Noun Phrase
/ˈloʊ.kəl.i ˈreɡ.jə.lɚ ˈfʌŋk.ʃən/
The term "locally regular function" typically appears in mathematical analysis and topology. It refers to a function that behaves regularly (i.e., is continuous and differentiable) within a localized region of its domain. This can pertain to functions that might not be globally regular due to singularities or discontinuities elsewhere in their domain.
Frequency of use among mathematicians and in formal written contexts is relatively high, especially in advanced mathematical texts, discussions, and research papers. It is less common in everyday spoken language, as it relates to specialized topics in mathematics.
Locally regular functions often exhibit nice properties near their points of definition.
(Las funciones localmente regulares a menudo exhiben buenas propiedades cerca de sus puntos de definición.)
In mathematical analysis, it is crucial to identify locally regular functions for solving differential equations.
(En análisis matemático, es crucial identificar funciones localmente regulares para resolver ecuaciones diferenciales.)
A locally regular function can be approximated by polynomials in its vicinity.
(Una función localmente regular puede ser aproximada por polinomios en su vecindad.)
In the context of "locally regular function," there aren't widely recognized idiomatic expressions; however, in mathematics, we can express ideas involving local regularity and continuity.
A function is said to be continuous if it behaves like a locally regular function.
(Se dice que una función es continua si se comporta como una función localmente regular.)
We need to ensure that our assumptions about locally regular functions hold true in this region.
(Necesitamos asegurarnos de que nuestras suposiciones sobre funciones localmente regulares sean ciertas en esta región.)
When dealing with discontinuities, one must consider the locally regular functions in the neighborhood of interest.
(Al tratar con discontinuidades, uno debe considerar las funciones localmente regulares en la vecindad de interés.)
Locally regular functions play a significant role in the theory of distributions.
(Las funciones localmente regulares juegan un papel importante en la teoría de distribuciones.)
The adjective "local" derives from the Latin word "localis," which means "pertaining to a place." The word "regular" comes from the Latin "regularis," which means "conforming to a rule." The term "function" originates from the Latin "functio," meaning "performance" or "execution." The combination of these terms illustrates the idea of functions behaving in a consistent or rule-based manner within a specific locality.
In summary, "locally regular function" is a term that encapsulates significant mathematical properties about the behavior of functions within specific regions, primarily used in advanced mathematical contexts.