Noun phrase
/ləʊˈkæl.i həˈmoʊ.dʒə.nəs ˈfʌŋk.ʃən/
A locally homogeneous function refers to a mathematical function that maintains a certain degree of uniformity or consistency within a specified neighborhood around a point in its domain. In other words, this function exhibits properties that are similar in a local context—if you zoom in on a small area around a point, the function appears consistent.
This term is primarily used in mathematical contexts, particularly in calculus and analysis. It is not a common phrase in everyday conversation and is used more frequently in written forms, particularly in academic and professional settings regarding mathematics and physics.
The researcher proved that the locally homogeneous function converges in the vicinity of the origin.
Исследователь доказал, что локально однородная функция сходится в окрестности начала координат.
To analyze the system's performance, we can assume that the locally homogeneous function behaves similarly when perturbed slightly.
Для анализа производительности системы мы можем предположить, что локально однородная функция ведет себя аналогично при небольших возмущениях.
By focusing on the locally homogeneous function, we can simplify our calculations significantly.
Сосредоточившись на локально однородной функции, мы можем значительно упростить наши вычисления.
"Locally homogeneous function" is not a phrase commonly found in idiomatic expressions in the English language, largely because it is a specialized mathematical term. However, it shares concepts related to locality and uniformity in various expressions. Here are few expressions that might be used in similar mathematical or analytical contexts:
"Locally defined"
The results are significant when considered in the locally defined context of our model.
(Результаты значительны, когда рассматриваются в локально заданном контексте нашей модели.)
"Homogeneous mixture"
The solution is a homogeneous mixture, meaning that the components are evenly distributed.
(Раствор представляет собой однородную смесь, что означает, что компоненты равномерно распределены.)
"Local minimum"
Finding the local minimum of the function can help us optimize our solution.
(Нахождение локального минимума функции может помочь нам оптимизировать наше решение.)
The term "locally homogeneous function" can be broken down into "locally," which stems from the Latin word "locus," meaning place or location; "homogeneous," derived from the Greek words "homos" (same) and "genes" (kind or type); and "function," from Latin "functio," meaning performance or execution. The connotation of the terms relates to properties that are consistent within a certain local area.
The term locally homogeneous function is quite specialized, and its usage is largely confined to fields dealing with advanced mathematics, such as analysis and topology.