腼腆 发表于 2025-3-23 13:37:40
,Langevin’S Equation in Geometric Form,tement 6.23 it follows that w(t) does not exist in the standard sense, but one can make its definition sensible in terms of distributions. White noise is useful for deriving clearly a well-posed differential equation for a physical process. Below, having introduced the Langevin’s equation in differe效果 发表于 2025-3-23 16:16:45
,Nelson’S Stochastic Mechanics,of classical physics but giving the same predictions as quantum mechanics. Stochastic mechanics can be considered as the third method of quantization different from the well known Hamiltonian and Lagrangian (based on the path integrals) methods. Each of the methods has its own scope of applicability价值在贬值 发表于 2025-3-23 20:16:09
Mathematics and Its Applicationshttp://image.papertrans.cn/o/image/703701.jpg饮料 发表于 2025-3-24 00:28:21
https://doi.org/10.1007/978-94-015-8634-4Probability theory; Stochastic processes; differential geometry; manifold; mathematical physics; stochast晚间 发表于 2025-3-24 03:56:07
978-90-481-4731-1Springer Science+Business Media Dordrecht 1996Ceramic 发表于 2025-3-24 10:16:47
,Elements of Coordinate — Free Differential Geometry,pace (e.g., the so-called generalized coordinates of mechanics) but a total coordinate system, applicable to all points, is absent. The notion of manifold is a mathematical formalization for such sets.Harrowing 发表于 2025-3-24 12:09:21
http://reply.papertrans.cn/71/7038/703701/703701_17.png飞镖 发表于 2025-3-24 16:38:47
The Lagrangian Approach To Hydrodynamics,Let Θ be a bounded domain in R. with a smooth boundary. Consider the space L. (Θ) of square integrable scalar functions. To define the Sobolev space H.(Θ) for all s ∈ Z we first set H°(Θ) = L.(Θ).Negotiate 发表于 2025-3-24 19:15:05
Book 1996tensively worked out in contemporary mathematics. In particular, during the last decades a new branch of Global Analysis, Stochastic Differential Geometry, was formed to meet the needs of Mathematical Physics. It deals with a lot of various second order differential equations on finite and infinite-achlorhydria 发表于 2025-3-25 01:10:40
http://reply.papertrans.cn/71/7038/703701/703701_20.png