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On the projections of Laplacians under Riemannian submersions
We give a condition on Riemannian submersions from a Riemannian manifold M to a Riemannian manifold N which will ensure that it induces a differential operator on N from the Laplace‐Beltrami operator on M. Equivalently, this condition ensures that a Riemannian submersion maps Brownian motion to a diffusion.
Huiling Le
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Ð¡ÑŠÑ‰Ð½Ð¾Ñ Ñ‚ и Ð¿Ñ€Ð°ÐºÑ‚Ð¸Ñ‡ÐµÑ ÐºÐ¸ Ð¸Ð·Ð¼ÐµÑ€ÐµÐ½Ð¸Ñ Ð½Ð° Ð»Ð¸Ð´ÐµÑ€Ñ Ñ‚Ð²Ð¾Ñ‚Ð¾ в Ð¼ÐµÐ¶Ð´ÑƒÐ½Ð°Ñ€Ð¾Ð´Ð½Ð¸Ñ Ð¼ÐµÐ½Ð¸Ð´Ð¶Ð¼ÑŠÐ½Ñ‚ [PDF]
СР̧Ð ⁄ ÐμÐ ⁄ Ð ⁄ СР̧Ð ⁄ ÐμÐ ⁄ Ð ⁄ Ð ⁄ Ð
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ÐŸÐµÑ€Ñ Ð¿ÐµÐºÑ‚Ð¸Ð²Ð¸ и проблеми на обучението по приложна етика в Ð£Ð½Ð¸Ð²ÐµÑ€Ñ Ð¸Ñ‚ÐµÑ‚Ð° за национално и Ñ Ð²ÐµÑ‚Ð¾Ð²Ð½Ð¾ Ñ Ñ‚Ð¾Ð¿Ð°Ð½Ñ Ñ‚Ð²Ð¾ [PDF]
ВаРÐμÐ ⁄ тР̧Ð ⁄ а ДраР⁄ аРР̧ÐμРа
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Рнализ и оценка на операционните Ñ€Ð¸Ñ ÐºÐ¾Ð²Ðµ [PDF]
Ð Ð ⁄ тР⁄ Ð ⁄ ГÐμруР⁄ Ð ⁄ Ð
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Приложение на дигиталните технологии в обучението [PDF]
Ð Ð ⁄ ð ̧РДÐμð ⁄ чÐμð
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