[數] 分歧問題
A spherical cavitated bifurcation problem is examined for a solid sphere composed of a class of compressible hyper-elastic materials.
研究了一類可壓縮超彈性材料組成的球體的空穴分岔問題。
An interesting problem in the study of bifurcation theory is to determine when two bifurcation problems are equivalent with respect to some group of equivalences.
在什麼條件下兩個分歧問題關于某一等價群而言是等價的，這在分歧理論研究中是很有意義的。
The bifurcation problem of dynamical formation and growth of cavity in a sphere composed of a power hardening material and a hyper-elastic material is discussed in this paper.
在簡單加載條件下，研究幂強化材料和超彈性材料組合球體中的動态孔穴生成和增長問題。
To solve the problem of vessel bifurcation and overlap, an adaptive tracking algorithm based on the constraint of directional information measure is proposed.
針對血管的疊加與分叉問題，本文提出了一種基于象素方向信息測度約束的自適應血管跟蹤方法。
The problem of applying bifurcation theory in influence of reactive power compensation upon voltage stability etc.
分析研究了分叉理論應用于無功補償對電壓穩定性影響等問題。
“Bifurcation problem”是數學、物理學和工程學中常見的術語，結合了“分叉”現象與系統行為變化研究的核心問題。以下是詳細解釋：
Bifurcation（分叉）
源自拉丁語 bifurcus（兩叉的），指一個系統、結構或路徑在特定條件下分裂成兩個或多個分支的現象。
核心特征：
Problem（問題）
指需要解決或分析的難題，通常涉及理論推導、數值計算或實驗驗證。
常見類型：穩定性分析、解的路徑追蹤、臨界參數确定等。
“Bifurcation problem”指研究系統在參數變化時發生分叉的數學問題，重點關注分叉點的存在性、類型及其對系統行為的影響。
典型場景：
在分叉分析中，常用以下形式的微分方程描述系統：
$$
frac{dx}{dt} = f(x, mu)
$$
其中 $mu$ 為參數。當 $mu$ 變化到臨界值 $mu_c$ 時，系統可能發生分叉，如叉式分叉的條件為：
$$
f(x, mu) = mu x - x = 0 quad Rightarrow quad x=0 text{ 或 } x=pmsqrt{mu}
$$
“Bifurcation problem”是研究系統因參數變化導緻結構突變的複雜問題，需結合數學理論與實際背景分析分叉機制。如需擴展學習，可參考動力系統或非線性科學領域的文獻。
Bifurcation（分歧）refers to the splitting of a single entity into two or more separate parts or pathways. This term is commonly used in mathematics, physics, and biology to describe a point where a system undergoes a qualitative change in behavior.
Example: The bifurcation of the river into two separate streams created a beautiful landscape.
Usage: In science and engineering, bifurcation is used to describe the point where a system changes its behavior.
Definition: Bifurcation is the splitting of a single entity into two or more separate parts or pathways.
Synonyms: Division, Separation, Branching off
Antonyms: Convergence, Merging, Unification
Problem（問題）refers to a matter or situation that presents difficulty or perplexity and requires a solution or resolution. This term is commonly used in various fields, including mathematics, science, business, and everyday life.
Example: The problem of global warming requires immediate attention from world leaders.
Usage: Problem is used to describe a matter or situation that requires a solution or resolution.
Definition: Problem is a matter or situation that presents difficulty or perplexity and requires a solution or resolution.
Synonyms: Issue, Challenge, Difficulty
Antonyms: Solution, Answer, Resolution
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