is not integrable.

However, many functions that can be obtained as limits are not Riemann-integrable, and so such limit theorems do not hold with the Riemann integral.

If a function has an integral, it is said to be integrable.

If a function is known in advance to be Riemann integrable, then this technique will give the correct value of the integral.

If one uses the Henstock–Kurzweil integral one can have the mean value theorem in integral form without the additional assumption that derivative should be continuous as every derivative is Henstock–Kurzweil integrable.

In 1922, Andrey Kolmogorov published an article entitled "Une série de Fourier-Lebesgue divergente presque partout" in which he gave an example of a Lebesgue-integrable function whose Fourier series diverges almost everywhere.

In fact, besides integrable functions, the Laplace transform is a one-to-one mapping from one function space into another in many other function spaces as well, although there is usually no easy characterization of the range.

In particular, any locally integrable function has a distributional derivative.

Advertentie

Common combinations with integrable

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "integrable" in a sentence?
An example: "If the type of partition is limited too much, some non-integrable functions may appear to be integrable." This page contains 10+ example sentences with the word "integrable" from authentic English texts.
What does "integrable" mean?
Integrable means: Able to be integrated.
How many example sentences with "integrable" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "integrable", drawn from a database of millions of English sentences.