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Superhelix
A superhelix is a molecular structure in which a helix is itself coiled into a helix. This is significant to both proteins and genetic material, such as overwound circular DNA. The earliest significant reference in molecular biology is from 1971, by F. B. Fuller: A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.'' About the writhing number, mathematician W. F. Pohl says: It is well known that the writhing number is a standard measure of the global geometry of a closed space curve.'' Contrary to intuition, a topological property, the linking number, arises from the geometric properties twist and writhe according to the following relationship: :''L''''k''= ''T'' + ''W'', whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helices
A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word ''helix'' comes from the Greek word ''ἕλιξ'', "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called ''helicoid''. Properties and types The ''pitch'' of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. A ''conic helix'', also known as a ''conic spiral'', may be defined as a spiral on a conic surface, with the distance to the apex an ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Helix
A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helices, and many proteins have helical substructures, known as alpha helices. The word ''helix'' comes from the Greek word ''ἕλιξ'', "twisted, curved". A "filled-in" helix – for example, a "spiral" (helical) ramp – is a surface called '' helicoid''. Properties and types The ''pitch'' of a helix is the height of one complete helix turn, measured parallel to the axis of the helix. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. A circular helix (i.e. one with constant radius) has constant band curvature and constant torsion. A '' conic helix'', also known as a ''conic spiral'', may be defined as a spiral on a conic surface, with the distance to the ape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Closeup Ropes
A close-up or closeup in filmmaking, television production, still photography, and the comic strip medium is a type of shot that tightly frames a person or object. Close-ups are one of the standard shots used regularly with medium and long shots (cinematic techniques). Close-ups display the most detail, but they do not include the broader scene. Moving toward or away from a close-up is a common type of zooming. A close up is taken from head to neck, giving the viewer a detailed view of the subject's face. History Most early filmmakers, such as Thomas Edison, Auguste and Louis Lumière and Georges Méliès, tended not to use close-ups and preferred to frame their subjects in long shots, similar to the stage. Film historians disagree as to the filmmaker who first used a close-up. One of the best claims is for George Albert Smith in Hove, who used medium close-ups in films as early as 1898 and by 1900 was incorporating extreme close-ups in films such as ''As Seen Through a Tele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Mathematics And Mechanics
The ''Indiana University Mathematics Journal'' is a journal of mathematics published by Indiana University. Its first volume was published in 1952, under the name ''Journal of Rational Mechanics and Analysis'' and edited by Zachery D. Paden and Clifford Truesdell. In 1957, Eberhard Hopf became editor, the journal name changed to the ''Journal of Mathematics and Mechanics'', and Truesdell founded a separate successor journal, the '' Archive for Rational Mechanics and Analysis'', now published by Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in .... The ''Journal of Mathematics and Mechanics'' later changed its name again to the present name. The full text of all articles published under the various incarnations of this journal is available online from the journal's we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topoisomerase
DNA topoisomerases (or topoisomerases) are enzymes that catalyze changes in the topological state of DNA, interconverting relaxed and supercoiled forms, linked (catenated) and unlinked species, and knotted and unknotted DNA. Topological issues in DNA arise due to the intertwined nature of its double-helical structure, which, for example, can lead to overwinding of the DNA duplex during DNA replication and transcription. If left unchanged, this torsion would eventually stop the DNA or RNA polymerases involved in these processes from continuing along the DNA helix. A second topological challenge results from the linking or tangling of DNA during replication. Left unresolved, links between replicated DNA will impede cell division. The DNA topoisomerases prevent and correct these types of topological problems. They do this by binding to DNA and cutting the sugar-phosphate backbone of either one (type I topoisomerases) or both (type II topoisomerases) of the DNA strands. This transie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reidemeister Move
Kurt Werner Friedrich Reidemeister (13 October 1893 – 8 July 1971) was a mathematician born in Braunschweig (Brunswick), Germany. Life He was a brother of Marie Neurath. Beginning in 1912, he studied in Freiburg, Munich, Marburg, and Göttingen. In 1920, he got the staatsexamen (master's degree) in mathematics, philosophy, physics, chemistry, and geology. He received his doctorate in 1921 with a thesis in algebraic number theory at the University of Hamburg under the supervision of Erich Hecke. He became interested in differential geometry; he edited Wilhelm Blaschke's 2nd volume about that issue, and both made an acclaimed contribution to the Jena DMV conference in Sep 1921. In October 1922 (or 1923) he was appointed assistant professor at the University of Vienna. While there he became familiar with the work of Wilhelm Wirtinger on knot theory, and became closely connected to Hans Hahn and the Vienna Circle. Its manifesto (1929) lists one of Reidemeister's publications i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linking Number
In mathematics, the linking number is a numerical invariant that describes the linking of two closed curves in three-dimensional space. Intuitively, the linking number represents the number of times that each curve winds around the other. In Euclidean space, the linking number is always an integer, but may be positive or negative depending on the orientation of the two curves (this is not true for curves in most 3-manifolds, where linking numbers can also be fractions or just not exist at all). The linking number was introduced by Gauss in the form of the linking integral. It is an important object of study in knot theory, algebraic topology, and differential geometry, and has numerous applications in mathematics and science, including quantum mechanics, electromagnetism, and the study of DNA supercoiling. Definition Any two closed curves in space, if allowed to pass through themselves but not each other, can be moved into exactly one of the following standard positions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set endowed with a structure, called a '' topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies. A property that is invariant under such deformations is a topological property. Basic examples of topological properties are: the dimension, which allows distinguishing between a line and a surface; compactness, which allows distinguishing between a line and a circle; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proceedings Of The National Academy Of Sciences
''Proceedings of the National Academy of Sciences of the United States of America'' (often abbreviated ''PNAS'' or ''PNAS USA'') is a peer-reviewed multidisciplinary scientific journal. It is the official journal of the National Academy of Sciences, published since 1915, and publishes original research, scientific reviews, commentaries, and letters. According to '' Journal Citation Reports'', the journal has a 2021 impact factor of 12.779. ''PNAS'' is the second most cited scientific journal, with more than 1.9 million cumulative citations from 2008 to 2018. In the mass media, ''PNAS'' has been described variously as "prestigious", "sedate", "renowned" and "high impact". ''PNAS'' is a delayed open access journal, with an embargo period of six months that can be bypassed for an author fee (hybrid open access). Since September 2017, open access articles are published under a Creative Commons license. Since January 2019, ''PNAS'' has been online-only, although print issues a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Francis Pohl
William Francis Pohl (16 September 1937 – 9 December 1988) was an American mathematician, specializing in differential geometry and known for the Clifton–Pohl torus. Pohl received from the University of Chicago his B.A in 1957 and his M.A.1958. He completed his Ph.D. at Berkeley in 1961 under the direction of Shiing-Shen Chern with dissertation ''Differential Geometry of Higher Order''. His dissertation was published in 1962 in the journal ''Topology'' and has received over 120 citations in the mathematical literature. He was a member of the mathematics faculty at the University of Minnesota from September 1964 until his untimely death. Pohl engaged in a famous controversy arguing against Francis Crick Francis Harry Compton Crick (8 June 1916 – 28 July 2004) was an English molecular biologist, biophysicist, and neuroscientist. He, James Watson, Rosalind Franklin, and Maurice Wilkins played crucial roles in deciphering the helical stru ... but, in view of additio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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