according to first order

USAGE SUMMARY

The phrase "according to first order" is correct and usable in written English.
It can be used in contexts related to mathematics, logic, or scientific discussions where first-order principles or theories are being referenced. Example: "According to first order logic, every statement can be expressed in terms of quantifiers and predicates."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

7 human-written examples

The statistically optimized formulation released drug according to first order kinetics with a non-Fickian diffusion mechanism.

Acta Pharmaceutica Sinica B

Following a standard modeling approach, the network is partitioned in cells, whose vehicle densities change dynamically in time according to first order conservation laws.

Transportation Research Part C: Emerging Technologies

After the end of deformation, the mesophase decays and is replaced by oriented triclinic crystals which increase according to first order transformation kinetics.

Polymer

The spectra were analyzed according to first order and the descriptions of signals include: s = singlet, d = doublet, dd = doublet of doublets, t = triplet, q = quartet, m = multiplet.

AMB Express

Half-lives were calculated according to first order kinetics: t1/2 = ln(2)/slope.

Aging Cell

In state-space Bayesian models, the observed measurements depend on hidden states, which are assumed to evolve according to first order Markov chain.

BMC Systems Biology

Human-verified similar examples from authoritative sources

Similar Expressions

53 human-written examples

Experiments have been done according to second order central composite rotatable design and response surfaces of the outputs are plotted after regression analysis.

Journal of Materials Processing Technology

The SMC embedded in SHMC has been redefined according to first-order neighborhood with different lag in three-dimensional space.

Journal of Petroleum Exploration and Production Technology

PCP residues declined from 800 1000 mg kg−1 to 4 (0–9.4 mg kg−1) according to first-order kinetics.

International Biodeterioration & Biodegradation

According to first-order views, phenomenal consciousness consists in analog or fine-grained contents that are available to the first-order processes that guide thought and action.

SEP

The differences in rates of deactivation were interpreted in terms of deposition of a foulant according to first-order kinetics based on parallel deactivation.

Catalysis Today

Expert writing Tips

Best practice

When using "according to first order", ensure the context clearly defines what 'first order' refers to, such as kinetics, logic, or principles, to avoid ambiguity.

Common error

Avoid using "according to first order" without specifying the relevant domain (e.g., kinetics, logic). Lack of context can make the phrase vague and confusing for the reader.

Linguistic Context

The phrase "according to first order" functions as a prepositional phrase that modifies a verb or noun, indicating that a statement, process, or result is derived or determined based on a first-order principle or analysis. As Ludwig AI highlights, it is most frequently found in scientific contexts.

Expression frequency: Uncommon

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Academia

0%

Ludwig's WRAP-UP

In summary, "according to first order" is a prepositional phrase mainly used in formal and scientific contexts to indicate that a statement or result is based on fundamental principles or a first-order analysis. Ludwig AI indicates that it's grammatically correct and primarily appears in scientific domains. When employing this phrase, ensure clarity by specifying the relevant domain (e.g., kinetics, logic) to avoid ambiguity. Alternatives include "following first-order principles" or "based on first-order logic", depending on the context. This ensures that your writing is both precise and easily understood.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

following first-order principles

Emphasizes adherence to foundational principles rather than a direct claim of 'according to'.

based on first-order logic

Specifies the foundation as logic, providing a more specific context.

in accordance with first-order theory

Highlights alignment with a theoretical framework, which is more formal.

consistent with first-order approximations

Focuses on the consistency of results with approximations, indicating a level of simplification.

as per first-order analysis

Uses 'as per' to indicate that something is done following an analysis, sounding slightly more technical.

on the basis of first-order reasoning

Highlights the reasoning process behind a conclusion, focusing on foundational logic.

deriving from first-order considerations

Emphasizes the origin of an idea or result from fundamental considerations.

premised on first-order assumptions

Focuses on the underlying assumptions that are foundational to a conclusion.

grounded in first-order observations

Highlights that the information comes from a set of base level observations.

guided by first-order principles

Highlights the guiding influence of the principles.

FAQs

How do I use "according to first order" in a sentence?

Use "according to first order" to indicate that something follows from or is based on a fundamental or basic principle, theory, or analysis. For example, "According to first order kinetics, the reaction rate depends on the concentration of one reactant."

What does "according to first order" mean in chemistry?

In chemistry, "according to first order" typically refers to first-order kinetics, where the reaction rate is directly proportional to the concentration of one reactant. The rate doubles if the concentration of that reactant doubles.

Is there a difference between "according to first order" and "based on first order"?

"According to first order" and "based on first order" are often interchangeable, but "based on first order" might imply a broader foundation, while "according to first order" directly references a specific principle or rule. You could also try "following first-order principles".

What are some contexts where I might use "according to first order"?

You might use "according to first order" in discussions of kinetics, logic, systems theory, or any field where a hierarchical ordering of principles or approximations is relevant. Be sure to specify which 'first order' you're referencing for clarity.