jovial
发表于 2025-3-23 13:04:08
https://doi.org/10.1007/978-3-031-46906-0In contrast to the example given above, the application of singularity theory to the study of bifurcations of equilibrium states in the theory of elasticity is irreproachably founded.
并入
发表于 2025-3-23 14:30:37
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两栖动物
发表于 2025-3-23 19:32:02
Markov Chain Monte Carlo MethodsLoss of stability of an equilibrium state on change of parameter is not necessarily associated with the bifurcation of this equilibrium state: it can lose stability not only by colliding with another state, but also by itself.
侵略主义
发表于 2025-3-23 22:40:14
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沉思的鱼
发表于 2025-3-24 02:41:09
János Abonyi,László Nagy,Tamás RuppertA . in phase space is defined as follows: at every point of the space we have not just one velocity vector (as in the usual evolutionary system), but a whole set of vectors called the ..
接触
发表于 2025-3-24 10:31:13
János Abonyi,László Nagy,Tamás RuppertA smooth curve on the plane can have a tangent which touches it tangentially at any number of points, but this is not true for generic curves. By a small perturbation of the curve one can always achieve that no straight line will be tangential at more than two points.
上腭
发表于 2025-3-24 11:45:07
Aleksandr Lobanov,Alexander GasnikovMathematicians know well that going over to the complex case usually simplifies a problem, rather than making it more complicated. For example, every algebraic equation of degree . has exactly . complex roots, while it is a difficult problem to find the number of real roots.
Gourmet
发表于 2025-3-24 17:21:52
,Whitney’s Singularity Theory,In 1955 the American mathematician Hassler Whitney published the article ‘Mappings of the plane into the plane‘, laying the foundations for a new mathematical theory - the theory of singularities of smooth mappings.
驾驶
发表于 2025-3-24 22:23:43
A Catastrophe Machine,In contrast to the example given above, the application of singularity theory to the study of bifurcations of equilibrium states in the theory of elasticity is irreproachably founded.
使尴尬
发表于 2025-3-25 00:33:27
Bifurcations of Equilibrium States,An . is described mathematically by a vector field in phase space. A point of phase space defines the . of the system. The vector at this point indicates the velocity of change of the state.