Under suitable assumptions

USAGE SUMMARY

The phrase "Under suitable assumptions" is correct and usable in written English.
It can be used in contexts where you are discussing conditions or prerequisites that need to be met for a statement or conclusion to hold true. Example: "Under suitable assumptions, the theorem can be proven to hold for all integers."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Under suitable assumptions, we derive some strong convergence theorems.

Fixed Point Theory and Applications

Under suitable assumptions, they established the strong convergence of the sequences generated by the proposed schemes.

Fixed Point Theory and Applications

Under suitable assumptions, they proved the strong convergence of the sequences generated by the proposed schemes.

Fixed Point Theory and Applications

Under suitable assumptions, the global convergence of the hybrid splitting method is proved.

Journal of Inequalities and Applications

Under suitable assumptions, they proved that such sequence converge strongly to a solution of fixed point T.

Journal of Inequalities and Applications

Under suitable assumptions on the data, we establish the well-posedness of the problem with respect to weak solutions.

Boundary Value Problems

Under suitable assumptions, we obtain a sequence of solutions associated with a sequence of positive energies going toward infinity.

Journal of Inequalities and Applications

Under suitable assumptions on the frequency, we establish upper and lower bounds for the upper transport exponents.

Journal of Functional Analysis

Under suitable assumptions, we establish the general rates of energy decay of the initial and boundary value problem by using the energy perturbation method.

Boundary Value Problems

Under suitable assumptions, we establish a general decay result by multiplier techniques, which extends some existing results for a single equation to the case of a coupled system.

Boundary Value Problems

Under suitable assumptions of regularity, the RL and GL operators coincides, i.e., D t 0 α RL f ( t ) = GL D t 0 α f ( t ).

Advances in Difference Equations

Expert writing Tips

Best practice

When using "under suitable assumptions", clearly state or reference the specific assumptions being made to avoid ambiguity.

Common error

Avoid using "under suitable assumptions" without specifying what those assumptions are, as this can weaken your argument and make it difficult for others to validate your claims.

Linguistic Context

The phrase "under suitable assumptions" functions as a prepositional phrase that introduces a condition or set of conditions necessary for a statement to be valid. It serves as an adverbial modifier, indicating the circumstances under which a particular result or conclusion is true. Ludwig AI confirms the correct usage of the phrase.

Expression frequency: Common

Frequent in

Science

98%

Formal & Business

1%

News & Media

1%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "under suitable assumptions" is a common and grammatically correct way to introduce conditions necessary for a statement's validity, as confirmed by Ludwig AI. It's predominantly used in formal and scientific contexts to qualify claims and acknowledge preconditions. For clarity, always specify or reference the assumptions being made. While acceptable, explicitly stating the assumptions is preferable for rigor and transparency. Alternatives include "given appropriate conditions" or "assuming the right circumstances".

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

given appropriate conditions

Focuses on the conditions themselves being appropriate, rather than the act of assuming.

assuming the right circumstances

Emphasizes the external circumstances needed for validity.

provided specific conditions are satisfied

Highlights the need for the conditions to be actively met.

subject to certain stipulations

Introduces a slightly more formal tone with the word "stipulations".

contingent on specific criteria

Uses "contingent" to show dependence on particular criteria.

dependent on particular conditions

Directly states the dependence on specific conditions.

if certain criteria are met

A more straightforward and less formal way of expressing the same idea.

assuming these provisions hold

Uses "provisions" to indicate a set of requirements or conditions.

on the premise that

Highlights the underlying premise or foundation for the statement.

given the fulfillment of certain criteria

Emphasizes the fulfillment or completion of the stated criteria.

FAQs

How can I use "under suitable assumptions" in a sentence?

You can use "under suitable assumptions" to introduce a condition or set of conditions that must be true for a particular result or statement to hold. For example: "Under suitable assumptions, the theorem can be proven to hold for all integers."

What's a less formal way to say "under suitable assumptions"?

Alternatives like "given appropriate conditions", "assuming the right circumstances", or "if certain criteria are met" can be used in less formal contexts.

What does it mean to make an argument "under suitable assumptions"?

Making an argument "under suitable assumptions" means that the validity of the argument is contingent on the truth or applicability of specific conditions or premises. These conditions must be clearly defined to ensure the argument's soundness.

Is it better to explicitly state assumptions rather than use "under suitable assumptions"?

While "under suitable assumptions" is acceptable, explicitly stating the assumptions is often better for clarity and rigor. This eliminates ambiguity and allows readers to fully understand the basis of your argument or conclusion. It improves transparency and makes your work more verifiable.