be a positive differentiable

USAGE SUMMARY

The phrase "be a positive differentiable" is not correct in written English.
It seems to be an incomplete or improperly constructed expression, possibly intended to describe a mathematical function or property. Example: "For the function to be useful in optimization, it must be a positive differentiable function."

⚠ May contain grammatical issues

Science

Human-verified examples from authoritative sources

Exact Expressions

5 human-written examples

Definition 2.2 Let (N1, g1) and (N2, g2) be two Riemannian manifolds with Riemannian metrics g1 and g2, respectively, and λ be a positive differentiable function on N1.

Journal of Inequalities and Applications

Let (M_{1}) and (M_{2}) be two Riemannian manifolds with Riemannian metrics (g_{1}) and (g_{2},) respectively, and f be a positive differentiable function on (M_{1}).

Bulletin of Mathematical Sciences

They defined the manifolds based on (M_{1}) and (M_{2}), which are the two Riemannian manifolds of dimensions (n_{1}) and (n_{2}) endowed with Riemannian matrices (g_{1}) and (g_{2}) such that (f:M_{1}rightarrow 0, infty)) be a positive differentiable function on (M_{1}).

Journal of Inequalities and Applications

Let v t) be a positive differentiable function on (0, T) such that lim t → 0 + v t = v 0 ≥ 0, and v ′ t ≤ h t v t + k t v p t, t ∈ 0, T, where the functions h and k are continuous functions on (0, T), and p ≥ 0, p ≠ 1, is a constant.

Journal of Inequalities and Applications

Let (P x)) be a positive differentiable and decreasing function defined on ((0, r)) ((r>0)), let (A x)=sum _{n=n_{0}}^{infty}a_{n}x^{n}) and (B x)=sum_{n=n_{0}}^{infty}b_{n}x^{n}) be two real power series converging on ((-r, r)).

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

55 human-written examples

It follows from (P x)) is a positive differentiable and decreasing function on ((0, r)) that nP x -xP^{prime}(x)>0 (2.6) for all (xinP x -xP^{prime

Journal of Inequalities and Applications

Let be a positive and continuously differentiable function for and let If (2.10).

Advances in Difference Equations

Let q be a positive integer, assume that the function (f(t)) is at least ((2q+2))-times continuously differentiable on ([c,d]).

Journal of Inequalities and Applications

Without loss of generality, we suppose u be i-differentiable with respect to the x, t and also it be a positive fuzzy number ((forall tin [0,T])).

Mathematical Sciences

Suppose that ρ is a positive continuously differentiable function on the interval I such that ρ ′ ≥ 0 on I and (2) hold.

Journal of Inequalities and Applications

Suppose that ρ is a positive continuously differentiable function on the interval I such that ρ ′ ( t ) ≥ 0 on I and (34) hold.

Journal of Inequalities and Applications

Expert writing Tips

Best practice

When describing mathematical functions or properties, always specify the entity being described (e.g., "function", "curve", "value"). Ensure correct grammatical structure, such as "to be a positive differentiable function" or "is a positive differentiable function".

Common error

Avoid using the phrase "be a positive differentiable" in isolation. This incomplete structure lacks clarity. Specify the entity you are describing. For example, say "the function must be a positive differentiable function" instead of just "be a positive differentiable".

Linguistic Context

The phrase "be a positive differentiable" functions as an adjective phrase intended to describe a mathematical property. However, it is grammatically incomplete without specifying the entity being described (e.g., function, curve, value). Ludwig AI indicates that this phrase is not correct in written English.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, while "be a positive differentiable" intends to describe mathematical properties, it is grammatically incomplete. Ludwig AI confirms it's considered incorrect in standard written English. The phrase needs a specified entity (e.g., "function") to be accurate and clear. Use "to be a positive differentiable function" or "is a positive differentiable function" to improve clarity and grammatical correctness. Most usages appear in scientific publications, so a formal and scientific register is appropriate. Remember to specify the entity you're describing to avoid ambiguity.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

being a positive differentiable function

Adds the explicit mention of 'function', specifying the entity being described.

to be a differentiable positive function

Switches the order of adjectives and uses 'to be' instead of 'be a'.

it is a positive differentiable function

Adds a subject pronoun 'it is' for emphasis or clarity.

being a positively differentiable entity

Changes 'positive' to an adverb and uses a more generic noun 'entity'.

is a differentiable, positive function

Reorders adjectives, using a comma for separation, improving readability.

represent a positive, differentiable curve

Specifies "curve" as the subject and uses "represent" instead of "be".

denotes a differentiable and positive value

Specifies "value" as the subject and uses "denotes" instead of "be".

portrays a positive but differentiable feature

Specifies "feature" as the subject and uses "portrays" instead of "be", also uses "but" as a transition word.

acting as a differentiable, positive element

Specifies "element" as the subject and uses "acting as" instead of "be"

characterizing a positive, differentiable surface

Specifies "surface" as the subject and uses "characterizing" instead of "be".

FAQs

How to correctly use the terms "positive" and "differentiable" together in a mathematical context?

Ensure correct grammatical structure by specifying the entity being described (e.g., function, curve, value). For example, use "to be a positive differentiable function" or "is a positive differentiable function".

What does it mean for a function to be "positive" and "differentiable"?

A positive differentiable function has values greater than zero across its domain and possesses a derivative at every point in its domain. For example: "Let f be a differentiable function".

Which is the correct phrase, "be a positive differentiable function" or "be a positive and differentiable function"?

While both are acceptable, "be a positive and differentiable function" adds extra emphasis on the separate properties. Alternatively, consider "be a positive, differentiable function" for readability.

What are some examples of positive differentiable functions?

Examples include exponential functions (e.g., e^x), polynomials with positive coefficients over certain intervals, and trigonometric functions like sine and cosine within specific domains where they remain positive. A more specific example: "Let be a differentiable function".