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The phrase "a classical example is the" is correct and usable in written English.
It can be used when introducing a specific instance or case that exemplifies a broader concept or idea.
Example: "In discussing the principles of democracy, a classical example is the ancient Athenian system of governance."
Alternatives: "a prime example is the" or "a typical example is the".
Exact(14)
Advertising signals also serve to repel other males; a classical example is the territorial song of many songbirds.
A classical example is the wave-like propagation of perceptual dominance during binocular rivalry [35 38].
A classical example is the ordinary least squares (OLS) estimator proposed by Gauss in 1795 [1].
A classical example is the tf-idf (term frequency - inverse document frequency) document similarity used in document search.
A classical example is the perceptual enhancement of contrast borders (often referred to as Mach bands [52], [53]).
A classical example is the induction of fever in mammals, in which a systemic (intra-peritoneal or intravenous) injection of LPS provokes central nervous system responses leading to an increase in body temperature as well as other behavioral changes [34].
Similar(46)
Typically, genes involved in non-self recognition are among the most polymorphic loci in eukaryotic genomes, a classical example being the MHC/HLA loci in mammals [ 1].
A classical example is studying the effects of systematic deletions of genes on an organism's viability, with the resulting causal categorization of essential genes [ 4- 6].
A classical example is that of the antihypertensive agent debrisoquine; some patients experience hypotension together with high plasma levels of unmetabolized drug in concert with low excretion of the major 4-hydroxylated metabolite in the urine [ 6].
The adsorbed phase (q i ) in eqn (6) is related to the gas phase fugacity through an adsorption isotherm of which the classical example is the Langmuir isotherm: 7 An important difference between gas phase and adsorbed phase diffusion is the concentration level, being much higher in the case of adsorbed phase diffusion.
The classical example is the reassortment of avian and human strains of influenza A resulting in novel viruses with pandemic potential [38] [41], but examples abound for both animal and plant viruses [e.g., [3], [42] [48]].
More suggestions(15)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com