Trees and continuous mappings into the real line
نویسندگان
چکیده
منابع مشابه
Singularities of Piecewise Linear Mappings. I Mappings into the Real Line
In this note we consider piecewise linear mappings of combinatorial manifolds into the real line. We define—in a purely combinatorial way—a certain class of mappings called nondegenerate and we prove that every continuous mapping may be approximated by a nondegenerate one. Nondegenerate mappings on a combinatorial manifold behave like differentiable nondegenerate mappings on a differentiate man...
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بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی بیان شده اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...
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We consider the combinatorial problem of embedding a tree metric into the real line with low distortion. For two special families of trees — the family of complete binary trees and the family of subdivided stars — we provide embeddings whose distortion is provably optimal, up to a constant factor. We also prove that the optimal distortion of a linear embedding of a tree can be arbitrarily low o...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1981
ISSN: 0166-8641
DOI: 10.1016/0166-8641(81)90019-5