Sentence examples similar to without equation from inspiring English sources

The phrase "without equation" is not commonly used in written English and may be unclear in meaning.
It could be used in contexts where one is discussing a situation or concept that does not involve mathematical equations or formal calculations. Example: "The results were derived from empirical observations without equation, relying solely on experimental data."

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His influential book "Systems Architecting: Creating and Building Complex Systems" (1991) was "an engineering text without equations that looked at the expectations for a product's performance, its materials and their cost, and the necessary balance between them," said F. Stan Settles, a professor of astronautics and industrial and systems engineering at the university.

As discussed above, Ashlyn thinks she already understands diffusion adequately without equations, which could trigger and/or reinforce the epistemological stance that equations have no role to play in explaining biological phenomena.

The obtained criteria are in terms of linear matrix inequalities without transcendental equation, instead of nonlinear matrix inequalities, which reduces the computational burden.

However without an equation expressing precisely the relation of such an index to other concepts we are back to the situation where constraints are unknown.

Nevertheless, there is no way of accurately determining the value of ρ or ν s without using Equation 1 and the MESI instrument.

This is similar in spirit to our earlier analytical results for the invasion probability of the space-free Moran process (see equations (2)), and a 1D Moran process without motility (equation (3)).

He explains all without mathematical equations.

But, as Smolin must surely know, without the equations it is impossible to convey everything one needs to know to follow his arguments.

However, Coppersmith, Stern and Vaudenary gave an efficient algorithm [6] to compute A2, a part of the secret key, without solving equations over (mathbb {Z}/Nmathbb {Z}).

3) The analyses are largely described in the text without any equations; having the equations in the Methods or supplements would be much better, and several of the quantitative figures are described quite vaguely.

Except, in the law course, the original material comprises only a few hundred pages, not very large and without the equations.

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