Noun Phrase
/əˈdʒɔɪnt ˈbaʊndəri kənˈdɪʃənz/
"Adjoint boundary conditions" refer to a specific set of constraints used in mathematical models, particularly in the context of differential equations or optimal control problems. These conditions are linked with the adjoint state in various applications such as engineering, physics, and applied mathematics. The concept is primarily utilized in technical and scientific language, making it more common in written context, especially in research papers, textbooks, and academic literature than in everyday oral speech.
The researchers implemented adjoint boundary conditions to improve the accuracy of their simulation models.
(Исследователи внедрили условия границы аджойнта, чтобы повысить точность своих моделей симуляции.)
Understanding the role of adjoint boundary conditions is crucial when solving complex differential equations.
(Понимание роли условий границы аджойнта имеет решающее значение при решении сложных дифференциальных уравнений.)
The application of adjoint boundary conditions allowed for more efficient optimization of the system.
(Применение условий границы аджойнта позволило более эффективно оптимизировать систему.)
While "adjoint boundary conditions" does not have idiomatic expressions in common usage, the term is prevalent in technical discussions within specific fields. Below are relevant sentences using adjacent technical jargon instead:
The problem was solved using constraints rather than just standard boundary conditions, showcasing the mathematical intricacies involved.
(Проблема была решена с использованием ограничений, а не только стандартных условий границы, что продемонстрировало математические тонкости.)
By establishing a clear framework, researchers can ensure that all boundary conditions are met effectively.
(Создавая ясную структуру, исследователи могут гарантировать, что все условия границы выполняются эффективно.)
The project's success hinged on the accurate application of variational principles related to boundary conditions.
(Успех проекта зависел от точного применения вариационных принципов, связанных с условиями границы.)
Adopting a comprehensive approach to boundary conditions can lead to more reliable simulation outcomes.
(Применение комплексного подхода к условиям границы может привести к более надежным результатам моделирования.)
The term "adjoint" comes from the Latin word "adjungere," meaning "to join, connect." In mathematics, it refers to the adjunct or associate. "Boundary" comes from the Old French "abondeur," meaning "to bound or limit." The word "conditions" derives from the Latin "conditio," which means "a setting or stipulation."
Synonyms:
- Limiting conditions
- Constraints
- Boundary constraints
Antonyms:
- Free conditions
- Unconstrained state
- Open boundary conditions
This detailed overview provides foundational understanding as well as context for the term "adjoint boundary conditions" within various scholarly fields.