a minimum at

USAGE SUMMARY

The phrase "a minimum at" is correct and usable in written English.
It is typically used in mathematical or analytical contexts to indicate the lowest point or value of a function or dataset. Example: "The graph shows that the function has a minimum at x = 3."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

They show a minimum at the iso-electric point.

Chemical Engineering Science

Similar strategies kept financial losses to a minimum at other institutions.

The New York Times

Familiarity with writing rigorous proofs (at a minimum, at the level of CS 103).

Stanford University

The pressure drop has a minimum at a velocity of 0.3 m/s.

Powder Technology

Results: Both sensory and motor thresholds showed a smooth decrease to a minimum at approximately 3kHz.

Archives of Physical Medicine and Rehabilitation

Interestingly, the input power is found to be at a minimum at the diaphragm frequency.

Experimental Thermal and Fluid Science

The selectivity towards hydrogen peroxide passes through a minimum at a pyrolysis temperature of 700 °C.

Catalysis Today

The fractal analysis shows a minimum at a clearly lower gas velocity.

Chemical Engineering Science

2 passes through a minimum at 30% for 0.05 m HCl at all temperatures.

Electrochimica Acta

Effective diffusivities exhibit a minimum at a Cl/Zn ration of approximately 3.5.

Electrochimica Acta

It was observed that the o-Ps intensity shows a minimum at Tmin≈Tg+10 K.

Polymer

Expert writing Tips

Best practice

When using "a minimum at", ensure that the context clearly defines what is being minimized and at what specific condition or point the minimum is achieved. For example, specify the variable or function that reaches its minimum value.

Common error

Avoid using "a minimum at" without clearly stating what quantity or parameter is at its minimum. This can lead to confusion. Always provide the necessary context for clarity.

Linguistic Context

The phrase "a minimum at" functions as an adverbial phrase specifying the condition or location where a certain quantity, function, or value reaches its lowest point. Ludwig AI indicates that it's grammatically correct and usable in various contexts.

Expression frequency: Very common

Frequent in

Science

77%

News & Media

14%

Academia

9%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, "a minimum at" is a grammatically sound phrase typically used to indicate the lowest point of something, particularly in scientific and mathematical contexts. Ludwig AI confirms its correctness and usability. It's crucial to provide clear context when using this phrase to specify what exactly is at its minimum and under what conditions. While less common in informal settings, its precise nature makes it invaluable in formal and technical writing. Alternatives like "lowest point at" or "smallest value at" can be considered for stylistic variation.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

lowest point at

Replaces "minimum" with a more descriptive term, focusing on the physical or abstract lowest position.

smallest value at

Emphasizes the numerical aspect of the minimum, suitable for mathematical or statistical contexts.

the nadir at

Uses a more formal and less common synonym for "minimum", indicating the lowest point.

bottomed out at

Suggests a process of reaching a minimum and potentially starting to increase afterwards.

reaches its lowest at

Highlights the action of attaining a minimum value at a specified point.

is minimized at

Focuses on the state of being at the lowest possible value.

decline to the lowest point at

More descriptive alternative that focus on the decrease towards the lower value.

drops to the lowest level at

Focuses on the action of dropping to the minimal level.

the trough is at

Similar to "nadir", trough is the point after which the value goes up again.

plummets to the lowest value at

Focuses on the drastic and quick decrease that reached the lowest point.

FAQs

How is "a minimum at" used in a sentence?

It's used to indicate the point where a value or quantity is at its lowest. For example, "The function has "a minimum at" x = 2."

What are some alternatives to saying "a minimum at"?

Alternatives include "lowest point at", "smallest value at", or "the nadir at", depending on the specific context.

In what contexts is "a minimum at" commonly used?

It's frequently used in scientific, mathematical, and technical writing to describe the lowest point of a graph, function, or measured value. News and media sources also use it when reporting on quantitative information.

Is there a difference between "a minimum at" and "at a minimum"?

Yes, ""a minimum at"" specifies the location or condition where something is at its lowest. "At a minimum" generally means 'the least possible' or 'the bare essential'.