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Arrangements of planes in space

G.L. Alexanderson, John E. Wetzel
1981 Discrete Mathematics  
In a recently published summary article (Arrangements of byperpl2nes; matroids and graphs, in  ...  We conclude with some nor&vial new bounds for the counters of an arbitrary arrangement in E3 and two specific examples. ' This is indeed the case.  ...  P* and if Arrangements of planes irt. space the arrangement is not planar, Furfhemore, ~12 the summ(ands in these formulas are non-negative.  ... 
doi:10.1016/0012-365x(81)90002-9 fatcat:btkhxngtffctvhntj4amlbohdi

On the Interpretation of the Indications of Atomic Structure Presented by Crystals when Interposed in the Path of X-rays

W. Barlow
1914 Proceedings of the Royal Society A  
of deformation of an atomic system arranged according to either of the three space-lattices possessing cubic symmetry, considerable enough to profoundly alter the nature of the arrangement, can take place  ...  Bragg states in his exposition of the method of investigating the structure of crystals by means of X-rays, th a t a slight symmetrical distortion of the arrangem ent of the atoms, which would reduce the  ...  precisely the same in the space-lattice arrangement as in any one of the point-system arrangements derived from this space-lattice by the defined method; and this is true whatever the direction chosen  ... 
doi:10.1098/rspa.1914.0096 fatcat:crc7zxpaz5dpvop4tidxzsvo6y

Review of Crystalline Structures of Some Selected Homologous Series of Rod-Like Molecules Capable of Forming Liquid Crystalline Phases

Peter Zugenmaier
2011 International Journal of Molecular Sciences  
It is of valuable interest to know possible conformations and possible packing arrangements as prerequisites to model liquid crystalline structures.  ...  The crystal structures of four homologous series of rod-like molecules are reviewed, two of which form hydrogen bonds and two with a symmetric chemical constitution.  ...  Figure 34 . 34 Representation of the packing arrangement of TBAA-6, space group C2/c, in projection on the a,c-and b,c-plane.  ... 
doi:10.3390/ijms12117360 pmid:22174604 pmcid:PMC3233410 fatcat:ybo7x5olanee3k6vk3pf5smvza

Topology of plane arrangements and their complements [article]

Victor A. Vassiliev
2014 arXiv   pre-print
This is a glossary of notions and methods related with the topological theory of collections of affine planes, including braid groups, configuration spaces, order complexes, stratified Morse theory, simplicial  ...  The emphasis on the most geometrical explanation is done; applications and analogies in the differential topology are outlined.  ...  Homotopy type of an affine plane arrangement and stable homotopy type of its complement Let our spaces S i be affine planes in R N forming the arrangement L.  ... 
arXiv:1407.7236v1 fatcat:cijduyr7kva63de5pdsuvy44b4


1986 Le Journal de Physique Colloques  
The resulting crystal can not in general be viewed as a space-filling arrangement of a small number of different "Penrose tiles."  ...  of atoms correspond to an arrangement of hypersurface segments.  ...  We now want to describe structures which can be formed by arrangements of atoms in 3D space.  ... 
doi:10.1051/jphyscol:1986313 fatcat:vxxy5mrkefc6bnhv3gzwmlcwvi

A resolution of the sylvester-gallai problem of J.-P. serre

L. M. Kelly
1986 Discrete & Computational Geometry  
Introduction Almost from the beginning of the study of algebraic curves in which imaginary points were admitted, it has been known that a general plane cubic curve has nine inflection points which form  ...  in real space.  ...  Hirzebruch studies "arrangements of lines" in the complex plane and associates with each such arrangement algebraic surfaces, calculates their Chern numbers and applies the Miyaoka-Yau inequality.  ... 
doi:10.1007/bf02187687 fatcat:2a5zhzxndba63m6n7rktiqmoo4

$4$ planes in ${\mathbb R}^4$

E. Batzies
2007 Proceedings of the American Mathematical Society  
For k = 4, this leads to an explicit computation of the moduli space A 4,4 (R) of central 2-arrangements in R 4 mod GL 4 (R) and its subspace A 2,4 (C) of those classes that contain a complex hyperplane  ...  arrangement.  ...  So far, the class of central 2-arrangements of k planes in R 4 is not understood in general.  ... 
doi:10.1090/s0002-9939-07-08186-5 fatcat:pt6oeijv6ragjdwfwpkznksjd4

Improvement of Isolation between Transmitting and Receiving Antennas of E-plane arranged Waveguide Slot Arrays by using Layers of Slit pairs with Half-wavelength Spacing

Kohei Jitosho, Takashi Tomura, Jiro Hirokawa
2020 IEICE Communications Express  
This structure is expected to improve the isolation between transmitting and receiving antennas arranged in the E-plane.  ...  In this paper, we propose loading layers of slit pairs with halfwavelength spacing over a corporate-feed waveguide slot array antenna in the 30 GHz band.  ...  The isolation between E-plane arranged antennas becomes worse than that of H-plane arranged antennas, affecting the radiation pattern of the slots.  ... 
doi:10.1587/comex.2020xbl0148 fatcat:w3lezhvxb5a6zbxsydrpfvek2m

K-Levels of Concave Surfaces

Katoh, Tokuyama
2002 Discrete & Computational Geometry  
We show that for any line l in space, there are at most k(k + 1) tangent planes through l to the k-level of an arrangement of concave surfaces.  ...  This is a generalization of Lovász's lemma, which is a key constituent in the analysis of the complexity of k-levels of planes.  ...  From any line l in the space, there are at most k(k + 1) tangent planes through l to concave vertices of the k-level of an arrangement of planes in the three-dimensional space.  ... 
doi:10.1007/s00454-001-0086-z fatcat:3tbztepwj5bjrbgzabo2dtazca

Problems of the simulation and modeling the lightning protection of high structures

Zoltán Tóth, István Kiss, Bálint Németh
2019 Pollack Periodica  
In the latter case, the increasing nominal power increases the dimensions of the turbine, and the risk of a strike, too.  ...  Besides that, some investigations of high buildings for negative and positive lightning were evaluated to determine the change of the attractive space.  ...  Open Access statement This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits  ... 
doi:10.1556/606.2019.14.2.20 fatcat:cj5mbihwjffwxpibpjobu6bn6a


O. L. Sponsler
1926 The Journal of General Physiology  
The longitudinal planes were considered when discussing the diffraction patterns from the 0 ° position of the fiber block, t A study of the transverse and the diagonal planes is undertaken in the present  ...  It was shown there that certain sets of planes of atoms, the existence of which was indicated by the diffraction lines, extended lengthwise of the fibers, while other sets were transverse and still others  ...  In the latter all planes of a given set are equal in reflecting power and therefore no double spacing occurs. That must mean that every plane has both Q and R arrangements in it.  ... 
doi:10.1085/jgp.9.5.677 pmid:19872283 pmcid:PMC2140850 fatcat:vw2kjpqqpbcxxkaeteftwvvmwm

Page 135 of Journal of Chemical Education Vol. 18, Issue 3 [page]

1941 Journal of Chemical Education  
space arrangement of the atoms or groups within the mole- cules.  ...  A unique consequence of this directional distribution of the valence forces in space is the phenomenon of stereoisomerism, or space isomerism, which implies that the isomers differ in the three-dimensional  ... 

Rigid body motion measurements with Fourier lensless holography

N. Bolognini, H. J. Rabal, E. E. Sicre, M. Garavaglia
1981 Applied Optics  
In this case, a three-recording-plates set, in a trihedral arrangement attached to an object, registers the interference between spherical and plañe coherent wave fronts.  ...  If, between two such exposures, the arrangement is translated or rotated in the space, the two overlapping interference patterns registered will produce low frequency moiré patterns.  ...  The authors wish to thank the Secretaria de Estado de Ciencia y Tecnologia, Argentina and the Organization of American States, for providing financial support for this work.  ... 
doi:10.1364/ao.20.002342 pmid:20332955 fatcat:wrhwjsaggbclleiywtvtzx6cpq

Page 480 of Mechanical Engineering Vol. 47, Issue 6 [page]

1925 Mechanical Engineering  
The distances between planes may be different in the various systems and the three sets of planes may form any angles with each other.  ...  The points of intersection of these planes constitute a space lattice. Taking, for example, Fig. 6, we have here a portion from a “body-centered”!  ... 

The Crystalline Structure of Succinic Acid, Succinic Anhydride and Succinimide

K. Yardley
1924 Proceedings of the Royal Society A  
A brief consideration of these two sets of axial ratios shows that the same a, b axes have been taken for both, but that the (001) plane in the second set is the (101) plane in the first.  ...  There seemed to be no obvious advantage in using the elementary cell defined by the second set of axial ratios, hence the values given by Groth were used in the calculation of the spacings.  ...  Not every kind of two-fold symmetry of the molecule is possible in each of these space-groups. In C^1 the molecules are arranged as in fig. 1 , the elements of symmetry F ig. 1.  ... 
doi:10.1098/rspa.1924.0030 fatcat:ui2iywtwzngpbataz56g53kzx4
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