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Coordination Sequence
In crystallography and the theory of infinite vertex-transitive graphs, the coordination sequence of a vertex v is an integer sequence that counts how many vertices are at each possible distance from v. That is, it is a sequence n_0, n_1, n_2,\dots where each n_i is the number of vertices that are i steps away from v. If the graph is vertex-transitive, then the sequence is an invariant of the graph that does not depend on the specific choice of v. Coordination sequences can also be defined for sphere packings, by using either the contact graph of the spheres or the Delaunay triangulation of their centers, but these two choices may give rise to different sequences. As an example, in a square grid, for each positive integer i, there are 4i grid points that are i steps away from the origin. Therefore, the coordination sequence of the square grid is the sequence 1,4,8,12,16,20,\dots\ . in which, except for the initial value of one, each number is a multiple of four. The concept was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography" iycr2014.org. 12 July 2012 Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of Crystal system, crystal geometry, including those that are Aperiodic crystal, not periodic or quasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Uniform Tiling
In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings can exist in both the Euclidean plane and hyperbolic plane. Uniform tilings are related to the finite uniform polyhedra; these can be considered uniform tilings of the sphere. Most uniform tilings can be made from a Wythoff construction starting with a symmetry group and a singular generator point inside of the fundamental domain. A planar symmetry group has a polygonal fundamental domain and can be represented by its group notation: the sequence of the reflection orders of the fundamental domain vertices. A fundamental domain triangle is denoted (''p q r''), where ''p'', ''q'', ''r'' are whole numbers > 1, i.e. ≥ 2; a fundamental domain right triangle is denoted (''p q'' 2). The triangle may exist as a spherical triangle, a Euclidean plane triangle, or a hyperbolic plane triangle, depending on the values of ''p'', ''q'', ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Crystallography
Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming 2014 the International Year of Crystallography.UN announcement "International Year of Crystallography" iycr2014.org. 12 July 2012 Crystallography is a broad topic, and many of its subareas, such as X-ray crystallography, are themselves important scientific topics. Crystallography ranges from the fundamentals of crystal structure to the mathematics of Crystal system, crystal geometry, including those that are Aperiodic crystal, not periodic or quasi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Acta Crystallogr
''Acta Crystallographica'' is a series of peer-reviewed scientific journals, with articles centred on crystallography, published by the International Union of Crystallography (IUCr). Originally established in 1948 as a single journal called ''Acta Crystallographica'', there are now six independent ''Acta Crystallographica'' titles: *'' Acta Crystallographica Section A: Foundations and Advances'' *'' Acta Crystallographica Section B: Structural Science, Crystal Engineering and Materials'' *'' Acta Crystallographica Section C: Structural Chemistry'' *'' Acta Crystallographica Section D: Structural Biology'' *'' Acta Crystallographica Section E: Crystallographic Communications'' *'' Acta Crystallographica Section F: Structural Biology Communications'' ''Acta Crystallographica'' has been noted for the high quality of the papers that it produces, as well as the large impact that its papers have had on the field of crystallography. The current six journals form part of the journal por ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Zeitschrift Für Kristallographie – Crystalline Materials
''Zeitschrift für Kristallographie – Crystalline Materials'' is a monthly peer-reviewed scientific journal published in English. The journal publishes theoretical and experimental studies in crystallography of both organic and inorganic substances. The editor-in-chief of the journal is from the University of Münster. The journal was founded in 1877 under the title ''Zeitschrift für Krystallographie und Mineralogie'' by crystallographer and mineralogist Paul Heinrich von Groth, who served as the editor for 44 years. It has used several titles over its history, with the present title having been adopted in 2010. The journal is indexed in a variety of databases and has a 2020 impact factor of 1.616. History The journal was established in 1877 by Paul von Groth as a German-language publication under the title ''Zeitschrift für Krystallographie und Mineralogie'', and he served as its editor until the end of 1920. Groth was appointed as the inaugural Professor of Mineralogy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Acta Crystallographica Section A
''Acta Crystallographica Section A: Foundations and Advances'' is a peer-reviewed structural science journal published bimonthly by the International Union of Crystallography. It contains papers describing fundamental developments in structural science. It was founded in 1967 when Acta Crystallographica was split into two sections and was initially titled ''Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography''. The journal's name changed in 1982 to ''Acta Crystallographica Section A: Foundations of Crystallography.'' The journal adopted its current title in 2013. Abstracting and indexing The journal is abstracted and indexed in Biological Abstracts, the Cambridge Structural Database, Ceramic Abstracts, Chemical Abstracts, Crossref, the Current Chemical Reactions Database, Google Scholar, the Inorganic Crystal Structure Database, INSPEC, Medline, Metals Abstracts/METADEX, PubMed Central, the Reaction Citation Index, the Science C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Proceedings Of The Royal Society A
''Proceedings of the Royal Society'' is the main research journal of the Royal Society. The journal began in 1831 and was split into two series in 1905: * Series A: for papers in physical sciences and mathematics. * Series B: for papers in life sciences. Many landmark scientific discoveries are published in the Proceedings, making it one of the most important science journals in history. The journal contains several articles written by prominent scientists such as Paul Dirac, Werner Heisenberg, Ernest Rutherford, Erwin Schrödinger, William Lawrence Bragg, Lord Kelvin, J.J. Thomson, James Clerk Maxwell, Dorothy Hodgkin and Stephen Hawking. In 2004, the Royal Society began '' The Journal of the Royal Society Interface'' for papers at the interface of physical sciences and life sciences. History The journal began in 1831 as a compilation of abstracts of papers in the '' Philosophical Transactions of the Royal Society'', the older Royal Society publication, that began in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Journal Of Solid State Chemistry
The ''Journal of Solid State Chemistry'' is a monthly peer-reviewed scientific journal published by Elsevier. The journal covers the chemical, structural, thermodynamic, electronic, and electromagnetic characteristics and properties of solids, including ceramics and amorphous materials. The editor-in-chief is M.G. Kanatzidis (Northwestern University). Abstracting and indexing This journal is abstracted and indexed by: * BioEngineering Abstracts * Chemical Abstracts Service * Coal Abstracts - International Energy Agency * Current Contents/Physics, Chemical, & Earth Sciences * Engineering Index * Science Abstracts * Science Citation Index According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 3.498. See also * Solid-state chemistry Solid-state chemistry, also sometimes referred as materials chemistry, is the study of the Chemical synthesis, synthesis, structure, and properties of solid phase materials. It therefore has a strong overlap with so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Quasi-polynomial
In mathematics, a quasi-polynomial (pseudo-polynomial) is a generalization of polynomials. While the coefficients of a polynomial come from a ring, the coefficients of quasi-polynomials are instead periodic functions with integral period. Quasi-polynomials appear throughout much of combinatorics as the enumerators for various objects. A quasi-polynomial can be written as q(k) = c_d(k) k^d + c_(k) k^ + \cdots + c_0(k), where c_i(k) is a periodic function with integral period. If c_d(k) is not identically zero, then the degree of q is d. Equivalently, a function f \colon \mathbb \to \mathbb is a quasi-polynomial if there exist polynomials p_0, \dots, p_ such that f(n) = p_i(n) when i \equiv n \bmod s. The polynomials p_i are called the constituents of f. Examples * Given a d-dimensional polytope P with rational vertices v_1,\dots,v_n, define tP to be the convex hull of tv_1,\dots,tv_n. The function L(P,t) = \#(tP \cap \mathbb^d) is a quasi-polynomial in t of degree d. In this case ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Michael O'Keeffe (chemist)
Michael O’Keeffe (born April 3, 1934) is a British-American chemist. He is currently Regents’ Professor Emeritus in the School of Molecular Sciences at Arizona State University. As a scientist, he is particularly known for his contributions to the field of reticular chemistry. In 2019, he received the Gregori Aminoff Prize in Crystallography from the Royal Swedish Academy of Sciences. Early life and education Michael O’Keeffe was born in Bury St Edmunds, Suffolk, England, on the 3rd April, 1934. He was one of four children born to Dr. E. Joseph O’Keeffe, an immigrant from Ireland, and his mother Marjorie G. O’Keeffe (née Marten). From 1942 to 1951 he attended Prior Park College (Bath) and then from 1951 to 1957 the University of Bristol: B.Sc. in chemistry (1954), Ph.D. (1958, mentor Frank S. Stone). He spent 1958-1959 at Philips Natuurkundig Laboratorium (group of Evert W. Gorter) then did postdoctoral research at Indiana University (mentor Walter J. Moore). 1960-6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Vertex-transitive Graph
In the mathematics, mathematical field of graph theory, an Graph automorphism, automorphism is a permutation of the Vertex (graph theory), vertices such that edges are mapped to edges and non-edges are mapped to non-edges. A graph is a vertex-transitive graph if, given any two vertices and of , there is an automorphism such that :f(v_1) = v_2.\ In other words, a graph is vertex-transitive if its automorphism group Group action (mathematics), acts Group_action#Remarkable properties of actions, transitively on its vertices.. A graph is vertex-transitive if and only if its graph complement is, since the group actions are identical. Every symmetric graph without isolated vertex, isolated vertices is vertex-transitive, and every vertex-transitive graph is Regular graph, regular. However, not all vertex-transitive graphs are symmetric (for example, the edges of the truncated tetrahedron), and not all regular graphs are vertex-transitive (for example, the Frucht graph and Tietze's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fritz Laves
Fritz Henning Emil Paul Berndt Laves (27 February 1906 – 12 August 1978) was a German crystallographer who served as the president of the German Mineralogical Society from 1956 to 1958. He is the namesake of Laves phases and the Laves tilings; the Laves graph, a highly-symmetrical three-dimensional crystal structure that he studied, was named after him by H. S. M. Coxeter. Education and career Laves was born in Hanover, the son of a judge and the great-grandson of architect Georg Ludwig Friedrich Laves. He grew up in Göttingen, where his interests included piano music as well as collecting rocks and minerals. He began his university studies in geology in 1924 at the University of Innsbruck, and continued at the University of Göttingen before moving to ETH Zurich for doctoral studies under Paul Niggli. In 1929 he took a faculty position under Victor Goldschmidt at Göttingen. He tried unsuccessfully to prevent Goldschmidt from being dismissed in 1933, and later had diffi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |