uniformly asymptotical (english) - meaning, definition, translation, pronunciation

Part of Speech

Adjective

Phonetic Transcription

/ˈjunɪˌfɔːrmli æsˈɪmptəkl/

Meaning and Usage

"Uniformly asymptotical" is a term primarily used in mathematical and statistical contexts. It refers to a property of functions or sequences that converge to a limit in a uniform manner as they approach infinity or some singular value. The term "uniformly" suggests that this convergence occurs uniformly across the domain, while "asymptotical" pertains to the behavior of a function as its argument tends toward some limit.

Frequency of use: The term is specialized and is used more frequently in written contexts, particularly in academic papers, textbooks, and mathematical literature rather than in everyday oral communication.

Example Sentences

1. "The solutions to the differential equation are uniformly asymptotical, indicating consistent behavior across all values of the input."

2. "Решения дифференциального уравнения являются равномерно асимптотическими, что указывает на последовательное поведение при всех значениях входных данных."

3. "Researchers proved that under specific conditions, the sequence converges uniformly asymptotical to the desired limit."

4. "Исследователи доказали, что при определенных условиях последовательность сходится равномерно асимптотически к желаемому пределу."

5. "In probability theory, the uniform asymptotical properties of estimators can lead to more reliable inference."

6. "В теории вероятностей равномерные асимптотические свойства оценщиков могут привести к более надежным выводам."

Idiomatic Expressions

The phrase "uniformly asymptotical" does not lend itself well to common idiomatic expressions as it is quite specialized in its application. However, when exploring mathematical and statistical discourse, practitioners might encounter related phrases or contexts where "uniformly" and "asymptotic" are frequently used. Below are some phrases relevant to these concepts:

1. "As we approach the limit, the function becomes uniformly asymptotic."

2. "Когда мы стремимся к пределу, функция становится равномерно асимптотической."

3. "Uniformly asymptotic techniques are essential for analyzing the efficiency of algorithms."

4. "Равномерно асимптотические методы необходимы для анализа эффективности алгоритмов."

5. "In statistical theory, uniformly asymptotic normality is a critical concept for understanding estimators."

6. "В статистической теории равномерная асимптотическая нормальность является критически важным понятием для понимания оценок."

Etymology

The word "uniformly" derives from the Latin "uniformis," meaning "of one form," composed of "uni-" meaning "one" and "form." The term "asymptotical" comes from the Greek "asumptōtos," which means "not falling together," indicating that a curve approaches a straight line but never actually intersects it.

Synonyms and Antonyms

• Synonyms: consistently convergent, uniformly convergent
• Antonyms: erratically divergent, inconsistent, non-uniform

By exploring the meanings, contextual uses, and related phrases for "uniformly asymptotical," one can appreciate its significant role in mathematical language and analysis.