by an integer k

USAGE SUMMARY

The phrase "by an integer k" is correct and usable in written English.
It can be used in mathematical or programming contexts to specify that a quantity is being modified or affected by a specific integer value. Example: "The function will increase the variable x by an integer k to adjust its value."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

The hopping Hamiltonian can be written as H test = ∑ i, j = 1 N v A i j ( Γ M ) a i † a j = ∑ k = 1 N v ϵ ( k ) η k † η k. (5)The eigenmodes of H test, labeled by an integer k, and with energy ϵ ( k ), define our notion of particle.

Journal of Theoretical and Applied Physics

In the experiment size was indexed by an integer k from 0 to 4. In each case the radius multiplier was 2k+.5.

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

Input: An m ×  n mutation matrix A, integer k > 0.

Algorithms for Molecular Biology

Since K e n ( Φ p ) ≠ K e n and Φ p is nontrivial, there exists, by Definition 3.2, an integer k ∈ N, such that g k = 0 and k ≥ 1.

Journal of Inequalities and Applications

For an integer k ≥ 0, we denote by S ( n, k ) the set of k-tuples ( n 1, …, n k ) of integers ≥2 satisfying n 1 < n, n 1 + ⋯ + n k ≤ n.

Journal of Inequalities and Applications

Input: An undirected graph G= V, E) and an integer k.

Algorithms for Molecular Biology

We reduce from CLUSTER EDITING: Input: An undirected graph G = V, E ) and an integer k.

Algorithms for Molecular Biology

For efficiency concerns, our program takes an integer K as input.

Database : the journal of biological databases and curation

The number of genes gained by the new genome is a random integer, k, chosen from a Poisson distribution, P(k) = h k exp(- h)/ k!

Biology Direct

It addresses the following objective: given a dataset of n units described by m attributes and a positive integer k (the number of clusters), group the n units into k clusters so that the total sum of the distances of each unit to its nearest cluster center is minimized.

Health and Quality of Life Outcomes

By (2.8), there exists a positive integer k such that η n + 1 = d 2 ( Z k + 1, Z k ) < δ.

Fixed Point Theory and Applications

Expert writing Tips

Best practice

When using "by an integer k", ensure the context clearly defines the role of 'k'. Is it a multiplier, an index, or an offset?

Common error

Avoid using "by an integer k" without explicitly defining the range or purpose of 'k'. Ambiguity can lead to misinterpretations in mathematical or programming contexts.

Linguistic Context

The phrase "by an integer k" functions as a prepositional modifier, specifying the manner in which something is being changed or related to an integer value. As Ludwig AI confirms, it's grammatically correct and usable, particularly in mathematical and programming contexts.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "by an integer k" is a grammatically correct and usable expression, primarily found in formal and scientific contexts. As Ludwig AI confirms, it's most often used to specify a mathematical relationship or an algorithmic step involving an integer value. While infrequent, its usage demands clarity in defining the role and scope of 'k' to avoid ambiguity. Alternatives like "multiplied by an integer k" or "indexed by an integer k" can provide more specific connotations depending on the intended meaning.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

multiplied by an integer k

Changes the operation from an unspecified influence to a specific multiplication.

scaled by an integer k

Replaces the general modification with a term emphasizing proportional change.

incremented by an integer k

Specifies an increase, rather than a general modification.

decremented by an integer k

Specifies a decrease, rather than a general modification.

offset by an integer k

Suggests a shift or displacement determined by the integer.

indexed by an integer k

Implies that the integer is used as an index in a sequence or array.

parameterized by an integer k

Highlights the integer as a parameter that influences some other value or function.

quantified by an integer k

Focuses on the integer as a measure or quantity.

determined by an integer k

Emphasizes that the integer is a factor in determining something.

controlled by an integer k

Indicates the integer is used to manage or influence something.

FAQs

How to use "by an integer k" in a sentence?

Use "by an integer k" to specify a change or relationship involving a whole number. For instance, "The value is incremented by an integer k, where k represents the number of iterations."

What does "by an integer k" mean in mathematics?

In mathematics, "by an integer k" indicates that a quantity is being modified or related to a whole number value, k. The specific meaning depends on the context, such as multiplication, addition, or indexing.

What can I say instead of "by an integer k"?

Alternatives include "multiplied "by an integer k"", "indexed "by an integer k"", or "offset "by an integer k"", depending on the specific mathematical or logical operation.

Is it better to say "using an integer k" or "by an integer k"?

Both are grammatically correct, but ""by an integer k"" typically implies a mathematical operation or modification, while "using an integer k" is more general and could refer to any use of the integer.