A non-linear lower bound for planar epsilon-nets
... family of subsets F of Rm , a set Y ⊂ Rm is a weak -net for X with respect to F if any F ∈ F that satisfies |F ∩ X| ≥ |X| contains at least one point of Y . The difference between this notion and that of a (strong) -net considered in the previous subsection is that here Y does not have to necessa ...
... family of subsets F of Rm , a set Y ⊂ Rm is a weak -net for X with respect to F if any F ∈ F that satisfies |F ∩ X| ≥ |X| contains at least one point of Y . The difference between this notion and that of a (strong) -net considered in the previous subsection is that here Y does not have to necessa ...
generalizations of borsuk-ulam theorem
... Conner-Floyd proved in their book [1] the following theorem which is a generalization of the classical Borsuk-Ulam theorem: Let /: Sn^>M be a continuous map of the n-sphere to a differentiable manifold of dimension m, and T be a fixed point free differentiable involution on Sn. Assume that m^n and / ...
... Conner-Floyd proved in their book [1] the following theorem which is a generalization of the classical Borsuk-Ulam theorem: Let /: Sn^>M be a continuous map of the n-sphere to a differentiable manifold of dimension m, and T be a fixed point free differentiable involution on Sn. Assume that m^n and / ...
623Notes 12.8-9
... column” proofs. However, we will show similarity by providing a similarity statement, in addition to identifying the appropriate similarity theorem: SSS, ASA or AA. To do this we identify the ratios of lengths of corresponding sides and show that the ratios are equal to each other and to the ratio o ...
... column” proofs. However, we will show similarity by providing a similarity statement, in addition to identifying the appropriate similarity theorem: SSS, ASA or AA. To do this we identify the ratios of lengths of corresponding sides and show that the ratios are equal to each other and to the ratio o ...
Honors Geometry - Sacred Heart Academy
... Slope – rise over run, formula (3.4) Slopes of parallel and perpendicular lines postulates (3.4) Slope-intercept form of a line (3.5) Writing and graphing equations using slope-intercept form (3.5) Point-slope and Standard Form of a line (3.5) Theorems involving perpendicular lines (3.6) Perpendicu ...
... Slope – rise over run, formula (3.4) Slopes of parallel and perpendicular lines postulates (3.4) Slope-intercept form of a line (3.5) Writing and graphing equations using slope-intercept form (3.5) Point-slope and Standard Form of a line (3.5) Theorems involving perpendicular lines (3.6) Perpendicu ...
Riemann–Roch theorem
The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates the complex analysis of a connected compact Riemann surface with the surface's purely topological genus g, in a way that can be carried over into purely algebraic settings.Initially proved as Riemann's inequality by Riemann (1857), the theorem reached its definitive form for Riemann surfaces after work of Riemann's short-lived student Gustav Roch (1865). It was later generalized to algebraic curves, to higher-dimensional varieties and beyond.