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Patch Colorings and Rigid Colorings of the Rational n-Space

Grzegorz Kubicki, Jenő Lehel, Michał Morayne
2002 Journal of combinatorial theory. Series B (Print)  
We investigate k-colorings of the rational n-space, Q n , such that any two points at distance one get distinct colors.  ...  We prove that the existence of a patch k-coloring of Q n implies the existence of a k-coloring of R n . We show that every 2-coloring of Q 2 or Q 3 , and every 4-coloring of Q 4 is rigid.  ...  ACKNOWLEDGMENTS The authors are grateful to both referees for the careful reading and for their helpful comments.  ... 
doi:10.1006/jctb.2001.2062 fatcat:hzgr5bu2xjhjlbzdndbybgtqia

Page 3214 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
of the rational n-space.  ...  +. for all x € A, and if A has a patch k- coloring, then there exists a k-coloring of R”; in particular, if Q” has a patch k-coloring then there exists a k-coloring of R”. If @ =(C\,...  ... 

A SELF-RECORDING DEVICE FOR TESTING THE COLOR SENSE

J. Ellis Jennings
1914 Journal of the American Medical Association  
The position of the patches of color and the circular openings have been arranged in an absolutely symmetrical design, so iiiÜBlI n n ni h es m n n HBBii illBlBIÏ n n n n o n n n liiiiiii Jennings* self-recording  ...  cord, and a half dilated rigid cervix.  ... 
doi:10.1001/jama.1914.25710120002016c fatcat:mt4e7rus7bg4vkhjcnm2pai5dq

Highly accurate 5-axis flank CNC machining with conical tools

Amaia Calleja, Pengbo Bo, Haizea González, Michael Bartoň, Luis Norberto López de Lacalle
2018 The International Journal of Advanced Manufacturing Technology  
The space of lines that admit tangential motion of an associated truncated cone along a general, doubly curved, free-form surface is explored.  ...  These lines serve as discrete positions of conical axes in 3D space.  ...  The first and third authors have been supported by the Spanish Ministry of economy (MIMECOR) Implantacin de una solucin integral para la fabricacin y reparacin de componentes de turbo maquinaria (Turbo  ... 
doi:10.1007/s00170-018-2033-7 fatcat:pkesmjzhlnaz7c6jr3trmwjb6y

Kernel principal component analysis network for image classification [article]

Dan Wu, Jiasong Wu, Rui Zeng, Longyu Jiang, Lotfi Senhadji, Huazhong Shu
2015 arXiv   pre-print
First, mapping the data into higher space with kernel principal component analysis to make the data linearly separable. Then building a two-layer KPCANet to obtain the principal components of image.  ...  In order to classify the nonlinear feature with linear classifier and improve the classification accuracy, a deep learning network named kernel principal component analysis network (KPCANet) is proposed  ...  Suppose that the patch size is 1 2 k k × at all stages, and all the input images are of size m n × .  ... 
arXiv:1512.06337v1 fatcat:qnwldiyk3fe37hb7rpxoyiqxim

Tilings of the plane and Thurston semi-norm [article]

J.-R. Chazottes, J.-M. Gambaudo, F. Gautero
2013 arXiv   pre-print
We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional  ...  This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact 3-manifolds.  ...  Figure 5 5 shows now a patch tiled with rational prototiles. Figure 5 . 5 A patch of the rational Penrose tiling.  ... 
arXiv:1205.5118v2 fatcat:vxhuwt3rjfe3bm6cethkzpegky

Tilings of the plane and Thurston semi-norm

Jean-René Chazottes, Jean-Marc Gambaudo, François Gautero
2014 Geometriae Dedicata  
We show that the problem of tiling the Euclidean plane with a finite set of polygons (up to translation) boils down to prove the existence of zeros of a non-negative convex function defined on a finite-dimensional  ...  This function is a generalisation, in the framework of branched surfaces, of the Thurston semi-norm originally defined for compact 3-manifolds.  ...  Figure 5 . 5 A patch of the rational Penrose tiling. Remark 3.2.  ... 
doi:10.1007/s10711-013-9932-4 fatcat:srsrqvegircipa5agb2knotdaa

Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution

Pengbo Bo, Michael Bartoň, Denys Plakhotnik, Helmut Pottmann
2016 Computer-Aided Design  
We seek both an optimal shape of the milling tool as well as its optimal path in 3D space and propose an optimization based framework where these entities are the unknowns.  ...  We present several examples showing that the proposed method recovers exact envelopes, including semi-envelopes and incomplete data, and for general free-form objects it detects envelope sub-patches.  ...  The first author was partially supported by The National Natural Science Foundation of China  ... 
doi:10.1016/j.cad.2016.04.004 fatcat:sayhu4xry5g6xa4t7zbonjxy2e

Function of 5-Hydroxytryptamine Type 3 Receptors-A Computational Approachq
Function of 5-Hydroxytryptamine Type 3 Receptors-A Computational Approach

Schilbach A
2016 Neurology & Neurotherapy Open Access Journal  
Flexible and rigid docking simulations around key residues resulted in a number of low-energy (high affinity) configurations of ligand binding.  ...  Antagonists of the 5-HT3 receptor are currently one of the most effective therapeutic agents in treatment of chemotherapy-induced nausea, vomiting, and irritable bowel syndrome.  ...  Click 'Hydrogen Bonding' -choose 'Activate as Spheres' (color green -default) and adjust radii + spacing for optimum view.  ... 
doi:10.23880/nnoaj-16000102 fatcat:6yjz62l5jjapjjqhnebi75q5ku

Recent Advances in Block Copolymer Self‐Assembly for the Fabrication of Photonic Films and Pigments

Zhen Wang, Chun Lam Clement Chan, Tianheng H. Zhao, Richard M. Parker, Silvia Vignolini
2021 Advanced Optical Materials  
In the third section, recent advances in exploiting confined self-assembly of block copolymers to produce photonic pigments are introduced and the diversity of structures that can be achieved with this  ...  history and recent progress of 1D photonic films, also commonly referred to as photonic multilayer structures.  ...  By selectively swelling the QP2VP block, both the domain spacing (d) and the refractive index contrast (Δn = n PS -n QP2VP ) of the multilayered photonic crystal increase, allowing for reflection of visible  ... 
doi:10.1002/adom.202100519 fatcat:d6inoynljfeq7kshxxjsx24b3a

Conjugacies for Tiling Dynamical Systems

Charles Holton, Charles Radin, Lorenzo Sadun
2004 Communications in Mathematical Physics  
We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being finite type is invariant under topological conjugacy.  ...  For substitution tiling systems under rather general conditions, including the Penrose and pinwheel systems, we show that substitutions are invertible and that conjugacies are generalized sliding block  ...  The authors are grateful for the support of the Banff International Research Station, at which we formulated and proved Theorem 3.  ... 
doi:10.1007/s00220-004-1195-3 fatcat:26b7vwpn4famhpnx75m72b7nly

Shape-From-Silhouette Across Time Part I: Theory and Algorithms

Kong-man (German) Cheung, Simon Baker, Takeo Kanade
2004 International Journal of Computer Vision  
The algorithm is first developed for rigid objects and then extended to articulated objects.  ...  To break the alignment ambiguity, we combine stereo information with silhouette information and derive a Temporal SFS algorithm which consists of two steps: (1) estimate the motion of the objects over  ...  Ñ ® Ã ° Í ¤ » y À ¬ y c ¾ 3 ¬ y H 3 Ņ y H 3 Ñ ® Ã ° Í° Ó (7) (R T , -R T t) 2D Color Images Initial motion estimate (R, t) t 1 t 2 Time Colored Surface Touching Points ("3D Images") R T -R T t W 2 i Error  ... 
doi:10.1007/s11263-005-4881-5 fatcat:pumir6crzveidku4f2ynua4nkm

GIS-Based Urban Agglomeration Landscape Dynamic Observation and Simulation Prediction Algorithm

Meng Liu, Yanqiong Li
2022 Journal of Sensors  
Raster data is to determine the specific position of each pixel through the vertical and horizontal row and column relationship of the pixel, which is relatively simple in structure and easy to topology  ...  has a very large space to play.  ...  Therefore, urban ecological corridors should be constructed rationally and used as links to connect discrete patches to form a scientific and rational ecological network and urban green space system.  ... 
doi:10.1155/2022/8117539 fatcat:gefuseuyd5hbhp2m2pfdo2moli

A Preliminary Revision of the Lepidopterous Family Notodontidæ

B. Neumoegen, Harrison G. Dyar
1894 Transactions of the American Entomological Society (1890)  
The marks are confused and largely reduced to irro rations, while the color is pale. Base and median space shaded with yellowish Expanse 25 mm. Hab.?Central United States to Mexico.  ...  A deep smoky brown shade obtains over the space between the third and fourth lines, and also subapically ; fourth line widened and white on costa, the rusty patch outside of it very obscure.  ...  Synopsis of Species.  ... 
fatcat:tejwlimlczf7rkkjbun67xwwye

Page 175 of American Medical Times Vol. 1, Issue 10 [page]

1860 American Medical Times  
These fat-containing cells were found not only in the white patches, but in parts of the retina which were unchanged in color.  ...  and its border indistinct ; then appear the white specks and patches scattered over the fundus in the vicinity of the optic nerve: lastly, extravasations of blood usually take place upon the white spots  ... 
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