[数] 分歧问题
A spherical cavitated bifurcation problem is examined for a solid sphere composed of a class of compressible hyper-elastic materials.
研究了一类可压缩超弹性材料组成的球体的空穴分岔问题。
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.
在什么条件下两个分歧问题关于某一等价群而言是等价的，这在分歧理论研究中是很有意义的。
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.
在简单加载条件下，研究幂强化材料和超弹性材料组合球体中的动态孔穴生成和增长问题。
To solve the problem of vessel bifurcation and overlap, an adaptive tracking algorithm based on the constraint of directional information measure is proposed.
针对血管的叠加与分叉问题，本文提出了一种基于象素方向信息测度约束的自适应血管跟踪方法。
The problem of applying bifurcation theory in influence of reactive power compensation upon voltage stability etc.
分析研究了分叉理论应用于无功补偿对电压稳定性影响等问题。
“Bifurcation problem”是数学、物理学和工程学中常见的术语，结合了“分叉”现象与系统行为变化研究的核心问题。以下是详细解释：
Bifurcation（分叉）
源自拉丁语 bifurcus（两叉的），指一个系统、结构或路径在特定条件下分裂成两个或多个分支的现象。
核心特征：
Problem（问题）
指需要解决或分析的难题，通常涉及理论推导、数值计算或实验验证。
常见类型：稳定性分析、解的路径追踪、临界参数确定等。
“Bifurcation problem”指研究系统在参数变化时发生分叉的数学问题，重点关注分叉点的存在性、类型及其对系统行为的影响。
典型场景：
在分叉分析中，常用以下形式的微分方程描述系统：
$$
frac{dx}{dt} = f(x, mu)
$$
其中 $mu$ 为参数。当 $mu$ 变化到临界值 $mu_c$ 时，系统可能发生分叉，如叉式分叉的条件为：
$$
f(x, mu) = mu x - x = 0 quad Rightarrow quad x=0 text{ 或 } x=pmsqrt{mu}
$$
“Bifurcation problem”是研究系统因参数变化导致结构突变的复杂问题，需结合数学理论与实际背景分析分叉机制。如需扩展学习，可参考动力系统或非线性科学领域的文献。
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（问题）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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