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Topic: 2D crystallographic group

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	Crystallographic restriction theorem - Wikipedia, the free encyclopedia
		The crystallographic restriction theorem in its basic form is the observation that the rotational symmetries of a crystal are limited to 2-fold, 3-fold, 4-fold, and 6-fold.
		Because discreteness requires that the spacings between lattice points have a lower bound, the group of rotational symmetries of the lattice at any point must be a finite group.
		For a 2D rotation, the trace is 2 cos θ; for a 3D rotation, 1 + 2 cos θ.
	en.wikipedia.org /wiki/Crystallographic_restriction_theorem (1296 words)

	Wallpaper group - Wikipedia, the free encyclopedia
		A wallpaper group (or plane symmetry group or plane crystallographic group) is a mathematical classification of a two-dimensional repetitive pattern, based on the symmetries in the pattern.
		Wallpaper groups are two-dimensional symmetry groups, intermediate in complexity between the one-dimensional frieze groups and the three-dimensional crystallographic groups (also called space groups).
		Mathematically, a wallpaper group or plane crystallographic group is a type of topologically discrete group of isometries of the Euclidean plane which contains two linearly independent translations.
	en.wikipedia.org /wiki/Wallpaper_group (4679 words)

	Point groups in three dimensions - Wikipedia, the free encyclopedia
		In geometry a point group in 3D is an isometry group in three dimensions that leaves the origin fixed, or correspondingly, an isometry group of a sphere.
		It is a subgroup of the orthogonal group O(3), the group of all isometries which leave the origin fixed, or correspondingly, the group of orthogonal matrices.
		, and is the symmetry group of the cube and octahedron.
	en.wikipedia.org /wiki/Schoenflies_notation (3390 words)

	Literature of Wade Group (Site not responding. Last check: 2007-10-24)
		While there is recent crystallographic and simulation evidence for opening of a substrate-access channel in cytochrome P450BM-3, for cytochrome P450cam, no such conformational changes have been observed either in different crystal structures or by standard molecular dynamics simulations.
		In these calculations, the pK(a) of the phenolic group of residue Tyr150 is the only one to stand out with an abnormally low value of 8.3, more than one pK(a) unit lower than the measured reference value for tyrosine in solution.
		Consistent with the crystallographic determination and studies employing hydrostatic pressure, we calculated that, although ten water molecules could in principle occupy the volume of the active site, occupation by five to six water molecules is thermodynamically most favorable.
	www-db.embl-heidelberg.de /jss/emblGroups/g_lit_63.html (8032 words)

	Grütter Research Group Publications 2003
		The crystallographic results show that a covalent adduct (oxime) is formed between AMA (an amino-oxy analogue of the natural substrate S-adenosyl-L-methionine (SAM)) and the pyridoxal 5'-phosphate (PLP) cofactor of ACC synthase.
		Site-directed mutagenesis of Escherichia coli glutamate decarboxylase, combined with analysis of the crystal structure, shows that a histidine residue buried in the protein core is critical for correct folding.
		We employed a combination of molecular modelling and crystallographic structure analysis to design renin inhibitors lacking the extended peptide-like backbone of earlier inhibitors, for improved pharmacokinetic properties.
	www.biochem.unizh.ch /publications/2003/pubMG2003.html (1799 words)

	Mathematics of The EPINET Project
		The concept has its roots in the theory of discrete groups, but the name was coined by Bill Thurston and his students by combining the terms orbit and manifold, since each point of an orbifold represents the entire orbit of a point under the group of symmetry operations of the pattern.
		A 2D orbifold is a 2-manifold with a finite number of punctures, corner, and cone points, so a compact description of these features can encode any discrete symmetry group of the sphere, euclidean, and hyperbolic planes.
		J.H. Conway, "The orbifold notation for surface groups." In Groups, combinatorics, and geometry, vol.
	epinet.anu.edu.au /mathematics/orbifold_notation (1310 words)

	The Geometry Junkyard: Symmetry and Group Theory
		The MSRI Computing Group uses another horoball diagram as their logo.
		Jonathan A. Poritz and coworkers investigate the fundamental domains of cyclic group actions on hyperbolic 3-space, resulting in lots of pretty pictures of overlapping spheres.
		Group theoretic mathematics for determining whether a polygon formed out of hexagons can be dissected into three-hexagon triangles, or whether a polygon formed out of squares can be dissected into restricted-orientation triominoes.
	www.ics.uci.edu /~eppstein/junkyard/sym.html (1155 words)

	British Crystallographic Association Industrial Group (Site not responding. Last check: 2007-10-24)
		The Industrial Group of the BCA are co-ordinating the UK implementation of an international round robin exercise on Powder Diffraction Sensitivity for the International Centre for Diffraction Data (ICDD).
		After an excellent lunch and wine courtesy of Rigaku, the BCA Industrial Group Award, a model of the kaolinite structure, was presented to Peter Salt in appreciation of a distinguished career in diffractometry.
		After thanking the Group for the honour, Peter then concentrated on the vital area of the errors in quantitative diffractometry.
	bca.cryst.bbk.ac.uk /bca/ig/oldrep.htm (2908 words)

	Volume 1 Chapter 14 Introduction to GSTAT
		Distance-based connectivity for the bonded residues of the crystal chemical unit is established using a set of 'standard' covalent radii during the building of each CSD entry.
		It also describes the differences that exist between the crystallographic connectivity tables employed in GSTAT, and the chemical connectivity tables that are used by the CSD programs QUEST (basic) and QUEST3D (graphics).
		Specifically, it provides absolute precision in the identification of the constituent atoms of a substructural fragment, in terms of both the 2D chemical constraints and the 3D geometrical constraints that must be satisfied.
	www.psc.edu /general/software/packages/cambridge/manual_5.16/html/volume1/z1c14093.html (1706 words)

	Internal Dynamics in a DNA Triple Helix Probed by 1H-15N-NMR Spectroscopy -- Jiang and Russu 82 (6): 3181 -- ...
		N at the amino group of the adenine in the fifth position.
		N at the N6 amino group of the adenine in position 5 (Fig.
		O at pH 5.3 and at 30°C. The rotation rate of the amino group in adenine A5 was measured as a function of temperature, in the temperature range from
	www.biophysj.org /cgi/content/full/82/6/3181 (2333 words)

	Molecular Hyperglossary: Organic Molecular information in Hypermedia Form
		This hyperglossary allows the reader to contribute 2D or 3D structural information about organic molecules and comments into a so-called electronic "form", and have this information accepted by the remote server after appropriate self-consistency checks have been performed.
		2D MDL molfiles, an attempt is made to calculate the stereochemistry from the bond type (wedge or dash) contained in the 2D file.
		The scope of such a hyperglossary could range from local use by a research group or department, as a component of an electronic conference (as here) or as an adjunct to an electronic journal.
	www.ch.ic.ac.uk /ectoc/papers/leach (1768 words)

	Graduate Prospectus 2006-07: Structural Biology
		My group, which forms a core component of the Institute for Structural Molecular Biology (ISMB), has established a research portfolio of broad scope that attempts to take advantage of modern NMR methodology to probe the relationship between protein structure and function.
		In collaboration with chemistry groups, x-ray crystallographers and biochemical engineers we are studying transketolase, cytochrome P450 enzymes from Actinomycetes, transaminases and Baeyer-Villiger monooxygenases.
		With various collaborators, both external and internal, the group continues to model the large family of these proteins and their ever-increasing number of specific inhibitors.
	www.biochem.ucl.ac.uk /graduate/gp6.htm (5027 words)

	Space Group Files
		A description of the format of the space group files is given in the Crystal Lattice Structure database.
		Finally, note that we haven't listed all 230 three-dimensional space groups, and we are unlikely to do so in the near future.
		In this case the space group description file is marked with an asterisk.
	cst-www.nrl.navy.mil /~mehl/space_group (353 words)

	Leonard Research Group - University of Pittsburgh MSE
		Unlike heteroepitaxy, where the underlying substrate has a significant role in determining the crystallographic nature of the film, these films have a polycrystalline morphology that consists of randomly oriented (or weakly textured) grains.
		Gaining a fundamental understanding of the surface kinetics and growth mechanisms in this type of deposition is the goal of this work, and may lead to better control over the film microstructure.
		Sketch of 2D island nucleation, growth, and impingement leading to a polycrystalline thin film.
	www.engr.pitt.edu /jleonard/Research/Research.htm (872 words)

	Surface Group, surface physics
		The twofold-symmetry direction is perpendicular to the tenfold direction and corresponds to either a 2P axis or a 2D axis.
		In this process, the bulk material acts chemically as an Al reservoir and crystallographically as a structural template on which the quasicrystalline phase is reassembled.
		Patterns recorded during sequential sputtering reveal that there exists a high degree of rotational alignment of crystallographic features at the Gd -GaN interface even though there is a large lattice mismatch between the film and the substrate.
	www.solid.phys.ethz.ch /erbudak/ar02.html (1362 words)

	The MOE Crystal Builder (Site not responding. Last check: 2007-10-24)
		When a unit cell is repeatedly translated to fill all of 2D or 3D space, the vertices of all the unit cells in the filled space constitute a lattice.
		For example in 2D, each primitive unit cell joins four lattice points, each of which counts for 1/4 because every lattice point is shared among four unit cells.
		We have extended the expression of planar (2D) groups to 3D molecules by interpreting two-sidedness as the conformation of the asymmetric unit above and below the slice of the plane.
	www.chemcomp.com /feature/crysbld.htm (1784 words)

	OhioLINK ETD: Dunkers, Joy
		Vibrational, crystallographic, and mechanistic studies of benzoxazine monomers and their resulting polybenzoxazines as novel phenolic resins
		The linear amine group is varied from methyl to amyl which alters the position of the peaks resulting from the benzoxazine ring but has little influence on the benzene ring vibrations.
		In addition, the hydrogen groups in the methylene bridge structure are deuterated to provide insight into vibrations due to the presence of the Mannich bridge structure.
	rave.ohiolink.edu /etdc/view?acc_num=case1058880772 (359 words)

	PMR: Platinum Group Metal Chalcogenides
		Platinum group metal chalcogenides have attracted considerable attention in recent years due to their relevance in catalysis and materials science.
		Platinum group metal chalcogenides have been employed in HDN reactions (89–93) and the activity is related to the acidic-basic properties of the active phase.
		The crystallographic microstructure and electrical characteristics of platinum group metals (mainly Pd) and Ni or Au ohmic contacts on ZnSe and on p-type (001) ZnTe layers have been investigated as a function of annealing temperature.
	www.platinummetalsreview.com /dynamic/article/view/48-1-016-029 (4440 words)

	Welcome to The EPINET project: Euclidean Patterns in Non-Euclidean Tilings
		The 3D Networks Index is a listing of the topologically distinct 3D euclidean networks generated by wrapping the 2D hyperbolic tilings onto appropriate periodic minimal surfaces.
		The 3D search page enables queries on topological properties of the networks and the crystallographic classes of their maximum symmetry spacegroups.
		Crystallographers and chemists may be interested in some well–known examples of 3D networks that have been collected in the Known 3D Networks Index.
	epinet.anu.edu.au (355 words)

	Dr Garrett M. Morris (Site not responding. Last check: 2007-10-24)
		MMDB: The Molecular Modeling Database - this is a compilation of all the Brookhaven Protein DataBank 3-dimensional structures of biomolecules from crystallographic and NMR studies.
		CCDC: Cambridge Crystallographic Data Centre and the Cambridge Structural Database, CSD, of organic and metal organic compounds.
		VMD - Visual Molecular Dynamics from the Theoretical Biophysics Group at the University of Illinois at Urbana-Champaign.
	www.scripps.edu /mb/olson/people/gmm (3985 words)

	Intermolecular Interactions in a Two-Layered Viral Capsid That Requires a Complex Symmetry Mismatch -- Limn and Roy 77 ...
		group is almost spherical, reinforcing the shape of the subcore
		In the lower part of the the figure is an alignment of BTV and AHSV helix 2 residues, with grouping of the different mutations used to assess helix 2 function.
		Class I was derived from consideration of the homology; class II is equivalent to class I but with a deliberate change of residue character; class III shows a change of character at residues homologous between BTV and AHSV.
	jvi.asm.org /cgi/content/full/77/20/11114 (5373 words)

	SBNet - Mid-term Evaluation Report
		The methods that were developed in the 1950's and 1960's for the phasing of the crystallographic diffraction data are still in use today.
		He is also interested in crystallographic methods development, and nearly all crystallographic models that have been described since ~1980 have been built with his computer graphics programs.
		These are groups with proven track records at the highest international level, adequate infra-structure, not dependent on a single excellent person, and firmly embedded in an academic setting.
	xray.bmc.uu.se /sbnet/midterm_1998.html (6814 words)

	European Crystallographic Association - SIG2: Charge, Spin and Momentum Density (Site not responding. Last check: 2007-10-24)
		The special interest group brings together experimentalists, computationalists and theoreticians studying all aspects of electronic charge, spin and momentum distributions in atoms, molecules and condensed matter.
		Its main objectives are to further the activities of the scientistst in their respective fields, to integrate concepts from the many experimental methodologies, from theory and computation, into a coherent understanding of spin, charge and momentum densities and to promote the application of this understanding in the whole of physics, chemistry and biology.
		crystallographic studies: interaction density including hydrogen bonds, topological analysis of the charge density, total electrostatic potential
	www.ecanews.org /sig2.htm (319 words)

	Curriculum Vitae Thomas Schneider (Site not responding. Last check: 2007-10-24)
		Diploma project 'Calculation of a 2D NOE Spectrum from a Molecular Dynamics Simulation of BPTI' in the group of Prof.
		Postdoctoral Fellow 'Kinetic Crystallography of Tryptophan Synthase' in the group of Prof.
		Group Leader at the FIRC Institute of Molecular Oncology, Milan, Italy.
	shelx.uni-ac.gwdg.de /~trs/cv.html (162 words)

	American Crystallographic Association 1998 Call For Papers
		Crystallographers have been interested in understanding the dramatic catalytic accelerations of enzymes since the first suggestion by Pauling that enzyme structures complement transition states.
		Crystallographic structures often probe a number of biological problems.
		The General Interest Group will organize three sessions that will include contributions from all areas of crystallography chosen from the submitted abstracts.
	www.hwi.buffalo.edu /ACA/ACA-Annual/Buffalo/cfp'98-web.html (5197 words)

	Magnetic Thin Films Research Group, University of York
		MEIS 2D plot of a CoAg heterogeneous alloy.
		Medium Energy Ion Scattering (MEIS) is particularly sensitive to defects within a crystalline structure such as stacking faults or displaced atoms.
		The energy and angle of the backscattered ions provide a measurement of atomic mass, depth, and structure of the target.
	www-users.york.ac.uk /~phys18/MEIS.htm (309 words)

	CCSL Mark 4 Update 57 17-Appendix A
		Generates the subgroup of a space group from the given generators.
		A specialist routine used during the input of space group symmetry to discover whether there is a centre of symmetry.
		Calculates the terms in the 2D averaged spherically symmetric form factor summation which depend on S,K, and R only.
	www.ill.fr /data_treat/libapa.html (5365 words)

	An Endogenous HIV Envelope-derived Peptide without the Terminal NH3+ Group Anchor Is Physiologically Presented by Major ...
		An Endogenous HIV Envelope-derived Peptide without the Terminal NH3+ Group Anchor Is Physiologically Presented by Major Histocompatibility Complex Class I Molecules -- Samino et al.
		group interaction is supported by the striking lack of effect of its loss in peptides elongated
		group anchor, as indicated by our evidence, is supported by the existence of peptides lacking
	www.jbc.org /cgi/content/full/279/2/1151 (6621 words)

	Read This: Euclid: The Creation of Mathematics
		Of course, it is a purely factual question whether Euclid's "magnitudes" have the structure of a group (Weil stated specifically that he was not attributing the abstract concept of a group to Euclid); but, for Dauben, such an observation is not "history".
		They are essentially the defining properties of a group with operators.
		It would have been instructive to point out that a regular dodecahedral crystal is impossible because of the "crystallographic restriction." Ordinary crystals are thought to be formed from regular lattices of atoms, and it is a theorem of geometry that such a lattice cannot have any 5-fold symmetries.
	www.maa.org /reviews/artmann.html (2231 words)

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