Solution of the Propeller Conjecture in $$\mathbb R ^3$$ R 3
نویسندگان
چکیده
منابع مشابه
Solution of the propeller conjecture in $\mathbb{R}^3$
It is shown that every measurable partition ${A_1,..., A_k}$ of $\mathbb{R}^3$ satisfies $$\sum_{i=1}^k||\int_{A_i} xe^{-\frac12||x||_2^2}dx||_2^2\le 9\pi^2.\qquad(*)$$ Let ${P_1,P_2,P_3}$ be the partition of $\mathbb{R}^2$ into $120^\circ$ sectors centered at the origin. The bound is sharp, with equality holding if $A_i=P_i\times \mathbb{R}$ for $i\in {1,2,3}$ and $A_i=\emptyset$ for $i\in \{4...
متن کاملEmbeddability in $\mathbb{R}^3$ is NP-hard
We prove that the problem of deciding whether a 2or 3-dimensional simplicial complex embeds into R is NP-hard. This stands in contrast with the lower dimensional cases which can be solved in linear time, and a variety of computational problems in R like unknot or 3-sphere recognition which are in NP∩ co-NP (assuming the generalized Riemann hypothesis). Our reduction encodes a satisfiability ins...
متن کاملAffine Configurations of 4 Lines in R R R 3
We prove that affine configurations of 4 lines in R3 are topologically and combinatorially homeomorphic to affine configurations of 6 points in R4.
متن کاملAn Enumerative Geometry Framework for Algorithmic Line Problems in $\mathbb R^3$
We investigate the enumerative geometry aspects of algorithmic line problems when the admissible bodies are balls or polytopes. For this purpose, we study the common tangent lines/transversals to k balls of arbitrary radii and 4− k lines in R3. In particular, we compute tight upper bounds for the maximum number of real common tangents/transversals in these cases. Our results extend the results ...
متن کامل(R)-(−)-Quinuclidin-3-ol
The structure of the title compound [alternatively called (R)-(-)-1-aza-bicyclo-[2.2.2]octan-3-ol], C7H13NO, at 100 K has hexa-gonal (P61) symmetry. The structure shows a twist along the C-N pseudo-threefold axis. In the crystal, mol-ecules are linked via O-H⋯N hydrogen bonds, forming infinite chains along the c-axis direction. The crystal studied was twinned by merohedry (twin law: 010, 100, 0...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2013
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-013-9530-0