above approximations

USAGE SUMMARY

The phrase "above approximations" is correct and usable in written English.
It can be used when referring to estimations or calculations mentioned earlier in a text or discussion. Example: "Based on the above approximations, we can conclude that the project will require additional resources."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

7 human-written examples

In Section 5, we investigate the ability of the above approximations to represent client RC distributions.

EURASIP Journal on Wireless Communications and Networking

Substituting the above approximations (3.36a) and (3.36b) into (3.12), the order of method (3.12) is retained, and hence we obtain the required numerical method of (O k^{2} + k^{2}h^{2} + h^{4})) based on spline in compression approximations (see [37 45]) for differential equation (1.1).

Advances in Difference Equations

Based on the above approximations, Equation (8) yields an estimated buffer size of L = 2 and L = 3 frames for the capsule (t F = 500 ms) and the conventional endoscopic (t F = 33.33 ms) sequences, respectively, thus confirming the applicability of the proposed scheme.

EURASIP Journal on Wireless Communications and Networking

With the above approximations, these wave functions do not depend on Qt, which in the vibrationally nonadiabatic limit determines only the shift of one potential well with respect to the other one.

Chemical Reviews

Then, if the initial and final potential wells experienced by the transferring proton are approximately harmonic, the conservation of energy gives −2 ce q0 Qt + ℏωp/2 = (n + 1/2)ℏωp (see Figure 44), that is 11.11Equations 11.10 and 11.11 exemplify the determination of Rt and Qt with the above approximations.

Chemical Reviews

In this case, with the above approximations, we see that (34) R ∗ = R tot k xr X ∗ k − r Y ∗ = Y tot k ry < R ∗ > k − y X ∗ = X tot k sx S k yx Y ∗ + k − x Thus the steady state emerges as the solution of the equation (35) R ∗ = α S 1 + β < R ∗ > with α and β defined exactly as above.

BMC Systems Biology

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

Thus the above approximation of function is not suitable.

EURASIP Journal on Advances in Signal Processing

Applying the above approximation, we first rewrite (31) as (38).

EURASIP Journal on Wireless Communications and Networking

Now, we present an explanation for the above approximation.

EURASIP Journal on Image and Video Processing

Clearly, an oscillation occurs for (|x| < 3), as predicted by the above approximation.

Advances in Difference Equations

However, as the results in [32] show, the above approximation may be very inaccurate.

EURASIP Journal on Wireless Communications and Networking

Expert writing Tips

Best practice

When using "above approximations", ensure that the approximations have been clearly defined and are readily accessible to the reader or listener. Avoid ambiguity by providing sufficient context.

Common error

Avoid using "above approximations" without explicitly stating or referencing which approximations you are referring to. Vague references can confuse your audience.

Linguistic Context

The phrase "above approximations" functions as a determiner phrase, specifically acting as a pre-modifier to the noun "approximations". As seen in Ludwig, it points back to approximations that have been previously mentioned or defined within the text.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "above approximations" is a phrase used to refer back to estimations or calculations previously mentioned, primarily found in formal and scientific writing. Ludwig indicates that while grammatically correct, it's crucial to ensure clear reference to avoid ambiguity. Alternatives like "previous estimations" or "earlier estimates" can offer stylistic variations. Proper usage involves clearly defined approximations, while common errors involve vague references. The frequency of the phrase is uncommon, predominantly appearing in science-related contexts.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

previous estimations

Replaces "approximations" with a direct synonym, emphasizing the estimations were made earlier.

earlier estimates

Uses "estimates" instead of "approximations" and "earlier" instead of "above" for a more straightforward phrasing.

aforementioned approximations

Substitutes "above" with "aforementioned" to specify that the approximations were previously mentioned.

stated approximations

Replaces "above" with "stated" to highlight that the approximations have been explicitly presented.

foregoing estimations

Uses "foregoing" instead of "above" and "estimations" instead of "approximations", maintaining a formal tone.

earlier simplifications

Emphasizes the simplification aspect, using "simplifications" instead of "approximations".

the approximations mentioned previously

Rephrases to explicitly state that the approximations were mentioned at an earlier point.

these preliminary estimates

Replaces "above approximations" with "preliminary estimates" referring to initial calculations.

the preceding estimations

Uses "preceding" to indicate that the estimations came before the current point of discussion.

assumptions already discussed

Focuses on the underlying assumptions rather than the approximations themselves.

FAQs

How can I use "above approximations" in a sentence?

You can use "above approximations" to refer to estimations or calculations that you have previously mentioned in your text. For example, you might say, "Based on the above approximations, we can proceed with the next step."

What are some alternatives to saying "above approximations"?

You can use alternatives such as "previous estimations", "earlier estimates", or "aforementioned approximations" depending on the specific context.

Is it correct to say "the above approximation" instead of "above approximations"?

Yes, you can use "the "above approximation"" if you are referring to a single approximation that has been previously mentioned. "Above approximations" is used when referring to multiple estimations.

What's the difference between "above approximations" and "following approximations"?

"Above approximations" refers to approximations that have already been stated, while "following approximations" would refer to approximations that will be presented next.